{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":892,"title":"Solve Rubik's Cube - Up to Two Face Moves","description":"A standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face/Vector numbering.\r\n\r\nThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\r\n\r\nMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice.  The loaded function r_new=rubick_rot(mov,r) implements moves 1-18: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2.\r\n\r\n\r\n\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/cube_small.gif\u003e\u003e\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/Cube_Map28_200.png\u003e\u003e\r\n\r\n\u003c\u003chttp://mathworks.com/matlabcentral/images/surf.gif\u003e\u003e\r\n\r\n\r\n  \r\n  \r\n  Input: (rubik)\r\n  \r\n  rubik: row vector of size 54\r\n  (The cube started [L=0,U=1,F=2,D=3,B=4,R=5] and then received one or two face moves.\r\n\r\n  Output: mov (A row vector of one or two of values {1:18})\r\n   mov: is a vector values 1:18 representing the moves in order to fix the cube: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2\r\n\r\n* Example:\r\n* If the cube was randomized by [1 9] UD', the one and only 2 move answer is [3 7] DU' which are the complements in reverse order. \r\n* Minimum moves is also required. Scramble by 13(U2) should return a [13], not [1 1] or [7 7]\r\n* \r\nVerifications will be by executing your move vector against the provided rubik and checking number of moves.\r\n\r\nThe function rubik_rot(mov,r) is available for usage\r\n\r\n\r\nThis is the next incremental solution step: Move optimization.\r\n\r\nAdditional Challenges will be solving the cube at even deeper depths for time and minimizing face moves utilized. This depth does not justify a time check.\r\n\r\n\r\n* \r\n* \u003chttp://kociemba.org/cube.htm Cube Theory: 20-moves Any Cube\u003e ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1062.82px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 447.983px 531.417px; transform-origin: 447.983px 531.417px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 340.283px 7.91667px; transform-origin: 340.283px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face/Vector numbering.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 316.733px 7.91667px; transform-origin: 316.733px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 352.917px 7.91667px; transform-origin: 352.917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice. The loaded function r_new=rubick_rot(mov,r) implements moves 1-18: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 134.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 67.4667px; text-align: center; transform-origin: 384px 67.4667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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\" 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border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 53.9px 7.91667px; transform-origin: 53.9px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eInput: (rubik)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 444.983px 10.2167px; transform-origin: 444.983px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 444.983px 10.2167px; transform-origin: 444.983px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 7.91667px; transform-origin: 107.8px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 69.3px 7.91667px; transform-origin: 69.3px 7.91667px; \"\u003erubik: row vector \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 38.5px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 38.5px 7.91667px; \"\u003eof size 54\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 444.983px 10.2167px; transform-origin: 444.983px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 323.4px 7.91667px; transform-origin: 323.4px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e(The cube started [L=0,U=1,F=2,D=3,B=4,R=5] and then received one or two face moves.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 444.983px 10.2167px; transform-origin: 444.983px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 444.983px 10.2167px; transform-origin: 444.983px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.45px 7.91667px; transform-origin: 219.45px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput: mov (A row vector of one or two of values {1:18})\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 444.983px 10.2167px; transform-origin: 444.983px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 419.65px 7.91667px; transform-origin: 419.65px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 7.91667px; transform-origin: 42.35px 7.91667px; \"\u003e mov: is a \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 377.3px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 377.3px 7.91667px; \"\u003evector values 1:18 representing the moves in order to fix the cube: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 51.0833px; transform-origin: 391px 51.0833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 29.1833px 7.91667px; transform-origin: 29.1833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 361.283px 7.91667px; transform-origin: 361.283px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the cube was randomized by [1 9] UD', the one and only 2 move answer is [3 7] DU' which are the complements in reverse order.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 281.6px 7.91667px; transform-origin: 281.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMinimum moves is also required. Scramble by 13(U2) should return a [13], not [1 1] or [7 7]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 339.217px 7.91667px; transform-origin: 339.217px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eVerifications will be by executing your move vector against the provided rubik and checking number of moves.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.033px 7.91667px; transform-origin: 157.033px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function rubik_rot(mov,r) is available for usage\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.65px 7.91667px; transform-origin: 188.65px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is the next incremental solution step: Move optimization.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 367.617px 7.91667px; transform-origin: 367.617px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAdditional Challenges will be solving the cube at even deeper depths for time and minimizing face moves utilized. This depth does not justify a time check.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 20.4333px; transform-origin: 391px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003ca target='_blank' href = \"http://kociemba.org/cube.htm\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCube Theory: 20-moves Any Cube\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function mov_vec = rubik_solve(r)\r\n% Single/Dual Rubik's Cube Move Solving Challenge\r\n% Available function to check/determine solution : rubik_rot(mov,r)\r\n% out=rubik_rot(mov,r) returns a moved cube array of size 54\r\n% Solved Cube vector\r\n%[00000000111111111222222222333333333444444444555555555]; % with spaces\r\n\r\n  mov_vec=[1 2]; % mov is a single or two value row vector {1-18}\r\nend","test_suite":"%%\r\n% Load function rubik_rot.m\r\ntic\r\nfname='https://sites.google.com/site/razapor/matlab_cody/rubik_rot.m?attredirects=0\u0026d=1';\r\nurlwrite(fname,'rubik_rot.m');\r\n%urlwrite('http://tinyurl.com/matlab-rubik-rot','rubik_rot.m') ; %dead tinyurl\r\nrehash path\r\ntoc\r\n\r\n\r\n%%\r\n% For mov=1 solution is 7. Need U' to solve U in 1 move\r\n% mov=1; % U  answer should be 7\r\n% Solved Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\nr1=rubik_rot(1,r); % Create Challenge Cube\r\n\r\nmov_vec=rubik_solve(r1);\r\n\r\nfor i=1:length(mov_vec) % Perform moves to see if it solves\r\n r1=rubik_rot(mov_vec(i),r1);\r\nend\r\n\r\nassert(isequal(length(mov_vec),1), [sprintf('Exp_moves=1 Exp Mov=7  moves=[')  sprintf('%i ',mov_vec(:)) sprintf(']\\n')])\r\n\r\nassert(isequal(r1,r),sprintf('Exp Mov=7  moves=[%i %i]\\n',mov_vec(:)))\r\n\r\n%%\r\n% For mov=14 the solution is 14. Need F2 to solve F2 in 1 move\r\n% Solved Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\nr1=rubik_rot(14,r); % Create Challenge Cube\r\n\r\nmov_vec=rubik_solve(r1);\r\n\r\nfor i=1:length(mov_vec) % Perform moves to see if it solves\r\n r1=rubik_rot(mov_vec(i),r1);\r\nend\r\n\r\nassert(isequal(length(mov_vec),1), [sprintf('Exp_moves=1 Exp Mov=14  moves=[')  sprintf('%i ',mov_vec(:)) sprintf(']\\n')])\r\n\r\nassert(isequal(r1,r),sprintf('Exp Mov=14  move=[%i]\\n',mov_vec(:))) \r\n\r\n\r\n%%\r\n% Starting Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\n\r\nr1=rubik_rot(2,r); % Create Challenge Cube, First Twist\r\nr1=rubik_rot(9,r1); % Create Challenge Cube, Second Twist\r\n\r\nmov_vec=rubik_solve(r1);\r\n\r\nfor i=1:length(mov_vec) % Perform moves to see if it solves\r\n r1=rubik_rot(mov_vec(i),r1);\r\nend\r\n\r\nassert(isequal(length(mov_vec),2), [sprintf('Exp_moves=2 Exp Mov=[3 8]  moves=[')  sprintf('%i ',mov_vec(:)) sprintf(']\\n')])\r\n\r\nassert(isequal(r1,r),sprintf('Exp Mov=[3 8]  moves=[%i %i]\\n',mov_vec(:)))\r\n\r\n%%\r\n% Anti-Hard code solution Test Case #1\r\n\r\ncmov=[7:12 1:6 13:18]; % Complementary Move\r\n\r\n% Starting Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\nmove_map=[  2 3 4 5 6   8 9 10 11 12    14 15 16 17 18;\r\n           1   3 4 5 6 7   9 10 11 12 13    15 16 17 18;\r\n           1 2   4 5 6 7 8   10 11 12 13 14    16 17 18;\r\n           1 2 3   5 6 7 8 9    11 12 13 14 15    17 18;\r\n           1 2 3 4   6 7 8 9 10    12 13 14 15 16    18;\r\n           1 2 3 4 5   7 8 9 10 11    13 14 15 16 17   ;\r\n             2 3 4 5 6   8 9 10 11 12    14 15 16 17 18;\r\n           1   3 4 5 6 7   9 10 11 12 13    15 16 17 18;\r\n           1 2   4 5 6 7 8   10 11 12 13 14    16 17 18;\r\n           1 2 3   5 6 7 8 9    11 12 13 14 15    17 18;\r\n           1 2 3 4   6 7 8 9 10    12 13 14 15 16    18;\r\n           1 2 3 4 5   7 8 9 10 11    13 14 15 16 17   ;\r\n             2 3 4 5 6   8 9 10 11 12    14 15 16 17 18;\r\n           1   3 4 5 6 7   9 10 11 12 13    15 16 17 18;\r\n           1 2   4 5 6 7 8   10 11 12 13 14    16 17 18;\r\n           1 2 3   5 6 7 8 9    11 12 13 14 15    17 18;\r\n           1 2 3 4   6 7 8 9 10    12 13 14 15 16    18;\r\n           1 2 3 4 5   7 8 9 10 11    13 14 15 16 17   ];\r\n\r\nmovt1=randi(18); \r\nmovt2=move_map(movt1,randi(15));% Avoid complementary moves\r\n\r\n\r\nr1=rubik_rot(movt1,r); % Create Challenge Cube: First Turn\r\nr1=rubik_rot(movt2,r1); % Create Challenge Cube: Second Turn\r\n\r\n\r\nmov_vec=rubik_solve(r1);\r\n\r\nfor i=1:length(mov_vec) % Perform moves to see if it solves\r\n r1=rubik_rot(mov_vec(i),r1);\r\nend\r\n\r\nassert(isequal(length(mov_vec),2), [sprintf('Exp_moves=2 Exp Mov=[%i %i]  moves=[',cmov(movt2),cmov(movt1))  sprintf('%i ',mov_vec(:)) sprintf(']\\n')])\r\n\r\nassert(isequal(r1,r),sprintf('Exp Mov=[%i %i]  moves=[%i %i]\\n',cmov(movt2),cmov(movt1),mov_vec(:)))\r\n\r\n%%\r\n% Anti-Hard code solution Test Case #2\r\n\r\ncmov=[7:12 1:6 13:18]; % Complementary Move\r\n\r\n% Starting Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\nmove_map=[  2 3 4 5 6   8 9 10 11 12    14 15 16 17 18;\r\n           1   3 4 5 6 7   9 10 11 12 13    15 16 17 18;\r\n           1 2   4 5 6 7 8   10 11 12 13 14    16 17 18;\r\n           1 2 3   5 6 7 8 9    11 12 13 14 15    17 18;\r\n           1 2 3 4   6 7 8 9 10    12 13 14 15 16    18;\r\n           1 2 3 4 5   7 8 9 10 11    13 14 15 16 17   ;\r\n             2 3 4 5 6   8 9 10 11 12    14 15 16 17 18;\r\n           1   3 4 5 6 7   9 10 11 12 13    15 16 17 18;\r\n           1 2   4 5 6 7 8   10 11 12 13 14    16 17 18;\r\n           1 2 3   5 6 7 8 9    11 12 13 14 15    17 18;\r\n           1 2 3 4   6 7 8 9 10    12 13 14 15 16    18;\r\n           1 2 3 4 5   7 8 9 10 11    13 14 15 16 17   ;\r\n             2 3 4 5 6   8 9 10 11 12    14 15 16 17 18;\r\n           1   3 4 5 6 7   9 10 11 12 13    15 16 17 18;\r\n           1 2   4 5 6 7 8   10 11 12 13 14    16 17 18;\r\n           1 2 3   5 6 7 8 9    11 12 13 14 15    17 18;\r\n           1 2 3 4   6 7 8 9 10    12 13 14 15 16    18;\r\n           1 2 3 4 5   7 8 9 10 11    13 14 15 16 17   ];\r\n\r\nmov2t1=randi(18); \r\nmov2t2=move_map(mov2t1,randi(15));% Avoid complementary moves\r\n\r\n\r\nr1=rubik_rot(mov2t1,r); % Create Challenge Cube: First Turn\r\nr1=rubik_rot(mov2t2,r1); % Create Challenge Cube: Second Turn\r\n\r\n\r\nmov_vec=rubik_solve(r1);\r\n\r\nfor i=1:length(mov_vec) % Perform moves to see if it solves\r\n r1=rubik_rot(mov_vec(i),r1);\r\nend\r\n\r\nassert(isequal(length(mov_vec),2), [sprintf('Exp_moves=2 Exp Mov=[%i %i]  moves=[',cmov(mov2t2),cmov(mov2t1))  sprintf('%i ',mov_vec(:)) sprintf(']\\n')])\r\n\r\nassert(isequal(r1,r),sprintf('Exp Mov=[%i %i]  moves=[%i %i]\\n',cmov(mov2t2),cmov(mov2t1),mov_vec(:)))\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2020-09-29T16:49:36.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2012-08-09T16:34:10.000Z","updated_at":"2020-09-29T16:50:43.000Z","published_at":"2012-08-09T20:21:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face/Vector numbering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice. The loaded function r_new=rubick_rot(mov,r) implements moves 1-18: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Input: (rubik)\\n\\nrubik: row vector of size 54\\n(The cube started [L=0,U=1,F=2,D=3,B=4,R=5] and then received one or two face moves.\\n\\nOutput: mov (A row vector of one or two of values {1:18})\\n mov: is a vector values 1:18 representing the moves in order to fix the cube: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the cube was randomized by [1 9] UD', the one and only 2 move answer is [3 7] DU' which are the complements in reverse order.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMinimum moves is also required. Scramble by 13(U2) should return a [13], not [1 1] or [7 7]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVerifications will be by executing your move vector against the provided rubik and checking number of moves.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function rubik_rot(mov,r) is available for usage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the next incremental solution step: Move optimization.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAdditional Challenges will be solving the cube at even deeper depths for time and minimizing face moves utilized. This depth does not justify a time check.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://kociemba.org/cube.htm\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCube Theory: 20-moves Any 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\",\"relationship\":null},{\"partUri\":\"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ZlA7JVAkBiHkCSHkAiARDQBkGAVWIADW31GbJIB+uxGGnACE/ACGIgCPewArrgDLogC7IgCLVgAY3gCT4ADYIAlSBIWB3BARmgBZIgAGNglRCAGGjZBGpJHYpgAWPQCGPwliugBV2wYM9hA2yJHpJgWu4BH3EgCUkAl2QQB03ACgrwHKCVGK7ZBmMQBPqQmj6pAGfABWnpBuAQmZZnVMcVAIepAG0gAQIgC1xwBpiwAuaxCbLQGFzAlt//xQZHoAhu4JFBsJKPEAtmUB02QFtjkATsMZv0RR/2gV8CkALeIAH34Q1moAAMsGKyEAdcIAwCIAAS4A1xgpXmJZkdsYXokA7lcAwZkAeLcCUQAAjSlQJ/gAVvkgIwEmXZlQF1YF4pkgJ5kBeKUZUSsAJ7sAg8BgjyQA9YIgt5YAaplQf0IZf08Qf96QS5qWD6sCBOkAH3kQKS4AdsAAjW8CYvsggOyhGvEEjToCyucip5gF2LQAZtQCZkACcxMiNHQGVgkJsp4AWY4CoCkFoNwAmKsAkMYGFKwmNMMANgAAZt+iqxUmQ7wCd0OgP6BAZVsgMXtgeBwARDIABeYA2L/5ArM7BhUboR2MAAJ8YzcuAqgwIrG5YoizJnqNBpgJACYypk+4AtbbBfgYAKvOAHYLAFTOAHizAMZEAG+8BjW3AEicIEnCAHKLZhhXJl8nAFDPAII1INKOAKnCAEVMAGbdpopjBnJgAGPSaZHKALBFAE9WA3c7YH8iAHM2AlJsAJezAKhEJoc0ZodiYEJCAKTGApnABoD3OnO8AJCbAPooICJnAKF/orRTAvJsADGUACKFAPVIACa1YNWWcre6AEVKAM0SAHQkANAksy1fBonIAtSoAsKABwJEAEPGMC9WAs1YBpe3BpDFsPQmAK5OItoZAAPFANn2pnk1Y1QzAEPP9AsQmQADRWaNhGBkUQMHvwro2WAURQBe5CLFVABSTgJzywB/WgbKh2bSQQDUBwA7z2A2eTCS3QAt9SD5wALgCHAsogayiAAolAADzAA37yA1VQBcqQBYiAbexiLpgCMrJ2ZzxwAilzAomwLfbid1RQZ9d2ti0gDkXgbwWDAplADaFAN2k7L8AWDQgHMi57AiwgcyoDBcx2A2WjuCKXLkAQDQCHM4SgD6ZbugSAM/pwB9FwAndQN9GQCIkAAiDQbkaQMvditYkAL8SQBSEwBZmgBAkAArRDbnHLAxEgAwnwtuxWbSlzNiIABPJGOxFwNiNgO9MmAlCQCyxQdycgOn//R7tdkziXUAYABzJAcwkigGwn8G6pmwFAcwcnkAWyVjWZQADfCwIk0HEnEDcRsGt3YL8+I29lIHPqFg1GYATIZgQSlwVGcMDytjSYc29VYwQEp8Bec2w5GwGuWwbz224/57oAtzojcAJLEAHVAzIhUAYyIAKt4AilMDQDRzr3dgMRkAWmkztedwkvIGu4I3LECwJRAwOpcwdpVwZi0zZbAwJG3AoR8DyCozg2/AKm0wrhaztlkA270woEcAlEHDVWVwoA1wqfAAUhkDswAAXLUzzZ8AnGQD/h8AlRsHCtIMStwAJLUAaq0zriEwKlUArhIAKpwzxLoMbiozNerG1W/9wK2QA8I6DHUwACraC+h2M8ZBwDUUDCMDAFk3MJh6MJUBAO21MKVucH33B0gzMCITB7ufB0DiQDU/AAtqAJE2AL48AA59ABj1AGIQADLAAF2cA8XqcBfjc9ABQFFxAFuVAGs6M73QsDIeB0dXd3I3AJVlcGMdB7kLDGLPDHuaAGuTAF4XABsxAC48wNynx9uuAWJAFw35NBFdAMVNcDFdAPNdB5uVAD4yAFBwBUHUEKmiACEkRAmqAJkIAHnwBFDBQFIsR7vgd8wkd8F3QByFcB3ADRsBcOkMANoNcP/sANfvcAqXABxjABNaABX5AKLFQDNHAO3QAPuxRP0ZIKn//nCAFoAA+gARhQRqmAAAXwBh1wDsvIgebAAeUAG45gQsBXAY4ABcUXRVNkz82HP25c0sTXDOADCZAwBZrgCM5nQ6D0fxXQAwUAejRE0zgkBc6HBNlgCZPwC2BIEkEFcB/gD6kQA5MERh+gSW9AevJ3C+rwDSrtCJd0Aa3Q0zkU1dUngAZAgDttgKFURzWkRlwER6EkSmWkRT3kAgxwSxyhCiLIgYBFWC8oBWJkAOPwBh7wlJgYAB0Qf5GgD9jEQyq4AT1gSc/3BjWwQ5rk2KBURmRUQ+NQ2pOkAmDk0y/oSQXwTaTkPkn4iOVwfkPEkJuoDh1ggrogBR8gBVIgg2//8HwxSIHT5IPgRE6nhErNNISuhAHedN5vEEtE6ALf9xu5tIQybYkcIYqaWIIhMQ3Q9IMGEEt8MEenJN40eINDKOA56Eqy9Abg5ACuJIcFEISVkFcRBt0P1htCJFj4TVH0BxYU4AFIMIQO7kzb5IMe0ErUlN4D7oNByIff5AAvnofmJA15hYG/wQFrMSfmAC0C8VCbGORCPuQjuFy6UAwLhRH/YA7qcCHL8OQUEOVSPuVUXuVWfuVYnuVavuVZ/uQfURFKvg1DZYJEXuZmrolM3olKbg4SeeZu/uYUZQ5qLhCEFVEbsYWXqAugwFGp0RJuwAgfZQVZVVIn1RPxOI8s/1WPL/UEnrACMkULNAUANoUDWBEJXrENFkkWGxhRimgR0ULm5SCKoA4WBwALYZUZAGBZMKEDeqAFJdCOswiPKkWPaHWPjHAPhQDpMtWPcEALGFVTdHAL5jDUuNSM5RAhx/AMFlEh25iQHcCQH5FLUqiQC7ALHDANoFALmPEEndASscgIK1AC7HgTsW7oKIWLurjo+MhWTZAVOMDrT/AU7z4IdOAMC3CQwLAA9JTvC9kWwREh07AMETlEC9DhHYENK2AICiALOdAJwsAKdiCLtiUByFAT5F7oeuALOSCP6K7oafUETPEXgjAGgkALVuCPRwEAv4gDoJABimQJwhEhxv81RBSpSM6wAnbQBPhwD50wBlwQVXYAALBQCFagDYUgC47pCQDQCT2vAGMgDPgAVvdgVjqw8eq+Vp2RWTYgCCsQlHQV72ugB7BABhsOUckwhRsRqaEuHHAREgdQF1pgASsQCwUKC4wAGmkwAJ6QBkv/BI3ABhAADpHxkutoHutYAj9ZCL7w8Vh/l6DRBUEgAT5RCJ5QUisgBjqQAXbuDJHAACovCIzQB6Cg9sCAhOXQU9OAmPhQ8QqgBWngBrOhioIQi3ZABp2ABtoAAImRlo5xHlrQBuSxCrLQCDbJFFn/F6LxkXWwAp2QA2jACMTfB36gCqHOAKAgBmnAF2IgBvf/AABqP1i/YQ66wAqKoADcsQcr4AY57x90kAYrcPeXFQRbfw90IAtagAyguZa+f5rzCRDeJORbAcCTjQFpfLip1cTCwyZu8HVqVALcvUb6/MRqosBGnTSwGjVJA0BduXIHKBz69wzlS5gL3MGEqSuWtwxB6pARsGKABS5NhNngMsaoHTtp3HDZtMKGLEFjSlg4E+SnDS1tHkqAYMZbkjh5zLTJIEuLmxIOIdYB2sTsGVmwgpRQtGJMnTOsliLDdzLlypY0YarzS5OGLEVx2tCRpSBfEHAQhVmwEWTTGQkKPH4k47HRIzeUWW2irAXC1iBewbb52iaIN0wKZEEYIywi/xdksSbLehSrxBhFY850CbKijWtZllCqZOlSMMpn7szR5MdgU5wUefwI45KvCTiirCbnJX1GUWcbaRUpOANghQVkVkuPQa1acZIkkuJ8xSRAwplVFAgiDsbGaAwCWSRgyo82zJAgDraY8ou5wJ4rJ4AADJOFDTJSwEIWCPERIIMjjoAgAwUUOWOMy87Y5Ags5mJFghLSaIIMBhBUQBhwFMHnDAskSC2F1fDTD7/+zEhilTjMSOGMOB4RAAIyNuniiDb2SyIFBbqoow5WJgTMueficWmbcn7RRYAt9mjjiDziyMAJb8IQwIk//hBgGC/yyICVM1wU5Y8UyHjvjDpkAf+TxCG2YEKUPUSRJB8IvioyPy0VEcCrFPY7Ax994jgijDhkScHDKQU4QoAwnHACAjGbewlNc7axtQNgLLFVFzKwEIUTV45YhJ4jnEihPyzyFACQLbw4woQ4zBMFz1Uy2MSGMxTYY8VHFnF0CHmY2AKQUVyZUgFJvDEDgibHIqMNAUakRxQ/UEzh2UqxcIUML7bYQgBMCIVAub9kRUmdbTjgwFZgdpmEklEyAGQGMPw4wosUJDkiBW+cAJjQPZs9ghcwjggCgjyxEIATfLiIQ55oFchgByYWYeMUJhqguIEdOJEnEJ05ASMQejg5BWc24mBgBldEEYWJIQRgA4wrWHX/wotg44Bgj1grLDMAfkaZYQ8BZhCAnjzymIGMSGcwIQNR8ug0D5Fn2AGVtY21EwxONgliGGKDyIAMJgC5+WiKwehZDlMakGcGnulx5RRHM3jEhB32YMMaQPbghOchRBnGFU5GAQMVVHjpmkzBApiGDDmuyIANQOjxvIHUOdlhBzBMuMIUKjJYBOMjqGgAahJEScFjoDkEYwswhBeFDHqGOIXmGQKhmZMhdmiAF4p3CEQAcEfRhxM5qDABkH2KKGKGnE3YwxRThDBB+x1mWN3CZfbw4wpO7GEPJhgCKuTBi93tQ2i88x39TKCMGTiLZN9DQRaOsAoBXMF7ewAEE6xB/7otHCED8MPZDK7QgAagb3fgM8Xa9oAKVzxiDzOYgRASMYorCEEZnOAENYjgu9+ZAAyA4MUeCEYh1qHkFwegAgpM4AdXyOFzTBiGKLIHhhlwggkMDET9TPCDUBRhD937Hg9C8YN4KY4JrtjDKbwwgzLswxoC8AMPpzeDIQCCdLwI4B5ySAT1EUAJeyiCElBAgh8oQQgkSEQozmgCVFwBBRkoQjWAt79Z+cEPVBDCKPzQADmYgABUIEIVqFBIcRTBBChAHyd+ZwoTGCEUQuBBBhS3DxQQQRxG2AMYUMiJLJjgUUU4wRFOMUBO6NCRoeBBEapQhR0KQQhUIAQhqUEFZf/wABE8qAcxs4ACJSiBCHvggRGIwYNwKoEKmEwJCXjACSqMwgQkqIc0eVANRZ5SmkUwYxWIQIBkNuCLoagCCk7AAzAswoyhUAJAt2iCFkSAhtQwZRRVyQkTMJSZRQiFOLJJhUTsgQSkrAIJlBGKbZIgAkA4AQqq8IMEJKAFMzWBEkxBBBKwUxmJIIAfUEANE4zCfTwY5Q/qMYpEKFKVuiRCOVFQDU6AsaAnuAEVRIECR1YjGiHgBCpiiYgfZIAaSihoMpUgPx78oApp/QEVeMADZaCAByaYqkxbkAUSZAEIQFAGCU4AAiPI1JF7SMAJWMrORNQjESaoBxH6CsYfEsH/kcr4gRFQQE6GEiERIABCC/bwA3GIgwd6BcJiO0qEBMhgBDT8QQuIkYhGKuEHJEhmJ5VRhUTogwF7CCkBqIGIFpAgATdYQgJgqtosALcMCRDBDSJgRhRkYrg3uMEJ2MkDaiTCuD+QK3B/wFsqhIKyLQArCbBahQQY4QZAyEQi1MoDwwIhC34ALWpBIIJJShYR0ShDNKpQhCxEIBE6NEI0qMED1xIjrj+IBgnuQF0gkCATSxBBerMwgktQFQgRIMAIiCvTzuZ0OWN6iR+iQYAynIC7ichCNhNxA2IAIQGJQAQxfpAJEYAgESRowV4TAIITKEMZGr7wCxL5YwrfAYzM/4zAJXJ5giXcYMYtgHFMs3CCMtyBwjAYbhZeUAriyrgMMGBBCEYg3xe8YAlrTkAmoHwJdmaiDGVgwCMIcec76+POj/BDnv3AAH3wmc5leCsB7hCBE/ghvXd9AQwyQYRo3FcEpeAxMVBwCRYImLSTlikxohEBEYjgyqEGwR0aLYNSgOAGl3hECGDQijmTAApl8MMdCKCPQGvkEexcr5t/DGQjkIAAjygDCRos3GjwNxPLVql0CZCALBghE9HIAk8JsGz+nuAEEbjDCDKB18JmIQF+1fYdTuBm4QY4AXe48onbnAg/GFvHnz7BHpabBbxKNwEE0HYCysDO5i6XwhEQ+P8SbO2HYoc7E3dw8wn8Om2/qvoOyx3BuiMAAm4DNgspPjeKM/GCiafZ3wl4wQgMHYEIxJS6Ao7AlZ8N7URsm9spRvTDHa7tE9zhiCRGyY8vMQIKg5y4NyhDBFggAj/w++cSvvgd2gyCH0dgBFmOgHOhDIJMvDzrhy51Ji5+ggSgPAKlCDAISkHyEdh6qyC/Lwug/XNDG4EFFR9BKeoOgxG8oAw/Tzs7wzH3E1wiBFPwsNkfDIJcXCACDChD2kcAAhCU4QU3EMEdStHoEYAaBHonubjbnom2Y1gGMvg55Dcv6RcYPdMhGL3JL9+KO5CZBaXIxgtaEYJLLKEVUNAyDF7/AIVLXKIVpQD4pKEgAxa0AsMjCEcuLhEFY4SAAOGAwSMIEAEZ6H0JeC+DpEtRBtZLncJmv0SaCfCCS3B5BMiHQe7XPAIYwEAG2chGLnIx61YsYfPIZ0EU6h6CRmMBGZg1EGABGCCAENC9MWuFKPADdsoFGQiBEPg7GCiDKWCBcCgDTVADNdCE+NOACSCAGDCzUpBAERiBvCO8VhDAF4iBF4C8F5CBv4NADLQ7yGuFXJA/35M/GYiCC2SBnwuHcAABTciFF/iEbEC+cPg9CLy9VtCAKXiBELiAKYCCEIgBbCgHNCkYr/k7MwuHT5iFGGSBKYgBSMCDKJiFT7iACYgB/32YBl2IAitMPgIgs3CAAigowFZ4gXBQLQLIhfx7wb9DPyGEAdYTwkNcwhWcu/qLglyIAjUQwhj8hFwohQu8QyhQAzzQACiAhAu4gEeIBlrxu7mLgQv4ggvIhSUIAQ2AQm74AFuAggkYhxqgAZSYhkfAQdWKggkMgU/wRP8Twh6EBDUoQ03wRSgIwPb7u3AYgVZohU+AgmzQgAvghlzgwCmARBlohRi4RjwAxE+8gCmEwln4xBpghnKYjnJgJw3oAW44xS+YAE3ghh7oB01whHqMAQ0Yh0c4BpjoBgsEATM0hjL8BE2cAkfghikYRg6MgjPcRDacgGqcAIrkhgmAhP8voMYvQEVvhAEoeMd+4IYznIIa0IAvqABNmIUKgIRUmIVUiIFXoIR0eImdM5hy2Mhc0ICVhIJZ6IcKmIAa6IEeeAAMkIIY6AbB6IAYoERHmIJvdIQLUINP4IYKqAANMMVwQMMp4MDEq8oJ0MmTBMGqpMYKQEUJTAUM4IZ+6Ad/0AAY4AYEeIBffIBxuAANwIAH8ABdKAdVAIZJMId2KIea9BpIsMoYwAAE+ACLJMoHeAADQAAXyIBXeAVgOARgWABgAIZXIIdsiAGJ1IBc+IQKuABH3MgJoEd3HEEZ+EZ4lMiqtMqybAZqvIAHqIFU2IAN+IBUWEtbqAFb8IcNeAD/RzCADbCFWUAAA/CAA7CEZegACsCVzBxMMvkABBiHB8DND6iBcUAABHiDB/gAFyCFc7AQdkiTMqiBKTCGGuAGY0DF9YxHtfTJVPgAA3iAGPBNu7wASFhDTXiAVKDFBwBODNjOxOQGW8CADxiHD/CHD5ACW9gAA3ABDIjQYiiH8aQE1tlCJHoJ3LSF7yzKVODOAqgBo0RKC3kJddgFUigAW7gAvNzPB0DOB9CEteyH+cRNx+ROAxiHx0QAxESADZhQf/CHxgROA6gB6qzOHphQBcUADEiFGvCASICJAAAGmNBQwDiElxgHKK2Bx9zRCTWASjiAE6WJW1gAXIiB3nzM/wfIhhjdAH+ogQLogQqYTyBNhR41gB+tziQdB1vgTlvgBgwogEHlTgSQggJ4TAd4Az11gUqYhnR8iQBYAJhQRwrRUpRQAT3lUQx4gxrAABfwgyQq0wCwh3XYhRqozQ8I0hrATgXV06AEznH4UT01VAXlTiE1gDfoBQNQgQEVUUalT2lwUiTwgAqlCWew0lkZMZbA1HJwhAJwASQogALwgH4czzIVjL5UjkPQB0KlT2o1AH/gUepEVELlUSD9gD390QZ9gwkN116dVQdQASlQVweogV6I1mOliUkdDGb9B2dFCUrQ0nOghG0wB3XMVpjggAVQR3J4BCcd1E2dzw/4AP9CVQGLndYCkAI/MNc3KIB5dQAH4AMVcIAC0NROJVkVeAMkGNk3kAJpINPnUAXW6ZoMsZAFcAaFfQ4OAIaExYVHgFVNjdACqNiLVQGQJVk+kAI+4IOibFp6LQCSNdmi7AUkwACkdYGmRQJpeNQTndSEtdkTjYeA3VmU6NmELQdc+FQkqFcDQAI+uNqLNYCkVYGlbVoH6AWVlYJ5LVkXENm89Vu9LQAkqIQMQIevVdaD+debfY4FKFuzRVua6AAPaFkpMAC+5QMH8AAHMACL7Vs+6IWRDV2ozVwkcAHRzdtpRYJekFau1QVstZB+XVYuLAzBuEyz5dcOSFuU0IVKcNn/N2ja0EUC4n0D0GVapz1Zu3UBaWBd1BXZXmheq21eadCFSfjL50CTKrWVdcRSltjCSA0Ad3gGzFwGzHSHbXiGAFDf9T0Ed1jf6LDMZ7AHfsDMBVgA8u0AS9AFaRhZ1G3aXkjd05XWXnhZ1n0D1yXeAH7e1kXdAZaGR7jfzNwGd7Dfnr3fDmCG+23cZaCQfzjY3A1hER5hEjbbZcgAGlgGdfgHFk7fDtgFyC1hGZ7hGQYGGsgABsiAaaCAZ9gGFm5hdQCGZSgGGpiGSDiAIz4AJV5iJm5iJ35iKI5iKZ5iKm7iSIiEaaCBYqAAYAgAH/7hH0ZYwsAQDDkEMj5jNE5jETVeYzZuYzd+YzdGmIMF44AAADs=\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":879,"title":"Perform Rubik's Cube Moves","description":"A standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face numbering.\r\n\r\nThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\r\n\r\nMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice. The F move would map 19 to 25,..., 7 goes to 18,..., and 23 is unchanged.\r\n\r\nThe moves X( R ), Y(U), and Z(F) rotate the entire cube with its associated face.\r\nX would map 23 to 14. (19:27) moves to (10:18). Only contents of 5 and 50 are unchanged There are also X' and X2 moves.\r\n\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/cube_small.gif\u003e\u003e\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/Cube_Map28_200.png\u003e\u003e\r\n\r\n\u003c\u003chttp://mathworks.com/matlabcentral/images/surf.gif\u003e\u003e\r\n\r\n\r\n  \r\n  \r\n  Input: (mov,rubik)\r\n  mov: is an integer 1:27 representing the moves in order: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2XYZX'Y'Z'X2Y2Z2\r\n  rubik: row vector of size 54\r\n  (A normal cube would have values 0:5 in locations 1:54,\r\n  The test input is generally numbered 1:54 to check that each tile is correctly remapped. A normal cube with 6 values may be used in testing)\r\n\r\n  Output: rubik vector of the input cubes values remapped based upon mov\r\n\r\nAll 27 moves are enumerated in the test suite\r\n\r\nFollow-up Challenges will be solving the cube at various move depths for time and actual face moves required.\r\n \r\nNote: Images inserted/linked to my free google web page. Used a gif and a png.\r\n\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003eA standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face numbering.\u003c/p\u003e\u003cp\u003eThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\u003c/p\u003e\u003cp\u003eMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice. The F move would map 19 to 25,..., 7 goes to 18,..., and 23 is unchanged.\u003c/p\u003e\u003cp\u003eThe moves X( R ), Y(U), and Z(F) rotate the entire cube with its associated face.\r\nX would map 23 to 14. (19:27) moves to (10:18). Only contents of 5 and 50 are unchanged There are also X' and X2 moves.\u003c/p\u003e\u003cimg src=\"https://sites.google.com/site/razapor/matlab_cody/cube_small.gif\"\u003e\u003cimg src=\"https://sites.google.com/site/razapor/matlab_cody/Cube_Map28_200.png\"\u003e\u003cimg src=\"http://mathworks.com/matlabcentral/images/surf.gif\"\u003e\u003cpre class=\"language-matlab\"\u003eInput: (mov,rubik)\r\nmov: is an integer 1:27 representing the moves in order: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2XYZX'Y'Z'X2Y2Z2\r\nrubik: row vector of size 54\r\n(A normal cube would have values 0:5 in locations 1:54,\r\nThe test input is generally numbered 1:54 to check that each tile is correctly remapped. A normal cube with 6 values may be used in testing)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eOutput: rubik vector of the input cubes values remapped based upon mov\r\n\u003c/pre\u003e\u003cp\u003eAll 27 moves are enumerated in the test suite\u003c/p\u003e\u003cp\u003eFollow-up Challenges will be solving the cube at various move depths for time and actual face moves required.\u003c/p\u003e\u003cp\u003eNote: Images inserted/linked to my free google web page. Used a gif and a png.\u003c/p\u003e","function_template":"function r = rubik_rot(mov,r)\r\n  r=r;\r\nend","test_suite":"%%\r\n% Single move cases\r\nmov=1; % U\r\nr=1:54;\r\nr_exp=[19 2 3 22 5 6 25 8 9 12 15 18 11 14 17 10 13 16 46 20 21 49 23 24 52 26 27 28 29 30 31 32 33 34 35 36 37 38 7 40 41 4 43 44 1 45 47 48 42 50 51 39 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\nmov=7; % U'\r\nr=1:54;\r\nr_exp=[45 2 3 42 5 6 39 8 9 16 13 10 17 14 11 18 15 12 1 20 21 4 23 24 7 26 27 28 29 30 31 32 33 34 35 36 37 38 52 40 41 49 43 44 46 19 47 48 22 50 51 25 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\nmov=13; % U2\r\nr=1:54;\r\nr_exp=[46 2 3 49 5 6 52 8 9 18 17 16 15 14 13 12 11 10 45 20 21 42 23 24 39 26 27 28 29 30 31 32 33 34 35 36 37 38 25 40 41 22 43 44 19 1 47 48 4 50 51 7 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\nmov=19; % X\r\nr=1:54;\r\nr_exp=[7 4 1 8 5 2 9 6 3 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 10 11 12 13 14 15 16 17 18 48 51 54 47 50 53 46 49 52];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\nmov=22; % X'\r\nr=1:54;\r\nr_exp=[3 6 9 2 5 8 1 4 7 37 38 39 40 41 42 43 44 45 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 52 49 46 53 50 47 54 51 48];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\nmov=25; % X2\r\nr=1:54;\r\nr_exp=[9 8 7 6 5 4 3 2 1 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 54 53 52 51 50 49 48 47 46];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\n% Remaining CW Face moves 2-6\r\nmov=2; % F\r\nr=1:54;\r\nr_exp=[1 2 3 4 5 6 28 31 34 10 11 9 13 14 8 16 17 7 21 24 27 20 23 26 19 22 25 48 29 30 47 32 33 46 35 36 37 38 39 40 41 42 43 44 45 12 15 18 49 50 51 52 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=3; % D\r\nr=1:54;\r\nr_exp=[1 2 43 4 5 40 7 8 37 10 11 12 13 14 15 16 17 18 19 20 3 22 23 6 25 26 9 30 33 36 29 32 35 28 31 34 54 38 39 51 41 42 48 44 45 46 47 21 49 50 24 52 53 27];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=4; % L\r\nr=1:54;\r\nr_exp=[3 6 9 2 5 8 1 4 7 37 38 39 13 14 15 16 17 18 10 11 12 22 23 24 25 26 27 19 20 21 31 32 33 34 35 36 28 29 30 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=5; % B\r\nr=1:54;\r\nr_exp=[16 13 10 4 5 6 7 8 9 52 11 12 53 14 15 54 17 18 19 20 21 22 23 24 25 26 27 28 29 1 31 32 2 34 35 3 39 42 45 38 41 44 37 40 43 46 47 48 49 50 51 36 33 30];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=6; % R\r\nr=1:54;\r\nr_exp=[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 25 26 27 19 20 21 22 23 24 34 35 36 28 29 30 31 32 33 43 44 45 37 38 39 40 41 42 16 17 18 48 51 54 47 50 53 46 49 52];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\n% Remaining CCW Face moves 8-12\r\nmov=8; % F'\r\nr=1:54;\r\nr_exp=[1 2 3 4 5 6 18 15 12 10 11 46 13 14 47 16 17 48 25 22 19 26 23 20 27 24 21 7 29 30 8 32 33 9 35 36 37 38 39 40 41 42 43 44 45 34 31 28 49 50 51 52 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=9; % D'\r\nr=1:54;\r\nr_exp=[1 2 21 4 5 24 7 8 27 10 11 12 13 14 15 16 17 18 19 20 48 22 23 51 25 26 54 34 31 28 35 32 29 36 33 30 9 38 39 6 41 42 3 44 45 46 47 43 49 50 40 52 53 37];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=10; % L'\r\nr=1:54;\r\nr_exp=[7 4 1 8 5 2 9 6 3 19 20 21 13 14 15 16 17 18 28 29 30 22 23 24 25 26 27 37 38 39 31 32 33 34 35 36 10 11 12 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=11; % B'\r\nr=1:54;\r\nr_exp=[30 33 36 4 5 6 7 8 9 3 11 12 2 14 15 1 17 18 19 20 21 22 23 24 25 26 27 28 29 54 31 32 53 34 35 52 43 40 37 44 41 38 45 42 39 46 47 48 49 50 51 10 13 16];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=12; % R'\r\nr=1:54;\r\nr_exp=[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 43 44 45 19 20 21 22 23 24 16 17 18 28 29 30 31 32 33 25 26 27 37 38 39 40 41 42 34 35 36 52 49 46 53 50 47 54 51 48];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\n% Remaining Double Face moves 14-18\r\nmov=14; % F2\r\nr=1:54;\r\nr_exp=[1 2 3 4 5 6 48 47 46 10 11 34 13 14 31 16 17 28 27 26 25 24 23 22 21 20 19 18 29 30 15 32 33 12 35 36 37 38 39 40 41 42 43 44 45 9 8 7 49 50 51 52 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=15; % D2\r\nr=1:54;\r\nr_exp=[1 2 48 4 5 51 7 8 54 10 11 12 13 14 15 16 17 18 19 20 43 22 23 40 25 26 37 36 35 34 33 32 31 30 29 28 27 38 39 24 41 42 21 44 45 46 47 3 49 50 6 52 53 9];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=16; % L2\r\nr=1:54;\r\nr_exp=[9 8 7 6 5 4 3 2 1 28 29 30 13 14 15 16 17 18 37 38 39 22 23 24 25 26 27 10 11 12 31 32 33 34 35 36 19 20 21 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=17; % B2\r\nr=1:54;\r\nr_exp=[54 53 52 4 5 6 7 8 9 36 11 12 33 14 15 30 17 18 19 20 21 22 23 24 25 26 27 28 29 16 31 32 13 34 35 10 45 44 43 42 41 40 39 38 37 46 47 48 49 50 51 3 2 1];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=18; % R2\r\nr=1:54;\r\nr_exp=[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 34 35 36 19 20 21 22 23 24 43 44 45 28 29 30 31 32 33 16 17 18 37 38 39 40 41 42 25 26 27 54 53 52 51 50 49 48 47 46];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\n% Remaining Cube CW moves 20-21\r\nmov=20; % Y\r\nr=1:54;\r\nr_exp=[19 20 21 22 23 24 25 26 27 12 15 18 11 14 17 10 13 16 46 47 48 49 50 51 52 53 54 34 31 28 35 32 29 36 33 30 9 8 7 6 5 4 3 2 1 45 44 43 42 41 40 39 38 37];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=21; % Z\r\nr=1:54;\r\nr_exp=[30 33 36 29 32 35 28 31 34 3 6 9 2 5 8 1 4 7 21 24 27 20 23 26 19 22 25 48 51 54 47 50 53 46 49 52 43 40 37 44 41 38 45 42 39 12 15 18 11 14 17 10 13 16];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\n% Remaining Cube CCW moves 23-24\r\nmov=23; % Y\r\nr=1:54;\r\nr_exp=[45 44 43 42 41 40 39 38 37 16 13 10 17 14 11 18 15 12 1 2 3 4 5 6 7 8 9 30 33 36 29 32 35 28 31 34 54 53 52 51 50 49 48 47 46 19 20 21 22 23 24 25 26 27];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=24; % Z\r\nr=1:54;\r\nr_exp=[16 13 10 17 14 11 18 15 12 52 49 46 53 50 47 54 51 48 25 22 19 26 23 20 27 24 21 7 4 1 8 5 2 9 6 3 39 42 45 38 41 44 37 40 43 34 31 28 35 32 29 36 33 30];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\n% Remaining Cube Half Rotate moves 26-27\r\nmov=26; % Y\r\nr=1:54;\r\nr_exp=[46 47 48 49 50 51 52 53 54 18 17 16 15 14 13 12 11 10 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 1 2 3 4 5 6 7 8 9];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=27; % Z\r\nr=1:54;\r\nr_exp=[54 53 52 51 50 49 48 47 46 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 45 44 43 42 41 40 39 38 37 9 8 7 6 5 4 3 2 1];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\n% Verify that values in the array are returned and not positions\r\nmov=2; % F\r\nr=1:54;\r\nr=r*0; % The simplest Cube - Solid\r\nr_exp=r; \r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\n% Perform Sequence of moves and then back\r\nr=1:54;\r\nr_exp=r; \r\nmov=1; % U\r\nr=rubik_rot(mov,r);\r\nmov=2; % F\r\nr=rubik_rot(mov,r);\r\nmov=3; % D\r\nr=rubik_rot(mov,r);\r\nmov=4; % L\r\nr=rubik_rot(mov,r);\r\nmov=5; % B\r\nr=rubik_rot(mov,r);\r\nmov=6; % R\r\nr=rubik_rot(mov,r);\r\nmov=12; % R'\r\nr=rubik_rot(mov,r);\r\nmov=11; % B'\r\nr=rubik_rot(mov,r);\r\nmov=10; % L'\r\nr=rubik_rot(mov,r);\r\nmov=9; % D'\r\nr=rubik_rot(mov,r);\r\nmov=8; % F'\r\nr=rubik_rot(mov,r);\r\nmov=7; % U'\r\n\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-08-05T05:47:50.000Z","updated_at":"2026-03-28T16:32:39.000Z","published_at":"2012-08-05T19:30:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.gif\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/media/image1.png\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId3\",\"target\":\"/media/image2.gif\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face numbering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice. The F move would map 19 to 25,..., 7 goes to 18,..., and 23 is unchanged.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe moves X( R ), Y(U), and Z(F) rotate the entire cube with its associated face. X would map 23 to 14. (19:27) moves to (10:18). Only contents of 5 and 50 are unchanged There are also X' and X2 moves.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Input: (mov,rubik)\\nmov: is an integer 1:27 representing the moves in order: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2XYZX'Y'Z'X2Y2Z2\\nrubik: row vector of size 54\\n(A normal cube would have values 0:5 in locations 1:54,\\nThe test input is generally numbered 1:54 to check that each tile is correctly remapped. A normal cube with 6 values may be used in testing)\\n\\nOutput: rubik vector of the input cubes values remapped based upon mov]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll 27 moves are enumerated in the test suite\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollow-up Challenges will be solving the cube at various move depths for time and actual face moves required.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: Images inserted/linked to my free google web page. Used a gif and a png.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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\"},{\"partUri\":\"/media/image2.gif\",\"contentType\":\"image/gif\",\"content\":\"data:image/gif;base64,R0lGODlhbABsAPf/AJJ3Uu7u7omXaMytTFZ0bQhwrQiV0JmZmgG062mXiJGPWOPk5FlcW6jVhilvsy2QrqmwZXi4qPLpRlW3yM/Pz1bH1/3nNFSmtAuGuGpzalGaqAbD6vPz89nZ2ipPawmn2HvEtmanpobVyGikmWWId+fPSnmXeHOpl3mkh9flTyuIyHRuV4jY1YfJqApPkmWclXa7tU54hHvIxomndq2srS9ti//qKoPMuPyRKP+2KsqRR6jVeXSdgzKz0P/XKoW6mInUuKumWprWmZi5d4zFmYe0i4W7ppinZg5ZpejoO5PMmIPOxrPZeKWXVsnYWPq7MViIh1qWmRRommm2uoOqhpbWptuTOprIh7zOWHiyndnGQ7raZ//3KdjMOsvjZWDL16TMesfWYuK2S7irWHuHZluBd9nbRv3yNf/LKbecVXPO0+V7L5SrdLa4XPndNCVZiPqtNJujWpW4hv+sK6aSZOrZOtayPWKNgnXU2LbGY7iHR2iBajB7wLCMKFdnX8zcSqnFbZ3He76jTJdiQxweIKyESf3IMevr547UrWuRfMvFSJ+2abmXSKCFVkqFlkZWY2fCyqmcm6u0XP379vPu6hs1UvXz7nCtpMbNWGygjFWLk724Sn+geLmNUem7PGWss2tXN5DPooqgbHWKdJKbpV6UjJ3Si7DVarDhiDOFoO/v9NzgV6ykTmyxrnqTbePj3WtcTKibTHx/WUeFjMF2Q+jEQS2ivu709O7l41+eo3uEiuLd246wdx9epeOmPPr39N/f4N/k5dzMT7LKc5HZtMG5uGrS28nEwv/5Hs7N04KukdfU0szT02LS4Ofr7efn5//RIHSfkAk+hKKjp32wjI3Cjb/jcvGhKra6w2GLkN6gQPf390mRouTf4d/jPse8xfDdLYLQ0Y/SnB2BpNPPzf////v7+///+v/7+/v3+/Pv8Pv/+vv////7/+vn6ff7+/f799/j35Cwgfv7/6O+fJC+k9PS1secW8i8W+bZXDxERJGxb8TGykDD3B/B5AAAACH5BAEAAP8ALAAAAABsAGwAQAj/AP8JNLdNXYCDCBMqXMiwocOHECNKPKhum8CLAp+V28iRIzCNHUOW21YuGIMBAHQ88bXCExofjAp1OqOFjiE0tRpdm5OjkDaeenTwtNIJzhw4nZ4o1TOglo5BtHDgsNLoibZBg3DQGsSvHDqRHAMs6BhgI41d6v6BBLvAXcdz5zqqygCgyRkJsuoIS9Oolg8fsQS9jLVCKR0FbiycaSJMMasBFix0wSdhQCMATwz1HPBSUBofbmo1sVGnUeEnaAoBMDSIBkd+j0AJEgMgqJgm6jYeoHBILdiNC9Zy3JZh05E2ijKQqSOhSR3FsYTZOBNkkwUuivxosVEiThw7dRgI/ztzhpV1G1rGSLAgIYgZb0nitEmSRFIc+H+OhGElYEWTTeCMkY8WyjURBH0KBCFAGwqwJ0wTZZWzW29rdfAMMB1gCEwyyxxCgz6SLELPDGQs4sUiojiRAiYCYPFHCgIMs4UXR/AygyKKHOHEH2HsIYAFNsQxShcSMCCANUwswgYTpzDBBhhXyKGcAKLssYcoAriSgSj0NCCKF7LsQUYekuwzhCROzCCPKFu0KYCKKcSRm4S8+SbSIaMQwAk9JpiwBz1MMCHPEA2gMoQoYOwAhgmBmCKECURQMQQbTzbACw8tUJGHKIHsgIqPW1gjCgGnDLNHBmwM4WSip4gyxA47yP8zCidUFEGFKX746YopShBAhRBCKLNHEVX8YIIpyO7hignK8DDnhHaWQ0AGezBLDQo8EBGKEtkqEQoPifBQRBHZikNEIi3cgMIe2orDQxZAZLEHD94SkQAMCdDDyQ8tEFMGFeKE8sMo1QhRxCg/8NDsKIkok8geKFCTRcQniJBJKNSMMAK/QKBAwA1ARJBAKKGcQEALQABxwrN1rpWJyka0kEkC+lSiDwP6EFAGCX4QkEA0ZTxCwgkkMEDCHjwncgfPBCQSDQlljOD00FlkAQUU6CbyAgwREEBCBGC/8MIdRiSSCdhKV22yxgn4nAjTZWTCMwkE+OFHIgmQ8EjPifj/wTKFHC3BwiVQjBAODJmA8EIrI8AwwidTJBBCNn7c4fgJmVxSiuMwOE6A4SxE8AIIIhPwwiUglAICCyyM0IoIIkRwyRIiLDHCDSK0HsESMrxQ+AulZAODDOG8sAQIlxAQhQwstFLK6YqHMIIMUCw+BQF/R9vKBTFoUsEXF4QQwgP95KIBN/48kIstb2QQ10a6RAFDLqVA8sknuXyihhpRxABDODKIAiTUgAcNTGEKkIBCDDSQC010Lwr9i4IGLuCIXHyhAhfQwP6m8AIZ5OIBjtgf/6DwCfDFwBZfyMUsbFEDUuBiHhzJ3lr8sYEHPGADNYzBBzZggDcYQArZmNNv/8oxCWyk4gHG0EANJtCMC9hQAxPgRg/60Y9U7HADNSgABjBQgBikAgPjqAEGPoCAcdgChxh4gD/88YEsknEcCPhAAaRgCwRsUQpdxEUMgdERc+imTofgCC6m0bMMZOAAyxiiIjkADD9KSAoGGGMBIvmBcRjAAHLEQCTfAMkPRBIBoBwHFwvgAgeoQAV4VIEBVPCGApwSkr3gwxvegIRHUAIsAWhkDP/YmwiB5RC+VKRIOOCWkJjDD9LgQy/m6AA+KNMFkyyAKVWgTGc6QAoYOGUvkMBNJPTCAeD0gAt60QtpuAAJHkjk+8CijmJuhCR06s1A1AEMCkxDF4ZkgD73yf/PfvrznwANqEAHStCBGlIX06AAMNRhjn9UpCPwLMdHhNkRfsBiDbQwhB5ooQOY6GEOcxgEAHxgCE/ohCc+AYpQckAUoyBlJVuJilZkaoVBrOGmWOnKNsyxzjvxsRzmcOQhGJqRIU5UmLoohB0EkAZtNMICaRCDDxrxCFkwQhB18QFOCnGNa+hgBQAoBCNqwxNt6MClSVFKITjjA89YACUAgEMO4LDWQmgFFscoxzvAYolAhoWX0RLJAvwqEgowIB8KaFAQMiALVjQhCUHIh2KCsAJB+GAAabCBGxrRCEHI4gzRcQxk0NOGyLTnPWeIgwDo4BnLhqYJQLKAc2xQixX/jAEZtdWHLPChhSakgQ5jcA6OmgBPaAknJMDsyDIyAIhFQAATxyHDEfLABFH84Q9e4NIRJKEA65xhE9ZtgwCaAA4ubMIPmMhAiFyxiCMo4LF3gcB74jOf+sSBPix6zyoEYAYJ4GUFEDiOACDwB0zEQQJdgMAKFEAlMhS3ZUPMpQl2pSw2WIMNZOASLziRqECYQB6cWIQA8uAEGvGiATsYgh/y4A0nCAAMQ4BAHADhJAWwIQP7GAYbTtGkGQQCxa5qABN4IQpYDYETTADEDB6RAXrIgQCA2MKlZrCDBgwhA5yohyk4DKsZyJAj6TjAIxKhhHpYiVZFMIESgFUrYBUB/wUC89MVkGWCH4RCHCggARWYsI9otEAJVSDAqxpgAiOgQEnUaIEJFkEFTphADlTQVhXERTIqUEEJRaDbm6tggkT8gBg8oEIibjAxQKOgDC1ARAvotWYqfHkjeCMBCajxg1PzwAiIyIQRTqCMUSgDERiLxsQSZgSQZSIL0agCCk4AsgjcgQdVsBcIYkcAI4QCESgYQQKIUI2KnYAKiQaCEcoQLmrwYGgRAEECQJaFMoDgBkvIxAk6yDjcJaAMtVtCAlpwghMk4NXliMAI7jA7EcCAADConR9GVwY/UO0OZQBb27Jwgxvs7GylmN0N7p2JjpchCxG4QSYSbrEswA4Gs/9bwhKYTbsXZIF2l0hAFjDnswRc4g7TvsEdEpCJFyTgdqVDXfJeALY7ADwcLJAe0l+QDTWEIxxluAAepuCHVoQgin54hPDKML8RlEIGMggBFC7BulZEoRViuwPzWLA1pIfgdSyAwSeQHo4QCI4FuWjF0y9xCRnA4AUxaMUSikc8GMTgBW6HwgXUAIIYfAISuYhBDFxDEMCu5QvNmKATH8ANKqaiBj0Y4zgegQ14BGAb23gH6n9BCkc44gK5gPwFLgA5DXyvArPg/BSiMIX95eICX/jCBC5QgeJrABLBn2DwNVGDB3zgA6mgYj8cYcUaXoAbH7BFDB6AACk8Yhe/AMb/MtTBgfJnj7Bk3CIoMfAGTbqAAJag6EY4sIBfRAKMN2zjONZYyUj2APsIsAGWBEqfFEpkZEcGsEYP0H62wEWg9AE+REbYZAAF4AEMEH8doQ5jwRGOBC3BFBIL4AzyJxL05EgbEQmT5AIYYAsqgAQFUACZpErSdErV5ExS4Ewq8E2ndE3S5AC9kE1I4AJ84AAu4AH64E4iIRYZCFiVFxLq4AzitwDAcAjb8Azu8AwBcAjPcAjA5A5eeAhT2AHJ4A5T+AzOcCG/kAy0xAcuUErKhATgxE3b5AJv0IZt6E29cE7ehId2GIQuIA3SQArmgAvPsABVuAAhuA0hCIbM0A0//6UbkUABASAQ2/CBI3iJmJiJmjiCAdBQF3FcHdEWI9gB+gALSYEGIvUXaaAD19AJ+JAGhuADOXENcpVSPSEUc9BSR5FWaNAJALAGMyUVa9AIOoBTWGEP5cABkxBhG7gRjjR+DVUhYvERC9ABy4CI7kBP7oCNiLgA8eAHAyAIsLASQdAEYmAIm8UKNoAdNoETOlGLP5EDQTEURbGLSvEEaxWLKBEVa1AIcvUEABAVtAAK0+AMjNSN9IeIwGAPg+UOB/FHkwiKHIGFIdFT5UADsGAHrCABjdAEbsAFTQAAjTAAndAInWAFVNEJdkAYjWEDsVAC6zgG+FAHcOULT4AUcP+gVmzlGaBRBwpAB9rQE5mhB4NwD7DgGiLxDAdwMxmgC6QAcCLhkENEAbIwBrIADql1Em5QBwBAB3ZgUgOgj0EwBtrwBLZlA7JVAkBiHkCSHkAiARDQBkGAVWIADW31GbJIB+uxGGnACE/ACGIgCPewArrgDLogC7IgCLVgAY3gCT4ADYIAlSBIWB3BARmgBZIgAGNglRCAGGjZBGpJHYpgAWPQCGPwliugBV2wYM9hA2yJHpJgWu4BH3EgCUkAl2QQB03ACgrwHKCVGK7ZBmMQBPqQmj6pAGfABWnpBuAQmZZnVMcVAIepAG0gAQIgC1xwBpiwAuaxCbLQGFzAlt//xQZHoAhu4JFBsJKPEAtmUB02QFtjkATsMZv0RR/2gV8CkALeIAH34Q1moAAMsGKyEAdcIAwCIAAS4A1xgpXmJZkdsYXokA7lcAwZkAeLcCUQAAjSlQJ/gAVvkgIwEmXZlQF1YF4pkgJ5kBeKUZUSsAJ7sAg8BgjyQA9YIgt5YAaplQf0IZf08Qf96QS5qWD6sCBOkAH3kQKS4AdsAAjW8CYvsggOyhGvEEjToCyucip5gF2LQAZtQCZkACcxMiNHQGVgkJsp4AWY4CoCkFoNwAmKsAkMYGFKwmNMMANgAAZt+iqxUmQ7wCd0OgP6BAZVsgMXtgeBwARDIABeYA2L/5ArM7BhUboR2MAAJ8YzcuAqgwIrG5YoizJnqNBpgJACYypk+4AtbbBfgYAKvOAHYLAFTOAHizAMZEAG+8BjW3AEicIEnCAHKLZhhXJl8nAFDPAII1INKOAKnCAEVMAGbdpopjBnJgAGPSaZHKALBFAE9WA3c7YH8iAHM2AlJsAJezAKhEJoc0ZodiYEJCAKTGApnABoD3OnO8AJCbAPooICJnAKF/orRTAvJsADGUACKFAPVIACa1YNWWcre6AEVKAM0SAHQkANAksy1fBonIAtSoAsKABwJEAEPGMC9WAs1YBpe3BpDFsPQmAK5OItoZAAPFANn2pnk1Y1QzAEPP9AsQmQADRWaNhGBkUQMHvwro2WAURQBe5CLFVABSTgJzywB/WgbKh2bSQQDUBwA7z2A2eTCS3QAt9SD5wALgCHAsogayiAAolAADzAA37yA1VQBcqQBYiAbexiLpgCMrJ2ZzxwAilzAomwLfbid1RQZ9d2ti0gDkXgbwWDAplADaFAN2k7L8AWDQgHMi57AiwgcyoDBcx2A2WjuCKXLkAQDQCHM4SgD6ZbugSAM/pwB9FwAndQN9GQCIkAAiDQbkaQMvditYkAL8SQBSEwBZmgBAkAArRDbnHLAxEgAwnwtuxWbSlzNiIABPJGOxFwNiNgO9MmAlCQCyxQdycgOn//R7tdkziXUAYABzJAcwkigGwn8G6pmwFAcwcnkAWyVjWZQADfCwIk0HEnEDcRsGt3YL8+I29lIHPqFg1GYATIZgQSlwVGcMDytjSYc29VYwQEp8Bec2w5GwGuWwbz224/57oAtzojcAJLEAHVAzIhUAYyIAKt4AilMDQDRzr3dgMRkAWmkztedwkvIGu4I3LECwJRAwOpcwdpVwZi0zZbAwJG3AoR8DyCozg2/AKm0wrhaztlkA270woEcAlEHDVWVwoA1wqfAAUhkDswAAXLUzzZ8AnGQD/h8AlRsHCtIMStwAJLUAaq0zriEwKlUArhIAKpwzxLoMbiozNerG1W/9wK2QA8I6DHUwACraC+h2M8ZBwDUUDCMDAFk3MJh6MJUBAO21MKVucH33B0gzMCITB7ufB0DiQDU/AAtqAJE2AL48AA59ABj1AGIQADLAAF2cA8XqcBfjc9ABQFFxAFuVAGs6M73QsDIeB0dXd3I3AJVlcGMdB7kLDGLPDHuaAGuTAF4XABsxAC48wNynx9uuAWJAFw35NBFdAMVNcDFdAPNdB5uVAD4yAFBwBUHUEKmiACEkRAmqAJkIAHnwBFDBQFIsR7vgd8wkd8F3QByFcB3ADRsBcOkMANoNcP/sANfvcAqXABxjABNaABX5AKLFQDNHAO3QAPuxRP0ZIKn//nCAFoAA+gARhQRqmAAAXwBh1wDsvIgebAAeUAG45gQsBXAY4ABcUXRVNkz82HP25c0sTXDOADCZAwBZrgCM5nQ6D0fxXQAwUAejRE0zgkBc6HBNlgCZPwC2BIEkEFcB/gD6kQA5MERh+gSW9AevJ3C+rwDSrtCJd0Aa3Q0zkU1dUngAZAgDttgKFURzWkRlwER6EkSmWkRT3kAgxwSxyhCiLIgYBFWC8oBWJkAOPwBh7wlJgYAB0Qf5GgD9jEQyq4AT1gSc/3BjWwQ5rk2KBURmRUQ+NQ2pOkAmDk0y/oSQXwTaTkPkn4iOVwfkPEkJuoDh1ggrogBR8gBVIgg2//8HwxSIHT5IPgRE6nhErNNISuhAHedN5vEEtE6ALf9xu5tIQybYkcIYqaWIIhMQ3Q9IMGEEt8MEenJN40eINDKOA56Eqy9Abg5ACuJIcFEISVkFcRBt0P1htCJFj4TVH0BxYU4AFIMIQO7kzb5IMe0ErUlN4D7oNByIff5AAvnofmJA15hYG/wQFrMSfmAC0C8VCbGORCPuQjuFy6UAwLhRH/YA7qcCHL8OQUEOVSPuVUXuVWfuVYnuVavuVZ/uQfURFKvg1DZYJEXuZmrolM3olKbg4SeeZu/uYUZQ5qLhCEFVEbsYWXqAugwFGp0RJuwAgfZQVZVVIn1RPxOI8s/1WPL/UEnrACMkULNAUANoUDWBEJXrENFkkWGxhRimgR0ULm5SCKoA4WBwALYZUZAGBZMKEDeqAFJdCOswiPKkWPaHWPjHAPhQDpMtWPcEALGFVTdHAL5jDUuNSM5RAhx/AMFlEh25iQHcCQH5FLUqiQC7ALHDANoFALmPEEndASscgIK1AC7HgTsW7oKIWLurjo+MhWTZAVOMDrT/AU7z4IdOAMC3CQwLAA9JTvC9kWwREh07AMETlEC9DhHYENK2AICiALOdAJwsAKdiCLtiUByFAT5F7oeuALOSCP6K7oafUETPEXgjAGgkALVuCPRwEAv4gDoJABimQJwhEhxv81RBSpSM6wAnbQBPhwD50wBlwQVXYAALBQCFagDYUgC47pCQDQCT2vAGMgDPgAVvdgVjqw8eq+Vp2RWTYgCCsQlHQV72ugB7BABhsOUckwhRsRqaEuHHAREgdQF1pgASsQCwUKC4wAGmkwAJ6QBkv/BI3ABhAADpHxkutoHutYAj9ZCL7w8Vh/l6DRBUEgAT5RCJ5QUisgBjqQAXbuDJHAACovCIzQB6Cg9sCAhOXQU9OAmPhQ8QqgBWngBrOhioIQi3ZABp2ABtoAAImRlo5xHlrQBuSxCrLQCDbJFFn/F6LxkXWwAp2QA2jACMTfB36gCqHOAKAgBmnAF2IgBvf/AABqP1i/YQ66wAqKoADcsQcr4AY57x90kAYrcPeXFQRbfw90IAtagAyguZa+f5rzCRDeJORbAcCTjQFpfLip1cTCwyZu8HVqVALcvUb6/MRqosBGnTSwGjVJA0BduXIHKBz69wzlS5gL3MGEqSuWtwxB6pARsGKABS5NhNngMsaoHTtp3HDZtMKGLEFjSlg4E+SnDS1tHkqAYMZbkjh5zLTJIEuLmxIOIdYB2sTsGVmwgpRQtGJMnTOsliLDdzLlypY0YarzS5OGLEVx2tCRpSBfEHAQhVmwEWTTGQkKPH4k47HRIzeUWW2irAXC1iBewbb52iaIN0wKZEEYIywi/xdksSbLehSrxBhFY850CbKijWtZllCqZOlSMMpn7szR5MdgU5wUefwI45KvCTiirCbnJX1GUWcbaRUpOANghQVkVkuPQa1acZIkkuJ8xSRAwplVFAgiDsbGaAwCWSRgyo82zJAgDraY8ou5wJ4rJ4AADJOFDTJSwEIWCPERIIMjjoAgAwUUOWOMy87Y5Ags5mJFghLSaIIMBhBUQBhwFMHnDAskSC2F1fDTD7/+zEhilTjMSOGMOB4RAAIyNuniiDb2SyIFBbqoow5WJgTMueficWmbcn7RRYAt9mjjiDziyMAJb8IQwIk//hBgGC/yyICVM1wU5Y8UyHjvjDpkAf+TxCG2YEKUPUSRJB8IvioyPy0VEcCrFPY7Ax994jgijDhkScHDKQU4QoAwnHACAjGbewlNc7axtQNgLLFVFzKwEIUTV45YhJ4jnEihPyzyFACQLbw4woQ4zBMFz1Uy2MSGMxTYY8VHFnF0CHmY2AKQUVyZUgFJvDEDgibHIqMNAUakRxQ/UEzh2UqxcIUML7bYQgBMCIVAub9kRUmdbTjgwFZgdpmEklEyAGQGMPw4wosUJDkiBW+cAJjQPZs9ghcwjggCgjyxEIATfLiIQ55oFchgByYWYeMUJhqguIEdOJEnEJ05ASMQejg5BWc24mBgBldEEYWJIQRgA4wrWHX/wotg44Bgj1grLDMAfkaZYQ8BZhCAnjzymIGMSGcwIQNR8ug0D5Fn2AGVtY21EwxONgliGGKDyIAMJgC5+WiKwehZDlMakGcGnulx5RRHM3jEhB32YMMaQPbghOchRBnGFU5GAQMVVHjpmkzBApiGDDmuyIANQOjxvIHUOdlhBzBMuMIUKjJYBOMjqGgAahJEScFjoDkEYwswhBeFDHqGOIXmGQKhmZMhdmiAF4p3CEQAcEfRhxM5qDABkH2KKGKGnE3YwxRThDBB+x1mWN3CZfbw4wpO7GEPJhgCKuTBi93tQ2i88x39TKCMGTiLZN9DQRaOsAoBXMF7ewAEE6xB/7otHCED8MPZDK7QgAagb3fgM8Xa9oAKVzxiDzOYgRASMYorCEEZnOAENYjgu9+ZAAyA4MUeCEYh1qHkFwegAgpM4AdXyOFzTBiGKLIHhhlwggkMDET9TPCDUBRhD937Hg9C8YN4KY4JrtjDKbwwgzLswxoC8AMPpzeDIQCCdLwI4B5ySAT1EUAJeyiCElBAgh8oQQgkSEQozmgCVFwBBRkoQjWAt79Z+cEPVBDCKPzQADmYgABUIEIVqFBIcRTBBChAHyd+ZwoTGCEUQuBBBhS3DxQQQRxG2AMYUMiJLJjgUUU4wRFOMUBO6NCRoeBBEapQhR0KQQhUIAQhqUEFZf/wABE8qAcxs4ACJSiBCHvggRGIwYNwKoEKmEwJCXjACSqMwgQkqIc0eVANRZ5SmkUwYxWIQIBkNuCLoagCCk7AAzAswoyhUAJAt2iCFkSAhtQwZRRVyQkTMJSZRQiFOLJJhUTsgQSkrAIJlBGKbZIgAkA4AQqq8IMEJKAFMzWBEkxBBBKwUxmJIIAfUEANE4zCfTwY5Q/qMYpEKFKVuiRCOVFQDU6AsaAnuAEVRIECR1YjGiHgBCpiiYgfZIAaSihoMpUgPx78oApp/QEVeMADZaCAByaYqkxbkAUSZAEIQFAGCU4AAiPI1JF7SMAJWMrORNQjESaoBxH6CsYfEsH/kcr4gRFQQE6GEiERIABCC/bwA3GIgwd6BcJiO0qEBMhgBDT8QQuIkYhGKuEHJEhmJ5VRhUTogwF7CCkBqIGIFpAgATdYQgJgqtosALcMCRDBDSJgRhRkYrg3uMEJ2MkDaiTCuD+QK3B/wFsqhIKyLQArCbBahQQY4QZAyEQi1MoDwwIhC34ALWpBIIJJShYR0ShDNKpQhCxEIBE6NEI0qMED1xIjrj+IBgnuQF0gkCATSxBBerMwgktQFQgRIMAIiCvTzuZ0OWN6iR+iQYAynIC7ichCNhNxA2IAIQGJQAQxfpAJEYAgESRowV4TAIITKEMZGr7wCxL5YwrfAYzM/4zAJXJ5giXcYMYtgHFMs3CCMtyBwjAYbhZeUAriyrgMMGBBCEYg3xe8YAlrTkAmoHwJdmaiDGVgwCMIcec76+POj/BDnv3AAH3wmc5leCsB7hCBE/ghvXd9AQwyQYRo3FcEpeAxMVBwCRYImLSTlikxohEBEYjgyqEGwR0aLYNSgOAGl3hECGDQijmTAApl8MMdCKCPQGvkEexcr5t/DGQjkIAAjygDCRos3GjwNxPLVql0CZCALBghE9HIAk8JsGz+nuAEEbjDCDKB18JmIQF+1fYdTuBm4QY4AXe48onbnAg/GFvHnz7BHpabBbxKNwEE0HYCysDO5i6XwhEQ+P8SbO2HYoc7E3dw8wn8Om2/qvoOyx3BuiMAAm4DNgspPjeKM/GCiafZ3wl4wQgMHYEIxJS6Ao7AlZ8N7URsm9spRvTDHa7tE9zhiCRGyY8vMQIKg5y4NyhDBFggAj/w++cSvvgd2gyCH0dgBFmOgHOhDIJMvDzrhy51Ji5+ggSgPAKlCDAISkHyEdh6qyC/Lwug/XNDG4EFFR9BKeoOgxG8oAw/Tzs7wzH3E1wiBFPwsNkfDIJcXCACDChD2kcAAhCU4QU3EMEdStHoEYAaBHonubjbnom2Y1gGMvg55Dcv6RcYPdMhGL3JL9+KO5CZBaXIxgtaEYJLLKEVUNAyDF7/AIVLXKIVpQD4pKEgAxa0AsMjCEcuLhEFY4SAAOGAwSMIEAEZ6H0JeC+DpEtRBtZLncJmv0SaCfCCS3B5BMiHQe7XPAIYwEAG2chGLnIx61YsYfPIZ0EU6h6CRmMBGZg1EGABGCCAENC9MWuFKPADdsoFGQiBEPg7GCiDKWCBcCgDTVADNdCE+NOACSCAGDCzUpBAERiBvCO8VhDAF4iBF4C8F5CBv4NADLQ7yGuFXJA/35M/GYiCC2SBnwuHcAABTciFF/iEbEC+cPg9CLy9VtCAKXiBELiAKYCCEIgBbCgHNCkYr/k7MwuHT5iFGGSBKYgBSMCDKJiFT7iACYgB/32YBl2IAitMPgIgs3CAAigowFZ4gXBQLQLIhfx7wb9DPyGEAdYTwkNcwhWcu/qLglyIAjUQwhj8hFwohQu8QyhQAzzQACiAhAu4gEeIBlrxu7mLgQv4ggvIhSUIAQ2AQm74AFuAggkYhxqgAZSYhkfAQdWKggkMgU/wRP8Twh6EBDUoQ03wRSgIwPb7u3AYgVZohU+AgmzQgAvghlzgwCmARBlohRi4RjwAxE+8gCmEwln4xBpghnKYjnJgJw3oAW44xS+YAE3ghh7oB01whHqMAQ0Yh0c4BpjoBgsEATM0hjL8BE2cAkfghikYRg6MgjPcRDacgGqcAIrkhgmAhP8voMYvQEVvhAEoeMd+4IYznIIa0IAvqABNmIUKgIRUmIVUiIFXoIR0eImdM5hy2Mhc0ICVhIJZ6IcKmIAa6IEeeAAMkIIY6AbB6IAYoERHmIJvdIQLUINP4IYKqAANMMVwQMMp4MDEq8oJ0MmTBMGqpMYKQEUJTAUM4IZ+6Ad/0AAY4AYEeIBffIBxuAANwIAH8ABdKAdVAIZJMId2KIea9BpIsMoYwAAE+ACLJMoHeAADQAAXyIBXeAVgOARgWABgAIZXIIdsiAGJ1IBc+IQKuABH3MgJoEd3HEEZ+EZ4lMiqtMqybAZqvIAHqIFU2IAN+IBUWEtbqAFb8IcNeAD/RzCADbCFWUAAA/CAA7CEZegACsCVzBxMMvkABBiHB8DND6iBcUAABHiDB/gAFyCFc7AQdkiTMqiBKTCGGuAGY0DF9YxHtfTJVPgAA3iAGPBNu7wASFhDTXiAVKDFBwBODNjOxOQGW8CADxiHD/CHD5ACW9gAA3ABDIjQYiiH8aQE1tlCJHoJ3LSF7yzKVODOAqgBo0RKC3kJddgFUigAW7gAvNzPB0DOB9CEteyH+cRNx+ROAxiHx0QAxESADZhQf/CHxgROA6gB6qzOHphQBcUADEiFGvCASICJAAAGmNBQwDiElxgHKK2Bx9zRCTWASjiAE6WJW1gAXIiB3nzM/wfIhhjdAH+ogQLogQqYTyBNhR41gB+tziQdB1vgTlvgBgwogEHlTgSQggJ4TAd4Az11gUqYhnR8iQBYAJhQRwrRUpRQAT3lUQx4gxrAABfwgyQq0wCwh3XYhRqozQ8I0hrATgXV06AEznH4UT01VAXlTiE1gDfoBQNQgQEVUUalT2lwUiTwgAqlCWew0lkZMZbA1HJwhAJwASQogALwgH4czzIVjL5UjkPQB0KlT2o1AH/gUepEVELlUSD9gD390QZ9gwkN116dVQdQASlQVweogV6I1mOliUkdDGb9B2dFCUrQ0nOghG0wB3XMVpjggAVQR3J4BCcd1E2dzw/4AP9CVQGLndYCkAI/MNc3KIB5dQAH4AMVcIAC0NROJVkVeAMkGNk3kAJpINPnUAXW6ZoMsZAFcAaFfQ4OAIaExYVHgFVNjdACqNiLVQGQJVk+kAI+4IOibFp6LQCSNdmi7AUkwACkdYGmRQJpeNQTndSEtdkTjYeA3VmU6NmELQdc+FQkqFcDQAI+uNqLNYCkVYGlbVoH6AWVlYJ5LVkXENm89Vu9LQAkqIQMQIevVdaD+debfY4FKFuzRVua6AAPaFkpMAC+5QMH8AAHMACL7Vs+6IWRDV2ozVwkcAHRzdtpRYJekFau1QVstZB+XVYuLAzBuEyz5dcOSFuU0IVKcNn/N2ja0EUC4n0D0GVapz1Zu3UBaWBd1BXZXmheq21eadCFSfjL50CTKrWVdcRSltjCSA0Ad3gGzFwGzHSHbXiGAFDf9T0Ed1jf6LDMZ7AHfsDMBVgA8u0AS9AFaRhZ1G3aXkjd05XWXnhZ1n0D1yXeAH7e1kXdAZaGR7jfzNwGd7Dfnr3fDmCG+23cZaCQfzjY3A1hER5hEjbbZcgAGlgGdfgHFk7fDtgFyC1hGZ7hGQYGGsgABsiAaaCAZ9gGFm5hdQCGZSgGGpiGSDiAIz4AJV5iJm5iJ35iKI5iKZ5iKm7iSIiEaaCBYqAAYAgAH/7hH0ZYwsAQDDkEMj5jNE5jETVeYzZuYzd+YzdGmIMF44AAADs=\"}]}"},{"id":882,"title":"Solve Rubik's Cube - One Rotation","description":"A standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face/Vector numbering.\r\n\r\nThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\r\n\r\nMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice.  The loaded function r_new=rubick_rot(mov,r) implements moves 1-18: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2.\r\n\r\n\r\n\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/cube_small.gif\u003e\u003e\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/Cube_Map28_200.png\u003e\u003e\r\n\r\n\u003c\u003chttp://mathworks.com/matlabcentral/images/surf.gif\u003e\u003e\r\n\r\n\r\n  \r\n  \r\n  Input: (rubik)\r\n  \r\n  rubik: row vector of size 54\r\n  (The cube started [L=0,U=1,F=2,D=3,B=4,R=5] and then receives one face move.\r\n\r\n  Output: mov (A single value that solves the cube, 1:18)\r\n   mov: is an integer 1:18 representing the moves in order: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2\r\n\r\nThe function rubik_rot(mov,r) is available for usage\r\n\r\nAdditional Challenges will be solving the cube at even deeper depths for time and minimizing face moves utilized.\r\n\r\n* This easiest Rubik's Cube challenge is solely to whet everyone's appetite.\r\n* \r\n* The superflip will have to wait for a later challenge.\r\n* \u003chttp://kociemba.org/cube.htm Cube Theory: 20-moves Any Cube\u003e \r\n \r\nNote: Images inserted/linked to my free google web page. Used a gif and a png.","description_html":"\u003cp\u003eA standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face/Vector numbering.\u003c/p\u003e\u003cp\u003eThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\u003c/p\u003e\u003cp\u003eMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice.  The loaded function r_new=rubick_rot(mov,r) implements moves 1-18: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2.\u003c/p\u003e\u003cimg src=\"https://sites.google.com/site/razapor/matlab_cody/cube_small.gif\"\u003e\u003cimg src=\"https://sites.google.com/site/razapor/matlab_cody/Cube_Map28_200.png\"\u003e\u003cimg src=\"http://mathworks.com/matlabcentral/images/surf.gif\"\u003e\u003cpre class=\"language-matlab\"\u003eInput: (rubik)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003erubik: row vector of size 54\r\n(The cube started [L=0,U=1,F=2,D=3,B=4,R=5] and then receives one face move.\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eOutput: mov (A single value that solves the cube, 1:18)\r\n mov: is an integer 1:18 representing the moves in order: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2\r\n\u003c/pre\u003e\u003cp\u003eThe function rubik_rot(mov,r) is available for usage\u003c/p\u003e\u003cp\u003eAdditional Challenges will be solving the cube at even deeper depths for time and minimizing face moves utilized.\u003c/p\u003e\u003cul\u003e\u003cli\u003eThis easiest Rubik's Cube challenge is solely to whet everyone's appetite.\u003c/li\u003e\u003cli\u003e\u003c/li\u003e\u003cli\u003eThe superflip will have to wait for a later challenge.\u003c/li\u003e\u003cli\u003e\u003ca href=\"http://kociemba.org/cube.htm\"\u003eCube Theory: 20-moves Any Cube\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eNote: Images inserted/linked to my free google web page. Used a gif and a png.\u003c/p\u003e","function_template":"function mov = rubik_solve(r)\r\n% Single Rubik's Cube Move Solving Challenge\r\n% Available function to check/determine solution : rubik_rot(mov,r)\r\n% out=rubik_rot(mov,r) returns a moved cube array of size 54\r\n% Solved Cube vector\r\n%[000000000111111111222222222333333333444444444555555555]; % with spaces\r\n\r\n  mov=1; % mov is a single value 1-18 for this Challenge\r\nend","test_suite":"%%\r\n% Load function rubik_rot.m\r\ntic\r\n%https://sites.google.com/site/razapor/matlab_cody/rubik_rot.m?attredirects=0\u0026d=1\r\n%urlwrite('http://tinyurl.com/matlab-rubik-rot','rubik_rot.m') ;\r\nurlwrite('https://sites.google.com/site/razapor/matlab_cody/rubik_rot.m','rubik_rot.m') ;\r\nrehash path\r\ntoc\r\n%%\r\n% For mov=1 solution is 7. Need U' to solve U in 1 move\r\nmov_map=[7:12 1:6 13:18]; % Complementary Move\r\n\r\nmov=1; % U\r\nmov_exp1=mov_map(mov);\r\n\r\n% Solved Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\ntic\r\nr=rubik_rot(mov,r); % Create Challenge Cube\r\ntoc\r\nmov=0;\r\nassert(isequal(rubik_solve(r),mov_exp1))\r\ntoc\r\n%%\r\n% For mov=8 solution is 2. Need F to solve F' in 1 move\r\nmov_map=[7:12 1:6 13:18]; % Complementary Move\r\n\r\nmov=8; % F'\r\nmov_exp2=mov_map(mov);\r\n\r\n% Solved Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\n\r\nr=rubik_rot(mov,r); % Create Challenge Cube\r\nmov=0;\r\nassert(isequal(rubik_solve(r),mov_exp2))\r\n%%\r\n% For mov=15 solution is 15. Need D2 to solve D2 in 1 move\r\nmov_map=[7:12 1:6 13:18]; % Complementary Move\r\n\r\nmov=15; % D2\r\nmov_ex3p=mov_map(mov);\r\n\r\n% Solved Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\n\r\nr=rubik_rot(mov,r); % Create Challenge Cube\r\nmov=0;\r\nassert(isequal(rubik_solve(r),mov_ex3p))\r\n%%\r\n% Anti-Hard code solution Test Case #1\r\nmov_map=[7:12 1:6 13:18]; % Complementary Move\r\n\r\nmov=randi(18); % anti-hard code \r\nAmov_exp=mov_map(mov);\r\n\r\n% Solved Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\n\r\nr=rubik_rot(mov,r); % Create Challenge Cube\r\nAmov=mov;\r\nmov=0;\r\nassert(isequal(rubik_solve(r),Amov_exp),sprintf('mov=%i mov_exp=%i Provided answer=%i\\n',Amov,Amov_exp,rubik_solve(r)))\r\n%%\r\n% Anti-Hard code solution Test Case #2\r\nmov_map=[7:12 1:6 13:18]; % Complementary Move\r\n\r\nmov=randi(18); % anti-hard code \r\nmovB_exp=mov_map(mov);\r\n\r\n% Solved Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\n\r\nr=rubik_rot(mov,r); % Create Challenge Cube\r\nmovB=mov;\r\nmov=0;\r\nassert(isequal(rubik_solve(r),movB_exp),sprintf('mov=%i mov_exp=%i Provided answer=%i\\n',movB,movB_exp,rubik_solve(r)))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2017-10-16T02:14:45.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-08-05T20:46:31.000Z","updated_at":"2026-03-30T18:55:45.000Z","published_at":"2012-08-05T22:50:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.gif\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/media/image1.png\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId3\",\"target\":\"/media/image2.gif\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face/Vector numbering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice. The loaded function r_new=rubick_rot(mov,r) implements moves 1-18: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Input: (rubik)\\n\\nrubik: row vector of size 54\\n(The cube started [L=0,U=1,F=2,D=3,B=4,R=5] and then receives one face move.\\n\\nOutput: mov (A single value that solves the cube, 1:18)\\n mov: is an integer 1:18 representing the moves in order: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function rubik_rot(mov,r) is available for usage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAdditional Challenges will be solving the cube at even deeper depths for time and minimizing face moves utilized.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis easiest Rubik's Cube challenge is solely to whet everyone's appetite.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe superflip will have to wait for a later challenge.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://kociemba.org/cube.htm\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCube Theory: 20-moves Any Cube\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: Images inserted/linked to my free google web page. 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\"},{\"partUri\":\"/media/image2.gif\",\"contentType\":\"image/gif\",\"content\":\"data:image/gif;base64,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\"}]}"},{"id":1123,"title":"Rubik's Cube: 30 Moves or Less : Minimum Moves","description":"This Challenge is to solve a thoroughly scrambled Rubik's cube in the least moves (30 moves max).\r\n\r\nRubik's Cube can be solved in 20 moves or less from any position.  The \u003chttp://kociemba.org/cube.htm Kociemba Two Phase algorithm\u003e can solve the Cube in 30 moves or less.  The basic theory is that any cube can transition to an H-cube by 12 moves using all possible 18 move types.  An H-cube is defined as having no rotations or flips of corners or edges, respectively, and has all middle edges in the middle row. The cube can be solved from any H-cube state in 18 moves or less using only the moves U U' U2 D D' D2 F2 L2 R2 B2. \u003chttp://kociemba.org/math/CubeDefs.htm#faceturns Definitions of Moves / Rotates / Flips for Corners and Edges\u003e. The Two-Phase algorithm typically solves in 24 moves or less.\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/cube_small.gif\u003e\u003e\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/Cube_Map48_200.png\u003e\u003e\r\n\r\nRubik's Cube has 48 faces that are assigned to a vector as in the above figure.\r\nU refers to the White face, F-Blue, L-Red, R-Orange, D-Yellow, and B-Green. Moves (1-6 UFDLBR 7-12 U'F'D'L'B'R' 13-18 U2F2D2L2B2R2) are clockwise looking towards the center, primes are CCW (eq U'), and twos are a half turn of a face.\r\n\r\n  The color to numeric coding is [RWBYGO] [012345]. \r\n  A solved cube is [0000 0000 1111 1111 2222 2222 3333 3333 4444 4444 5555 5555]\r\n\r\n*Input:* Cube\r\n\r\nCube is a 48 long row vector of values 0 thru 5.\r\n  \r\n*Output:* Move_Vector\r\n\r\nMove_Vector is an empty to 30 element vector of values 1:18\r\n\r\n*Constraint:* Solution must be 30 moves or less\r\n\r\n*Scoring:* Minimum number of moves \r\n\r\n\u003chttp://cube20.org/src/ Two Phase Source code\u003e is fairly complex and may require a 500MB database file. Its goal is to find solutions of 20 or less starting with Two Phase.\r\n\r\n\u003chttps://sites.google.com/site/razapor/matlab_cody/Cube30rev001.ppt?attredirects=0\u0026d=1 30 move Cube Solution in Matlab (rought draft)\u003e","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 936.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 468.35px; transform-origin: 407px 468.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 308.633px 7.91667px; transform-origin: 308.633px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis Challenge is to solve a thoroughly scrambled Rubik's cube in the least moves (30 moves max).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 219.95px 7.91667px; transform-origin: 219.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRubik's Cube can be solved in 20 moves or less from any position. The\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://kociemba.org/cube.htm\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eKociemba Two Phase algorithm\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.7px 7.91667px; transform-origin: 63.7px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can solve the Cube in 30 moves or less. The basic theory is that any cube can transition to an H-cube by 12 moves using all possible 18 move types. An H-cube is defined as having no rotations or flips of corners or edges, respectively, and has all middle edges in the middle row. The cube can be solved from any H-cube state in 18 moves or less using only the moves U U' U2 D D' D2 F2 L2 R2 B2.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://kociemba.org/math/CubeDefs.htm#faceturns\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eDefinitions of Moves / Rotates / Flips for Corners and Edges\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 151.317px 7.91667px; transform-origin: 151.317px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The Two-Phase algorithm typically solves in 24 moves or less.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 134.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 67.4667px; text-align: center; transform-origin: 384px 67.4667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.667px 7.91667px; transform-origin: 376.667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRubik's Cube has 48 faces that are assigned to a vector as in the above figure. U refers to the White face, F-Blue, L-Red, R-Orange, D-Yellow, and B-Green. Moves (1-6 UFDLBR 7-12 U'F'D'L'B'R' 13-18 U2F2D2L2B2R2) are clockwise looking towards the center, primes are CCW (eq U'), and twos are a half turn of a face.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 192.5px 7.91667px; transform-origin: 192.5px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; \"\u003eThe \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 177.1px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 177.1px 7.91667px; \"\u003ecolor to numeric coding is [RWBYGO] [012345]. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 300.3px 7.91667px; transform-origin: 300.3px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; \"\u003eA \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 292.6px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 292.6px 7.91667px; \"\u003esolved cube is [0000 0000 1111 1111 2222 2222 3333 3333 4444 4444 5555 5555]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4333px 7.91667px; transform-origin: 19.4333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.6833px 7.91667px; transform-origin: 18.6833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Cube\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 146.25px 7.91667px; transform-origin: 146.25px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCube is a 48 long row vector of values 0 thru 5.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.2667px 7.91667px; transform-origin: 25.2667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.8px 7.91667px; transform-origin: 42.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Move_Vector\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 189.433px 7.91667px; transform-origin: 189.433px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMove_Vector is an empty to 30 element vector of values 1:18\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.3333px 7.91667px; transform-origin: 37.3333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConstraint:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108.917px 7.91667px; transform-origin: 108.917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Solution must be 30 moves or less\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3833px 7.91667px; transform-origin: 28.3833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eScoring:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.35px 7.91667px; transform-origin: 86.35px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Minimum number of moves\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"http://cube20.org/src/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eTwo Phase Source code\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 301.833px 7.91667px; transform-origin: 301.833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is fairly complex and may require a 500MB database file. Its goal is to find solutions of 20 or less starting with Two Phase.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://sites.google.com/site/razapor/matlab_cody/Cube30rev001.ppt?attredirects=0\u0026amp;d=1\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e30 move Cube Solution in Matlab (rought draft)\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [v]=Rubik_Solver(cube)\r\n% moves 1-6 UFDLBR 7-12 U'F;D'L'B'R' 13-18 U2F2D2L2B2R2\r\n% Return v as a numeric row vector of k values in range 1:18\r\n  v=[];\r\nend","test_suite":"%%\r\nfeval(@assignin,'caller','score',30);\r\n%%\r\nvf=[ 17 2 3 20 5 22 7 8 11 13 16 10 15 9 12 14 41 18 19 44 21 46 23 24 25 26 27 28 29 30 31 32 33 34 6 36 4 38 39 1 40 42 43 37 45 35 47 48; \r\n  1 2 3 4 5 25 28 30 9 10 8 12 7 14 15 6 19 21 24 18 23 17 20 22 43 26 27 42 29 41 31 32 33 34 35 36 37 38 39 40 11 13 16 44 45 46 47 48 ;\r\n  1 2 38 4 36 6 7 33 9 10 11 12 13 14 15 16 17 18 3 20 5 22 23 8 27 29 32 26 31 25 28 30 48 34 35 45 37 43 39 40 41 42 19 44 21 46 47 24 ;\r\n  3 5 8 2 7 1 4 6 33 34 35 12 13 14 15 16 9 10 11 20 21 22 23 24 17 18 19 28 29 30 31 32 25 26 27 36 37 38 39 40 41 42 43 44 45 46 47 48 ;\r\n  14 12 9 4 5 6 7 8 46 10 11 47 13 48 15 16 17 18 19 20 21 22 23 24 25 26 1 28 2 30 31 3 35 37 40 34 39 33 36 38 41 42 43 44 45 32 29 27 ;\r\n  1 2 3 4 5 6 7 8 9 10 11 12 13 22 23 24 17 18 19 20 21 30 31 32 25 26 27 28 29 38 39 40 33 34 35 36 37 14 15 16 43 45 48 42 47 41 44 46 ;\r\n  40 2 3 37 5 35 7 8 14 12 9 15 10 16 13 11 1 18 19 4 21 6 23 24 25 26 27 28 29 30 31 32 33 34 46 36 44 38 39 41 17 42 43 20 45 22 47 48 ;\r\n  1 2 3 4 5 16 13 11 9 10 41 12 42 14 15 43 22 20 17 23 18 24 21 19 6 26 27 7 29 8 31 32 33 34 35 36 37 38 39 40 30 28 25 44 45 46 47 48 ;\r\n  1 2 19 4 21 6 7 24 9 10 11 12 13 14 15 16 17 18 43 20 45 22 23 48 30 28 25 31 26 32 29 27 8 34 35 5 37 3 39 40 41 42 38 44 36 46 47 33 ;\r\n  6 4 1 7 2 8 5 3 17 18 19 12 13 14 15 16 25 26 27 20 21 22 23 24 33 34 35 28 29 30 31 32 9 10 11 36 37 38 39 40 41 42 43 44 45 46 47 48 ;\r\n  27 29 32 4 5 6 7 8 3 10 11 2 13 1 15 16 17 18 19 20 21 22 23 24 25 26 48 28 47 30 31 46 38 36 33 39 34 40 37 35 41 42 43 44 45 9 12 14 ;\r\n  1 2 3 4 5 6 7 8 9 10 11 12 13 38 39 40 17 18 19 20 21 14 15 16 25 26 27 28 29 22 23 24 33 34 35 36 37 30 31 32 46 44 41 47 42 48 45 43 ;\r\n  41 2 3 44 5 46 7 8 16 15 14 13 12 11 10 9 40 18 19 37 21 35 23 24 25 26 27 28 29 30 31 32 33 34 22 36 20 38 39 17 1 42 43 4 45 6 47 48 ;\r\n  1 2 3 4 5 43 42 41 9 10 30 12 28 14 15 25 24 23 22 21 20 19 18 17 16 26 27 13 29 11 31 32 33 34 35 36 37 38 39 40 8 7 6 44 45 46 47 48 ;\r\n  1 2 43 4 45 6 7 48 9 10 11 12 13 14 15 16 17 18 38 20 36 22 23 33 32 31 30 29 28 27 26 25 24 34 35 21 37 19 39 40 41 42 3 44 5 46 47 8 ;\r\n  8 7 6 5 4 3 2 1 25 26 27 12 13 14 15 16 33 34 35 20 21 22 23 24 9 10 11 28 29 30 31 32 17 18 19 36 37 38 39 40 41 42 43 44 45 46 47 48 ;\r\n  48 47 46 4 5 6 7 8 32 10 11 29 13 27 15 16 17 18 19 20 21 22 23 24 25 26 14 28 12 30 31 9 40 39 38 37 36 35 34 33 41 42 43 44 45 3 2 1 ; \r\n  1 2 3 4 5 6 7 8 9 10 11 12 13 30 31 32 17 18 19 20 21 38 39 40 25 26 27 28 29 14 15 16 33 34 35 36 37 22 23 24 48 47 46 45 44 43 42 41 ];\r\n\r\n cube_orig=[zeros(1,8) ones(1,8) ones(1,8)*2 ones(1,8)*3 ones(1,8)*4 ones(1,8)*5]; \r\n tsum=0;\r\n Lbest=30;\r\n for cube_sets=1:4\r\n  if cube_sets==2,tsum=0;end\r\n encode=randi(18,1,80);\r\n fprintf('Encode: ');fprintf('%i ',encode);fprintf('\\n')\r\n r=cube_orig;\r\n for i= encode\r\n  r=r(vf(i,:));\r\n end\r\n encode=[]; % anti-shortcut\r\n encode_str='';\r\n cube=r;\r\n fprintf('%i',r);fprintf('\\n')\r\n\r\n% Time function\r\n ta=clock;\r\n [v]=Rubik_Solver(cube);\r\n t1=etime(clock,ta)*1000; % time in msec\r\n tsum=tsum+t1;\r\n Lv=length(v);\r\n assert(Lv\u003c=30)\r\n \r\n fprintf('Time: %.0f msec  Total Time %.0f\\n',t1,tsum)\r\n \r\n fprintf('Solution length %i\\n',length(v))\r\n fprintf('%i ',v);fprintf('\\n')\r\n \r\n r=cube;\r\n for i=v\r\n  r=r(vf(i,:));\r\n end\r\n \r\n fprintf('Solved Cube\\n');fprintf('%i',r);fprintf('\\n')\r\n\r\n tf=isequal(r,cube_orig);\r\n fprintf('Solved %i Moves %i \\n\\n\\n\\n',tf, Lv)\r\n assert(tf)\r\n assert(~isequal(1,2))\r\n if Lv\u003cLbest,Lbest=Lv;end\r\n \r\n end % cubesets\r\n\r\n %msiz=mtree('Rubik_Solver.m','-file').count\r\n\r\nfeval(  @assignin,'caller','score',min( 30,Lv )  );","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-12-17T02:11:05.000Z","updated_at":"2025-12-20T07:40:07.000Z","published_at":"2012-12-25T05:15:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to solve a thoroughly scrambled Rubik's cube in the least moves (30 moves max).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRubik's Cube can be solved in 20 moves or less from any position. The\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://kociemba.org/cube.htm\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKociemba Two Phase algorithm\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e can solve the Cube in 30 moves or less. The basic theory is that any cube can transition to an H-cube by 12 moves using all possible 18 move types. An H-cube is defined as having no rotations or flips of corners or edges, respectively, and has all middle edges in the middle row. The cube can be solved from any H-cube state in 18 moves or less using only the moves U U' U2 D D' D2 F2 L2 R2 B2.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://kociemba.org/math/CubeDefs.htm#faceturns\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eDefinitions of Moves / Rotates / Flips for Corners and Edges\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The Two-Phase algorithm typically solves in 24 moves or less.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRubik's Cube has 48 faces that are assigned to a vector as in the above figure. U refers to the White face, F-Blue, L-Red, R-Orange, D-Yellow, and B-Green. Moves (1-6 UFDLBR 7-12 U'F'D'L'B'R' 13-18 U2F2D2L2B2R2) are clockwise looking towards the center, primes are CCW (eq U'), and twos are a half turn of a face.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[The color to numeric coding is [RWBYGO] [012345]. \\nA solved cube is [0000 0000 1111 1111 2222 2222 3333 3333 4444 4444 5555 5555]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Cube\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCube is a 48 long row vector of values 0 thru 5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Move_Vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMove_Vector is an empty to 30 element vector of values 1:18\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConstraint:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Solution must be 30 moves or less\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Minimum number of moves\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://cube20.org/src/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTwo Phase Source code\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is fairly complex and may require a 500MB database file. Its goal is to find solutions of 20 or less starting with Two Phase.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/Cube30rev001.ppt?attredirects=0\u0026amp;d=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e30 move Cube Solution in Matlab (rought 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1137,"title":"Rubik's Cube: 30 Moves or Less : Cody Size","description":"This Challenge is to solve a thoroughly scrambled Rubik's cube with smallest code (30 moves max).\r\n\r\nRubik's Cube can be solved in 20 moves or less from any position.  The \u003chttp://kociemba.org/cube.htm Kociemba Two Phase algorithm\u003e can solve the Cube in 30 moves or less.  The basic theory is that any cube can transition to an H-cube by 12 moves using all possible 18 move types.  An H-cube is defined as having no rotations or flips of corners or edges, respectively, and has all middle edges in the middle row. The cube can be solved from any H-cube state in 18 moves or less using only the moves U U' U2 D D' D2 F2 L2 R2 B2. \u003chttp://kociemba.org/math/CubeDefs.htm#faceturns Definitions of Moves / Rotates / Flips for Corners and Edges\u003e. The Two-Phase algorithm typically solves in 24 moves or less.\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/cube_small.gif\u003e\u003e\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/Cube_Map48_200.png\u003e\u003e\r\n\r\nRubik's Cube has 48 faces that are assigned to a vector as in the above figure.\r\nU refers to the White face, F-Blue, L-Red, R-Orange, D-Yellow, and B-Green. Moves (1-6 UFDLBR 7-12 U'F'D'L'B'R' 13-18 U2F2D2L2B2R2) are clockwise looking towards the center, primes are CCW (eq U'), and twos are a half turn of a face.\r\n\r\n  The color to numeric coding is [RWBYGO] [012345]. \r\n  A solved cube is [0000 0000 1111 1111 2222 2222 3333 3333 4444 4444 5555 5555]\r\n\r\n*Input:* Cube\r\n\r\nCube is a 48 long row vector of values 0 thru 5.\r\n  \r\n*Output:* Move_Vector\r\n\r\nMove_Vector is an empty to 30 element vector of values 1:18\r\n\r\n*Constraint:* Solution must be 30 moves or less\r\n\r\n*Scoring:* Cody Size \r\n\r\n\u003chttp://cube20.org/src/ Two Phase Source code\u003e is fairly complex and may require a 500MB database file. Its goal is to find solutions of 20 or less starting with Two Phase.\r\n\r\n\u003chttps://sites.google.com/site/razapor/matlab_cody/Cube30rev001.ppt?attredirects=0\u0026d=1 30 move Cube Solution in Matlab (rought draft)\u003e","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 936.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 468.35px; transform-origin: 407px 468.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 309.417px 7.91667px; transform-origin: 309.417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis Challenge is to solve a thoroughly scrambled Rubik's cube with smallest code (30 moves max).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 219.95px 7.91667px; transform-origin: 219.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRubik's Cube can be solved in 20 moves or less from any position. The\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://kociemba.org/cube.htm\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eKociemba Two Phase algorithm\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.7px 7.91667px; transform-origin: 63.7px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can solve the Cube in 30 moves or less. The basic theory is that any cube can transition to an H-cube by 12 moves using all possible 18 move types. An H-cube is defined as having no rotations or flips of corners or edges, respectively, and has all middle edges in the middle row. The cube can be solved from any H-cube state in 18 moves or less using only the moves U U' U2 D D' D2 F2 L2 R2 B2.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://kociemba.org/math/CubeDefs.htm#faceturns\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eDefinitions of Moves / Rotates / Flips for Corners and Edges\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 151.317px 7.91667px; transform-origin: 151.317px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The Two-Phase algorithm typically solves in 24 moves or less.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 134.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 67.4667px; text-align: center; transform-origin: 384px 67.4667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.667px 7.91667px; transform-origin: 376.667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRubik's Cube has 48 faces that are assigned to a vector as in the above figure. U refers to the White face, F-Blue, L-Red, R-Orange, D-Yellow, and B-Green. Moves (1-6 UFDLBR 7-12 U'F'D'L'B'R' 13-18 U2F2D2L2B2R2) are clockwise looking towards the center, primes are CCW (eq U'), and twos are a half turn of a face.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 192.5px 7.91667px; transform-origin: 192.5px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; \"\u003eThe \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 177.1px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 177.1px 7.91667px; \"\u003ecolor to numeric coding is [RWBYGO] [012345]. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 300.3px 7.91667px; transform-origin: 300.3px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; \"\u003eA \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 292.6px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 292.6px 7.91667px; \"\u003esolved cube is [0000 0000 1111 1111 2222 2222 3333 3333 4444 4444 5555 5555]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4333px 7.91667px; transform-origin: 19.4333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.6833px 7.91667px; transform-origin: 18.6833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Cube\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 146.25px 7.91667px; transform-origin: 146.25px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCube is a 48 long row vector of values 0 thru 5.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.2667px 7.91667px; transform-origin: 25.2667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.8px 7.91667px; transform-origin: 42.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Move_Vector\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 189.433px 7.91667px; transform-origin: 189.433px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMove_Vector is an empty to 30 element vector of values 1:18\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.3333px 7.91667px; transform-origin: 37.3333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConstraint:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108.917px 7.91667px; transform-origin: 108.917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Solution must be 30 moves or less\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3833px 7.91667px; transform-origin: 28.3833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eScoring:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.85px 7.91667px; transform-origin: 33.85px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Cody Size\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"http://cube20.org/src/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eTwo Phase Source code\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 301.833px 7.91667px; transform-origin: 301.833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is fairly complex and may require a 500MB database file. Its goal is to find solutions of 20 or less starting with Two Phase.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://sites.google.com/site/razapor/matlab_cody/Cube30rev001.ppt?attredirects=0\u0026amp;d=1\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e30 move Cube Solution in Matlab (rought draft)\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [v]=Rubik_Solver(cube)\r\n% moves 1-6 UFDLBR 7-12 U'F;D'L'B'R' 13-18 U2F2D2L2B2R2\r\n% Return v as a numeric row vector of k values in range 1:18\r\n  v=[];\r\nend","test_suite":"%%\r\nvf=[ 17 2 3 20 5 22 7 8 11 13 16 10 15 9 12 14 41 18 19 44 21 46 23 24 25 26 27 28 29 30 31 32 33 34 6 36 4 38 39 1 40 42 43 37 45 35 47 48; \r\n  1 2 3 4 5 25 28 30 9 10 8 12 7 14 15 6 19 21 24 18 23 17 20 22 43 26 27 42 29 41 31 32 33 34 35 36 37 38 39 40 11 13 16 44 45 46 47 48 ;\r\n  1 2 38 4 36 6 7 33 9 10 11 12 13 14 15 16 17 18 3 20 5 22 23 8 27 29 32 26 31 25 28 30 48 34 35 45 37 43 39 40 41 42 19 44 21 46 47 24 ;\r\n  3 5 8 2 7 1 4 6 33 34 35 12 13 14 15 16 9 10 11 20 21 22 23 24 17 18 19 28 29 30 31 32 25 26 27 36 37 38 39 40 41 42 43 44 45 46 47 48 ;\r\n  14 12 9 4 5 6 7 8 46 10 11 47 13 48 15 16 17 18 19 20 21 22 23 24 25 26 1 28 2 30 31 3 35 37 40 34 39 33 36 38 41 42 43 44 45 32 29 27 ;\r\n  1 2 3 4 5 6 7 8 9 10 11 12 13 22 23 24 17 18 19 20 21 30 31 32 25 26 27 28 29 38 39 40 33 34 35 36 37 14 15 16 43 45 48 42 47 41 44 46 ;\r\n  40 2 3 37 5 35 7 8 14 12 9 15 10 16 13 11 1 18 19 4 21 6 23 24 25 26 27 28 29 30 31 32 33 34 46 36 44 38 39 41 17 42 43 20 45 22 47 48 ;\r\n  1 2 3 4 5 16 13 11 9 10 41 12 42 14 15 43 22 20 17 23 18 24 21 19 6 26 27 7 29 8 31 32 33 34 35 36 37 38 39 40 30 28 25 44 45 46 47 48 ;\r\n  1 2 19 4 21 6 7 24 9 10 11 12 13 14 15 16 17 18 43 20 45 22 23 48 30 28 25 31 26 32 29 27 8 34 35 5 37 3 39 40 41 42 38 44 36 46 47 33 ;\r\n  6 4 1 7 2 8 5 3 17 18 19 12 13 14 15 16 25 26 27 20 21 22 23 24 33 34 35 28 29 30 31 32 9 10 11 36 37 38 39 40 41 42 43 44 45 46 47 48 ;\r\n  27 29 32 4 5 6 7 8 3 10 11 2 13 1 15 16 17 18 19 20 21 22 23 24 25 26 48 28 47 30 31 46 38 36 33 39 34 40 37 35 41 42 43 44 45 9 12 14 ;\r\n  1 2 3 4 5 6 7 8 9 10 11 12 13 38 39 40 17 18 19 20 21 14 15 16 25 26 27 28 29 22 23 24 33 34 35 36 37 30 31 32 46 44 41 47 42 48 45 43 ;\r\n  41 2 3 44 5 46 7 8 16 15 14 13 12 11 10 9 40 18 19 37 21 35 23 24 25 26 27 28 29 30 31 32 33 34 22 36 20 38 39 17 1 42 43 4 45 6 47 48 ;\r\n  1 2 3 4 5 43 42 41 9 10 30 12 28 14 15 25 24 23 22 21 20 19 18 17 16 26 27 13 29 11 31 32 33 34 35 36 37 38 39 40 8 7 6 44 45 46 47 48 ;\r\n  1 2 43 4 45 6 7 48 9 10 11 12 13 14 15 16 17 18 38 20 36 22 23 33 32 31 30 29 28 27 26 25 24 34 35 21 37 19 39 40 41 42 3 44 5 46 47 8 ;\r\n  8 7 6 5 4 3 2 1 25 26 27 12 13 14 15 16 33 34 35 20 21 22 23 24 9 10 11 28 29 30 31 32 17 18 19 36 37 38 39 40 41 42 43 44 45 46 47 48 ;\r\n  48 47 46 4 5 6 7 8 32 10 11 29 13 27 15 16 17 18 19 20 21 22 23 24 25 26 14 28 12 30 31 9 40 39 38 37 36 35 34 33 41 42 43 44 45 3 2 1 ; \r\n  1 2 3 4 5 6 7 8 9 10 11 12 13 30 31 32 17 18 19 20 21 38 39 40 25 26 27 28 29 14 15 16 33 34 35 36 37 22 23 24 48 47 46 45 44 43 42 41 ];\r\n\r\n cube_orig=[zeros(1,8) ones(1,8) ones(1,8)*2 ones(1,8)*3 ones(1,8)*4 ones(1,8)*5]; \r\n tsum=0;\r\n Lbest=30;\r\n for cube_sets=1:1\r\n encode=randi(18,1,80);\r\n fprintf('Encode: ');fprintf('%i ',encode);fprintf('\\n')\r\n r=cube_orig;\r\n for i= encode\r\n  r=r(vf(i,:));\r\n end\r\n encode=[]; % anti-shortcut\r\n encode_str='';\r\n cube=r;\r\n fprintf('%i',r);fprintf('\\n')\r\n\r\n% Time function\r\n ta=clock;\r\n [v]=Rubik_Solver(cube);\r\n t1=etime(clock,ta)*1000; % time in msec\r\n tsum=tsum+t1;\r\n Lv=length(v);\r\n assert(Lv\u003c=30)\r\n \r\n fprintf('Time: %.0f msec  Total Time %.0f\\n',t1,tsum)\r\n \r\n fprintf('Solution length %i\\n',length(v))\r\n fprintf('%i ',v);fprintf('\\n')\r\n \r\n r=cube;\r\n for i=v\r\n  r=r(vf(i,:));\r\n end\r\n \r\n fprintf('Solved Cube\\n');fprintf('%i',r);fprintf('\\n')\r\n\r\n tf=isequal(r,cube_orig);\r\n fprintf('Solved %i Moves %i\\n\\n\\n\\n',tf, Lv)\r\n assert(tf)\r\n assert(~isequal(1,2)) % anti for he who shall not be named\r\n if Lv\u003cLbest,Lbest=Lv;end\r\n \r\n end % cubesets\r\n\r\n%msiz=mtree('Rubik_Solver.m','-file').count","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2020-09-29T17:08:46.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-12-25T01:45:13.000Z","updated_at":"2025-12-15T21:27:03.000Z","published_at":"2012-12-25T05:20:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to solve a thoroughly scrambled Rubik's cube with smallest code (30 moves max).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRubik's Cube can be solved in 20 moves or less from any position. The\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://kociemba.org/cube.htm\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKociemba Two Phase algorithm\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e can solve the Cube in 30 moves or less. The basic theory is that any cube can transition to an H-cube by 12 moves using all possible 18 move types. An H-cube is defined as having no rotations or flips of corners or edges, respectively, and has all middle edges in the middle row. The cube can be solved from any H-cube state in 18 moves or less using only the moves U U' U2 D D' D2 F2 L2 R2 B2.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://kociemba.org/math/CubeDefs.htm#faceturns\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eDefinitions of Moves / Rotates / Flips for Corners and Edges\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The Two-Phase algorithm typically solves in 24 moves or less.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRubik's Cube has 48 faces that are assigned to a vector as in the above figure. U refers to the White face, F-Blue, L-Red, R-Orange, D-Yellow, and B-Green. Moves (1-6 UFDLBR 7-12 U'F'D'L'B'R' 13-18 U2F2D2L2B2R2) are clockwise looking towards the center, primes are CCW (eq U'), and twos are a half turn of a face.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[The color to numeric coding is [RWBYGO] [012345]. \\nA solved cube is [0000 0000 1111 1111 2222 2222 3333 3333 4444 4444 5555 5555]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Cube\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCube is a 48 long row vector of values 0 thru 5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Move_Vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMove_Vector is an empty to 30 element vector of values 1:18\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConstraint:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Solution must be 30 moves or less\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Cody Size\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://cube20.org/src/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTwo Phase Source code\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is fairly complex and may require a 500MB database file. Its goal is to find solutions of 20 or less starting with Two Phase.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/Cube30rev001.ppt?attredirects=0\u0026amp;d=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e30 move Cube Solution in Matlab (rought 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Rubik's Cube - Up to Two Face Moves","description":"A standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face/Vector numbering.\r\n\r\nThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\r\n\r\nMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice.  The loaded function r_new=rubick_rot(mov,r) implements moves 1-18: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2.\r\n\r\n\r\n\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/cube_small.gif\u003e\u003e\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/Cube_Map28_200.png\u003e\u003e\r\n\r\n\u003c\u003chttp://mathworks.com/matlabcentral/images/surf.gif\u003e\u003e\r\n\r\n\r\n  \r\n  \r\n  Input: (rubik)\r\n  \r\n  rubik: row vector of size 54\r\n  (The cube started [L=0,U=1,F=2,D=3,B=4,R=5] and then received one or two face moves.\r\n\r\n  Output: mov (A row vector of one or two of values {1:18})\r\n   mov: is a vector values 1:18 representing the moves in order to fix the cube: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2\r\n\r\n* Example:\r\n* If the cube was randomized by [1 9] UD', the one and only 2 move answer is [3 7] DU' which are the complements in reverse order. \r\n* Minimum moves is also required. Scramble by 13(U2) should return a [13], not [1 1] or [7 7]\r\n* \r\nVerifications will be by executing your move vector against the provided rubik and checking number of moves.\r\n\r\nThe function rubik_rot(mov,r) is available for usage\r\n\r\n\r\nThis is the next incremental solution step: Move optimization.\r\n\r\nAdditional Challenges will be solving the cube at even deeper depths for time and minimizing face moves utilized. This depth does not justify a time check.\r\n\r\n\r\n* \r\n* \u003chttp://kociemba.org/cube.htm Cube Theory: 20-moves Any Cube\u003e ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1062.82px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 447.983px 531.417px; transform-origin: 447.983px 531.417px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 340.283px 7.91667px; transform-origin: 340.283px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face/Vector numbering.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 316.733px 7.91667px; transform-origin: 316.733px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 352.917px 7.91667px; transform-origin: 352.917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice. The loaded function r_new=rubick_rot(mov,r) implements moves 1-18: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 134.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 67.4667px; text-align: center; transform-origin: 384px 67.4667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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ArrgDLogC7IgCLVgAY3gCT4ADYIAlSBIWB3BARmgBZIgAGNglRCAGGjZBGpJHYpgAWPQCGPwliugBV2wYM9hA2yJHpJgWu4BH3EgCUkAl2QQB03ACgrwHKCVGK7ZBmMQBPqQmj6pAGfABWnpBuAQmZZnVMcVAIepAG0gAQIgC1xwBpiwAuaxCbLQGFzAlt//xQZHoAhu4JFBsJKPEAtmUB02QFtjkATsMZv0RR/2gV8CkALeIAH34Q1moAAMsGKyEAdcIAwCIAAS4A1xgpXmJZkdsYXokA7lcAwZkAeLcCUQAAjSlQJ/gAVvkgIwEmXZlQF1YF4pkgJ5kBeKUZUSsAJ7sAg8BgjyQA9YIgt5YAaplQf0IZf08Qf96QS5qWD6sCBOkAH3kQKS4AdsAAjW8CYvsggOyhGvEEjToCyucip5gF2LQAZtQCZkACcxMiNHQGVgkJsp4AWY4CoCkFoNwAmKsAkMYGFKwmNMMANgAAZt+iqxUmQ7wCd0OgP6BAZVsgMXtgeBwARDIABeYA2L/5ArM7BhUboR2MAAJ8YzcuAqgwIrG5YoizJnqNBpgJACYypk+4AtbbBfgYAKvOAHYLAFTOAHizAMZEAG+8BjW3AEicIEnCAHKLZhhXJl8nAFDPAII1INKOAKnCAEVMAGbdpopjBnJgAGPSaZHKALBFAE9WA3c7YH8iAHM2AlJsAJezAKhEJoc0ZodiYEJCAKTGApnABoD3OnO8AJCbAPooICJnAKF/orRTAvJsADGUACKFAPVIACa1YNWWcre6AEVKAM0SAHQkANAksy1fBonIAtSoAsKABwJEAEPGMC9WAs1YBpe3BpDFsPQmAK5OItoZAAPFANn2pnk1Y1QzAEPP9AsQmQADRWaNhGBkUQMHvwro2WAURQBe5CLFVABSTgJzywB/WgbKh2bSQQDUBwA7z2A2eTCS3QAt9SD5wALgCHAsogayiAAolAADzAA37yA1VQBcqQBYiAbexiLpgCMrJ2ZzxwAilzAomwLfbid1RQZ9d2ti0gDkXgbwWDAplADaFAN2k7L8AWDQgHMi57AiwgcyoDBcx2A2WjuCKXLkAQDQCHM4SgD6ZbugSAM/pwB9FwAndQN9GQCIkAAiDQbkaQMvditYkAL8SQBSEwBZmgBAkAArRDbnHLAxEgAwnwtuxWbSlzNiIABPJGOxFwNiNgO9MmAlCQCyxQdycgOn//R7tdkziXUAYABzJAcwkigGwn8G6pmwFAcwcnkAWyVjWZQADfCwIk0HEnEDcRsGt3YL8+I29lIHPqFg1GYATIZgQSlwVGcMDytjSYc29VYwQEp8Bec2w5GwGuWwbz224/57oAtzojcAJLEAHVAzIhUAYyIAKt4AilMDQDRzr3dgMRkAWmkztedwkvIGu4I3LECwJRAwOpcwdpVwZi0zZbAwJG3AoR8DyCozg2/AKm0wrhaztlkA270woEcAlEHDVWVwoA1wqfAAUhkDswAAXLUzzZ8AnGQD/h8AlRsHCtIMStwAJLUAaq0zriEwKlUArhIAKpwzxLoMbiozNerG1W/9wK2QA8I6DHUwACraC+h2M8ZBwDUUDCMDAFk3MJh6MJUBAO21MKVucH33B0gzMCITB7ufB0DiQDU/AAtqAJE2AL48AA59ABj1AGIQADLAAF2cA8XqcBfjc9ABQFFxAFuVAGs6M73QsDIeB0dXd3I3AJVlcGMdB7kLDGLPDHuaAGuTAF4XABsxAC48wNynx9uuAWJAFw35NBFdAMVNcDFdAPNdB5uVAD4yAFBwBUHUEKmiACEkRAmqAJkIAHnwBFDBQFIsR7vgd8wkd8F3QByFcB3ADRsBcOkMANoNcP/sANfvcAqXABxjABNaABX5AKLFQDNHAO3QAPuxRP0ZIKn//nCAFoAA+gARhQRqmAAAXwBh1wDsvIgebAAeUAG45gQsBXAY4ABcUXRVNkz82HP25c0sTXDOADCZAwBZrgCM5nQ6D0fxXQAwUAejRE0zgkBc6HBNlgCZPwC2BIEkEFcB/gD6kQA5MERh+gSW9AevJ3C+rwDSrtCJd0Aa3Q0zkU1dUngAZAgDttgKFURzWkRlwER6EkSmWkRT3kAgxwSxyhCiLIgYBFWC8oBWJkAOPwBh7wlJgYAB0Qf5GgD9jEQyq4AT1gSc/3BjWwQ5rk2KBURmRUQ+NQ2pOkAmDk0y/oSQXwTaTkPkn4iOVwfkPEkJuoDh1ggrogBR8gBVIgg2//8HwxSIHT5IPgRE6nhErNNISuhAHedN5vEEtE6ALf9xu5tIQybYkcIYqaWIIhMQ3Q9IMGEEt8MEenJN40eINDKOA56Eqy9Abg5ACuJIcFEISVkFcRBt0P1htCJFj4TVH0BxYU4AFIMIQO7kzb5IMe0ErUlN4D7oNByIff5AAvnofmJA15hYG/wQFrMSfmAC0C8VCbGORCPuQjuFy6UAwLhRH/YA7qcCHL8OQUEOVSPuVUXuVWfuVYnuVavuVZ/uQfURFKvg1DZYJEXuZmrolM3olKbg4SeeZu/uYUZQ5qLhCEFVEbsYWXqAugwFGp0RJuwAgfZQVZVVIn1RPxOI8s/1WPL/UEnrACMkULNAUANoUDWBEJXrENFkkWGxhRimgR0ULm5SCKoA4WBwALYZUZAGBZMKEDeqAFJdCOswiPKkWPaHWPjHAPhQDpMtWPcEALGFVTdHAL5jDUuNSM5RAhx/AMFlEh25iQHcCQH5FLUqiQC7ALHDANoFALmPEEndASscgIK1AC7HgTsW7oKIWLurjo+MhWTZAVOMDrT/AU7z4IdOAMC3CQwLAA9JTvC9kWwREh07AMETlEC9DhHYENK2AICiALOdAJwsAKdiCLtiUByFAT5F7oeuALOSCP6K7oafUETPEXgjAGgkALVuCPRwEAv4gDoJABimQJwhEhxv81RBSpSM6wAnbQBPhwD50wBlwQVXYAALBQCFagDYUgC47pCQDQCT2vAGMgDPgAVvdgVjqw8eq+Vp2RWTYgCCsQlHQV72ugB7BABhsOUckwhRsRqaEuHHAREgdQF1pgASsQCwUKC4wAGmkwAJ6QBkv/BI3ABhAADpHxkutoHutYAj9ZCL7w8Vh/l6DRBUEgAT5RCJ5QUisgBjqQAXbuDJHAACovCIzQB6Cg9sCAhOXQU9OAmPhQ8QqgBWngBrOhioIQi3ZABp2ABtoAAImRlo5xHlrQBuSxCrLQCDbJFFn/F6LxkXWwAp2QA2jACMTfB36gCqHOAKAgBmnAF2IgBvf/AABqP1i/YQ66wAqKoADcsQcr4AY57x90kAYrcPeXFQRbfw90IAtagAyguZa+f5rzCRDeJORbAcCTjQFpfLip1cTCwyZu8HVqVALcvUb6/MRqosBGnTSwGjVJA0BduXIHKBz69wzlS5gL3MGEqSuWtwxB6pARsGKABS5NhNngMsaoHTtp3HDZtMKGLEFjSlg4E+SnDS1tHkqAYMZbkjh5zLTJIEuLmxIOIdYB2sTsGVmwgpRQtGJMnTOsliLDdzLlypY0YarzS5OGLEVx2tCRpSBfEHAQhVmwEWTTGQkKPH4k47HRIzeUWW2irAXC1iBewbb52iaIN0wKZEEYIywi/xdksSbLehSrxBhFY850CbKijWtZllCqZOlSMMpn7szR5MdgU5wUefwI45KvCTiirCbnJX1GUWcbaRUpOANghQVkVkuPQa1acZIkkuJ8xSRAwplVFAgiDsbGaAwCWSRgyo82zJAgDraY8ou5wJ4rJ4AADJOFDTJSwEIWCPERIIMjjoAgAwUUOWOMy87Y5Ags5mJFghLSaIIMBhBUQBhwFMHnDAskSC2F1fDTD7/+zEhilTjMSOGMOB4RAAIyNuniiDb2SyIFBbqoow5WJgTMueficWmbcn7RRYAt9mjjiDziyMAJb8IQwIk//hBgGC/yyICVM1wU5Y8UyHjvjDpkAf+TxCG2YEKUPUSRJB8IvioyPy0VEcCrFPY7Ax994jgijDhkScHDKQU4QoAwnHACAjGbewlNc7axtQNgLLFVFzKwEIUTV45YhJ4jnEihPyzyFACQLbw4woQ4zBMFz1Uy2MSGMxTYY8VHFnF0CHmY2AKQUVyZUgFJvDEDgibHIqMNAUakRxQ/UEzh2UqxcIUML7bYQgBMCIVAub9kRUmdbTjgwFZgdpmEklEyAGQGMPw4wosUJDkiBW+cAJjQPZs9ghcwjggCgjyxEIATfLiIQ55oFchgByYWYeMUJhqguIEdOJEnEJ05ASMQejg5BWc24mBgBldEEYWJIQRgA4wrWHX/wotg44Bgj1grLDMAfkaZYQ8BZhCAnjzymIGMSGcwIQNR8ug0D5Fn2AGVtY21EwxONgliGGKDyIAMJgC5+WiKwehZDlMakGcGnulx5RRHM3jEhB32YMMaQPbghOchRBnGFU5GAQMVVHjpmkzBApiGDDmuyIANQOjxvIHUOdlhBzBMuMIUKjJYBOMjqGgAahJEScFjoDkEYwswhBeFDHqGOIXmGQKhmZMhdmiAF4p3CEQAcEfRhxM5qDABkH2KKGKGnE3YwxRThDBB+x1mWN3CZfbw4wpO7GEPJhgCKuTBi93tQ2i88x39TKCMGTiLZN9DQRaOsAoBXMF7ewAEE6xB/7otHCED8MPZDK7QgAagb3fgM8Xa9oAKVzxiDzOYgRASMYorCEEZnOAENYjgu9+ZAAyA4MUeCEYh1qHkFwegAgpM4AdXyOFzTBiGKLIHhhlwggkMDET9TPCDUBRhD937Hg9C8YN4KY4JrtjDKbwwgzLswxoC8AMPpzeDIQCCdLwI4B5ySAT1EUAJeyiCElBAgh8oQQgkSEQozmgCVFwBBRkoQjWAt79Z+cEPVBDCKPzQADmYgABUIEIVqFBIcRTBBChAHyd+ZwoTGCEUQuBBBhS3DxQQQRxG2AMYUMiJLJjgUUU4wRFOMUBO6NCRoeBBEapQhR0KQQhUIAQhqUEFZf/wABE8qAcxs4ACJSiBCHvggRGIwYNwKoEKmEwJCXjACSqMwgQkqIc0eVANRZ5SmkUwYxWIQIBkNuCLoagCCk7AAzAswoyhUAJAt2iCFkSAhtQwZRRVyQkTMJSZRQiFOLJJhUTsgQSkrAIJlBGKbZIgAkA4AQqq8IMEJKAFMzWBEkxBBBKwUxmJIIAfUEANE4zCfTwY5Q/qMYpEKFKVuiRCOVFQDU6AsaAnuAEVRIECR1YjGiHgBCpiiYgfZIAaSihoMpUgPx78oApp/QEVeMADZaCAByaYqkxbkAUSZAEIQFAGCU4AAiPI1JF7SMAJWMrORNQjESaoBxH6CsYfEsH/kcr4gRFQQE6GEiERIABCC/bwA3GIgwd6BcJiO0qEBMhgBDT8QQuIkYhGKuEHJEhmJ5VRhUTogwF7CCkBqIGIFpAgATdYQgJgqtosALcMCRDBDSJgRhRkYrg3uMEJ2MkDaiTCuD+QK3B/wFsqhIKyLQArCbBahQQY4QZAyEQi1MoDwwIhC34ALWpBIIJJShYR0ShDNKpQhCxEIBE6NEI0qMED1xIjrj+IBgnuQF0gkCATSxBBerMwgktQFQgRIMAIiCvTzuZ0OWN6iR+iQYAynIC7ichCNhNxA2IAIQGJQAQxfpAJEYAgESRowV4TAIITKEMZGr7wCxL5YwrfAYzM/4zAJXJ5giXcYMYtgHFMs3CCMtyBwjAYbhZeUAriyrgMMGBBCEYg3xe8YAlrTkAmoHwJdmaiDGVgwCMIcec76+POj/BDnv3AAH3wmc5leCsB7hCBE/ghvXd9AQwyQYRo3FcEpeAxMVBwCRYImLSTlikxohEBEYjgyqEGwR0aLYNSgOAGl3hECGDQijmTAApl8MMdCKCPQGvkEexcr5t/DGQjkIAAjygDCRos3GjwNxPLVql0CZCALBghE9HIAk8JsGz+nuAEEbjDCDKB18JmIQF+1fYdTuBm4QY4AXe48onbnAg/GFvHnz7BHpabBbxKNwEE0HYCysDO5i6XwhEQ+P8SbO2HYoc7E3dw8wn8Om2/qvoOyx3BuiMAAm4DNgspPjeKM/GCiafZ3wl4wQgMHYEIxJS6Ao7AlZ8N7URsm9spRvTDHa7tE9zhiCRGyY8vMQIKg5y4NyhDBFggAj/w++cSvvgd2gyCH0dgBFmOgHOhDIJMvDzrhy51Ji5+ggSgPAKlCDAISkHyEdh6qyC/Lwug/XNDG4EFFR9BKeoOgxG8oAw/Tzs7wzH3E1wiBFPwsNkfDIJcXCACDChD2kcAAhCU4QU3EMEdStHoEYAaBHonubjbnom2Y1gGMvg55Dcv6RcYPdMhGL3JL9+KO5CZBaXIxgtaEYJLLKEVUNAyDF7/AIVLXKIVpQD4pKEgAxa0AsMjCEcuLhEFY4SAAOGAwSMIEAEZ6H0JeC+DpEtRBtZLncJmv0SaCfCCS3B5BMiHQe7XPAIYwEAG2chGLnIx61YsYfPIZ0EU6h6CRmMBGZg1EGABGCCAENC9MWuFKPADdsoFGQiBEPg7GCiDKWCBcCgDTVADNdCE+NOACSCAGDCzUpBAERiBvCO8VhDAF4iBF4C8F5CBv4NADLQ7yGuFXJA/35M/GYiCC2SBnwuHcAABTciFF/iEbEC+cPg9CLy9VtCAKXiBELiAKYCCEIgBbCgHNCkYr/k7MwuHT5iFGGSBKYgBSMCDKJiFT7iACYgB/32YBl2IAitMPgIgs3CAAigowFZ4gXBQLQLIhfx7wb9DPyGEAdYTwkNcwhWcu/qLglyIAjUQwhj8hFwohQu8QyhQAzzQACiAhAu4gEeIBlrxu7mLgQv4ggvIhSUIAQ2AQm74AFuAggkYhxqgAZSYhkfAQdWKggkMgU/wRP8Twh6EBDUoQ03wRSgIwPb7u3AYgVZohU+AgmzQgAvghlzgwCmARBlohRi4RjwAxE+8gCmEwln4xBpghnKYjnJgJw3oAW44xS+YAE3ghh7oB01whHqMAQ0Yh0c4BpjoBgsEATM0hjL8BE2cAkfghikYRg6MgjPcRDacgGqcAIrkhgmAhP8voMYvQEVvhAEoeMd+4IYznIIa0IAvqABNmIUKgIRUmIVUiIFXoIR0eImdM5hy2Mhc0ICVhIJZ6IcKmIAa6IEeeAAMkIIY6AbB6IAYoERHmIJvdIQLUINP4IYKqAANMMVwQMMp4MDEq8oJ0MmTBMGqpMYKQEUJTAUM4IZ+6Ad/0AAY4AYEeIBffIBxuAANwIAH8ABdKAdVAIZJMId2KIea9BpIsMoYwAAE+ACLJMoHeAADQAAXyIBXeAVgOARgWABgAIZXIIdsiAGJ1IBc+IQKuABH3MgJoEd3HEEZ+EZ4lMiqtMqybAZqvIAHqIFU2IAN+IBUWEtbqAFb8IcNeAD/RzCADbCFWUAAA/CAA7CEZegACsCVzBxMMvkABBiHB8DND6iBcUAABHiDB/gAFyCFc7AQdkiTMqiBKTCGGuAGY0DF9YxHtfTJVPgAA3iAGPBNu7wASFhDTXiAVKDFBwBODNjOxOQGW8CADxiHD/CHD5ACW9gAA3ABDIjQYiiH8aQE1tlCJHoJ3LSF7yzKVODOAqgBo0RKC3kJddgFUigAW7gAvNzPB0DOB9CEteyH+cRNx+ROAxiHx0QAxESADZhQf/CHxgROA6gB6qzOHphQBcUADEiFGvCASICJAAAGmNBQwDiElxgHKK2Bx9zRCTWASjiAE6WJW1gAXIiB3nzM/wfIhhjdAH+ogQLogQqYTyBNhR41gB+tziQdB1vgTlvgBgwogEHlTgSQggJ4TAd4Az11gUqYhnR8iQBYAJhQRwrRUpRQAT3lUQx4gxrAABfwgyQq0wCwh3XYhRqozQ8I0hrATgXV06AEznH4UT01VAXlTiE1gDfoBQNQgQEVUUalT2lwUiTwgAqlCWew0lkZMZbA1HJwhAJwASQogALwgH4czzIVjL5UjkPQB0KlT2o1AH/gUepEVELlUSD9gD390QZ9gwkN116dVQdQASlQVweogV6I1mOliUkdDGb9B2dFCUrQ0nOghG0wB3XMVpjggAVQR3J4BCcd1E2dzw/4AP9CVQGLndYCkAI/MNc3KIB5dQAH4AMVcIAC0NROJVkVeAMkGNk3kAJpINPnUAXW6ZoMsZAFcAaFfQ4OAIaExYVHgFVNjdACqNiLVQGQJVk+kAI+4IOibFp6LQCSNdmi7AUkwACkdYGmRQJpeNQTndSEtdkTjYeA3VmU6NmELQdc+FQkqFcDQAI+uNqLNYCkVYGlbVoH6AWVlYJ5LVkXENm89Vu9LQAkqIQMQIevVdaD+debfY4FKFuzRVua6AAPaFkpMAC+5QMH8AAHMACL7Vs+6IWRDV2ozVwkcAHRzdtpRYJekFau1QVstZB+XVYuLAzBuEyz5dcOSFuU0IVKcNn/N2ja0EUC4n0D0GVapz1Zu3UBaWBd1BXZXmheq21eadCFSfjL50CTKrWVdcRSltjCSA0Ad3gGzFwGzHSHbXiGAFDf9T0Ed1jf6LDMZ7AHfsDMBVgA8u0AS9AFaRhZ1G3aXkjd05XWXnhZ1n0D1yXeAH7e1kXdAZaGR7jfzNwGd7Dfnr3fDmCG+23cZaCQfzjY3A1hER5hEjbbZcgAGlgGdfgHFk7fDtgFyC1hGZ7hGQYGGsgABsiAaaCAZ9gGFm5hdQCGZSgGGpiGSDiAIz4AJV5iJm5iJ35iKI5iKZ5iKm7iSIiEaaCBYqAAYAgAH/7hH0ZYwsAQDDkEMj5jNE5jETVeYzZuYzd+YzdGmIMF44AAADs=\" 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border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 53.9px 7.91667px; transform-origin: 53.9px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eInput: (rubik)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 444.983px 10.2167px; transform-origin: 444.983px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 444.983px 10.2167px; transform-origin: 444.983px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 7.91667px; transform-origin: 107.8px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 69.3px 7.91667px; transform-origin: 69.3px 7.91667px; \"\u003erubik: row vector \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 38.5px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 38.5px 7.91667px; \"\u003eof size 54\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 444.983px 10.2167px; transform-origin: 444.983px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 323.4px 7.91667px; transform-origin: 323.4px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e(The cube started [L=0,U=1,F=2,D=3,B=4,R=5] and then received one or two face moves.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 444.983px 10.2167px; transform-origin: 444.983px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 444.983px 10.2167px; transform-origin: 444.983px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.45px 7.91667px; transform-origin: 219.45px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput: mov (A row vector of one or two of values {1:18})\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 444.983px 10.2167px; transform-origin: 444.983px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 419.65px 7.91667px; transform-origin: 419.65px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 42.35px 7.91667px; transform-origin: 42.35px 7.91667px; \"\u003e mov: is a \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 377.3px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 377.3px 7.91667px; \"\u003evector values 1:18 representing the moves in order to fix the cube: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 51.0833px; transform-origin: 391px 51.0833px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 29.1833px 7.91667px; transform-origin: 29.1833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 361.283px 7.91667px; transform-origin: 361.283px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the cube was randomized by [1 9] UD', the one and only 2 move answer is [3 7] DU' which are the complements in reverse order.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 281.6px 7.91667px; transform-origin: 281.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMinimum moves is also required. Scramble by 13(U2) should return a [13], not [1 1] or [7 7]\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 339.217px 7.91667px; transform-origin: 339.217px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eVerifications will be by executing your move vector against the provided rubik and checking number of moves.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.033px 7.91667px; transform-origin: 157.033px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe function rubik_rot(mov,r) is available for usage\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.65px 7.91667px; transform-origin: 188.65px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is the next incremental solution step: Move optimization.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 367.617px 7.91667px; transform-origin: 367.617px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAdditional Challenges will be solving the cube at even deeper depths for time and minimizing face moves utilized. This depth does not justify a time check.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 20.4333px; transform-origin: 391px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003ca target='_blank' href = \"http://kociemba.org/cube.htm\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCube Theory: 20-moves Any Cube\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function mov_vec = rubik_solve(r)\r\n% Single/Dual Rubik's Cube Move Solving Challenge\r\n% Available function to check/determine solution : rubik_rot(mov,r)\r\n% out=rubik_rot(mov,r) returns a moved cube array of size 54\r\n% Solved Cube vector\r\n%[00000000111111111222222222333333333444444444555555555]; % with spaces\r\n\r\n  mov_vec=[1 2]; % mov is a single or two value row vector {1-18}\r\nend","test_suite":"%%\r\n% Load function rubik_rot.m\r\ntic\r\nfname='https://sites.google.com/site/razapor/matlab_cody/rubik_rot.m?attredirects=0\u0026d=1';\r\nurlwrite(fname,'rubik_rot.m');\r\n%urlwrite('http://tinyurl.com/matlab-rubik-rot','rubik_rot.m') ; %dead tinyurl\r\nrehash path\r\ntoc\r\n\r\n\r\n%%\r\n% For mov=1 solution is 7. Need U' to solve U in 1 move\r\n% mov=1; % U  answer should be 7\r\n% Solved Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\nr1=rubik_rot(1,r); % Create Challenge Cube\r\n\r\nmov_vec=rubik_solve(r1);\r\n\r\nfor i=1:length(mov_vec) % Perform moves to see if it solves\r\n r1=rubik_rot(mov_vec(i),r1);\r\nend\r\n\r\nassert(isequal(length(mov_vec),1), [sprintf('Exp_moves=1 Exp Mov=7  moves=[')  sprintf('%i ',mov_vec(:)) sprintf(']\\n')])\r\n\r\nassert(isequal(r1,r),sprintf('Exp Mov=7  moves=[%i %i]\\n',mov_vec(:)))\r\n\r\n%%\r\n% For mov=14 the solution is 14. Need F2 to solve F2 in 1 move\r\n% Solved Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\nr1=rubik_rot(14,r); % Create Challenge Cube\r\n\r\nmov_vec=rubik_solve(r1);\r\n\r\nfor i=1:length(mov_vec) % Perform moves to see if it solves\r\n r1=rubik_rot(mov_vec(i),r1);\r\nend\r\n\r\nassert(isequal(length(mov_vec),1), [sprintf('Exp_moves=1 Exp Mov=14  moves=[')  sprintf('%i ',mov_vec(:)) sprintf(']\\n')])\r\n\r\nassert(isequal(r1,r),sprintf('Exp Mov=14  move=[%i]\\n',mov_vec(:))) \r\n\r\n\r\n%%\r\n% Starting Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\n\r\nr1=rubik_rot(2,r); % Create Challenge Cube, First Twist\r\nr1=rubik_rot(9,r1); % Create Challenge Cube, Second Twist\r\n\r\nmov_vec=rubik_solve(r1);\r\n\r\nfor i=1:length(mov_vec) % Perform moves to see if it solves\r\n r1=rubik_rot(mov_vec(i),r1);\r\nend\r\n\r\nassert(isequal(length(mov_vec),2), [sprintf('Exp_moves=2 Exp Mov=[3 8]  moves=[')  sprintf('%i ',mov_vec(:)) sprintf(']\\n')])\r\n\r\nassert(isequal(r1,r),sprintf('Exp Mov=[3 8]  moves=[%i %i]\\n',mov_vec(:)))\r\n\r\n%%\r\n% Anti-Hard code solution Test Case #1\r\n\r\ncmov=[7:12 1:6 13:18]; % Complementary Move\r\n\r\n% Starting Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\nmove_map=[  2 3 4 5 6   8 9 10 11 12    14 15 16 17 18;\r\n           1   3 4 5 6 7   9 10 11 12 13    15 16 17 18;\r\n           1 2   4 5 6 7 8   10 11 12 13 14    16 17 18;\r\n           1 2 3   5 6 7 8 9    11 12 13 14 15    17 18;\r\n           1 2 3 4   6 7 8 9 10    12 13 14 15 16    18;\r\n           1 2 3 4 5   7 8 9 10 11    13 14 15 16 17   ;\r\n             2 3 4 5 6   8 9 10 11 12    14 15 16 17 18;\r\n           1   3 4 5 6 7   9 10 11 12 13    15 16 17 18;\r\n           1 2   4 5 6 7 8   10 11 12 13 14    16 17 18;\r\n           1 2 3   5 6 7 8 9    11 12 13 14 15    17 18;\r\n           1 2 3 4   6 7 8 9 10    12 13 14 15 16    18;\r\n           1 2 3 4 5   7 8 9 10 11    13 14 15 16 17   ;\r\n             2 3 4 5 6   8 9 10 11 12    14 15 16 17 18;\r\n           1   3 4 5 6 7   9 10 11 12 13    15 16 17 18;\r\n           1 2   4 5 6 7 8   10 11 12 13 14    16 17 18;\r\n           1 2 3   5 6 7 8 9    11 12 13 14 15    17 18;\r\n           1 2 3 4   6 7 8 9 10    12 13 14 15 16    18;\r\n           1 2 3 4 5   7 8 9 10 11    13 14 15 16 17   ];\r\n\r\nmovt1=randi(18); \r\nmovt2=move_map(movt1,randi(15));% Avoid complementary moves\r\n\r\n\r\nr1=rubik_rot(movt1,r); % Create Challenge Cube: First Turn\r\nr1=rubik_rot(movt2,r1); % Create Challenge Cube: Second Turn\r\n\r\n\r\nmov_vec=rubik_solve(r1);\r\n\r\nfor i=1:length(mov_vec) % Perform moves to see if it solves\r\n r1=rubik_rot(mov_vec(i),r1);\r\nend\r\n\r\nassert(isequal(length(mov_vec),2), [sprintf('Exp_moves=2 Exp Mov=[%i %i]  moves=[',cmov(movt2),cmov(movt1))  sprintf('%i ',mov_vec(:)) sprintf(']\\n')])\r\n\r\nassert(isequal(r1,r),sprintf('Exp Mov=[%i %i]  moves=[%i %i]\\n',cmov(movt2),cmov(movt1),mov_vec(:)))\r\n\r\n%%\r\n% Anti-Hard code solution Test Case #2\r\n\r\ncmov=[7:12 1:6 13:18]; % Complementary Move\r\n\r\n% Starting Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\nmove_map=[  2 3 4 5 6   8 9 10 11 12    14 15 16 17 18;\r\n           1   3 4 5 6 7   9 10 11 12 13    15 16 17 18;\r\n           1 2   4 5 6 7 8   10 11 12 13 14    16 17 18;\r\n           1 2 3   5 6 7 8 9    11 12 13 14 15    17 18;\r\n           1 2 3 4   6 7 8 9 10    12 13 14 15 16    18;\r\n           1 2 3 4 5   7 8 9 10 11    13 14 15 16 17   ;\r\n             2 3 4 5 6   8 9 10 11 12    14 15 16 17 18;\r\n           1   3 4 5 6 7   9 10 11 12 13    15 16 17 18;\r\n           1 2   4 5 6 7 8   10 11 12 13 14    16 17 18;\r\n           1 2 3   5 6 7 8 9    11 12 13 14 15    17 18;\r\n           1 2 3 4   6 7 8 9 10    12 13 14 15 16    18;\r\n           1 2 3 4 5   7 8 9 10 11    13 14 15 16 17   ;\r\n             2 3 4 5 6   8 9 10 11 12    14 15 16 17 18;\r\n           1   3 4 5 6 7   9 10 11 12 13    15 16 17 18;\r\n           1 2   4 5 6 7 8   10 11 12 13 14    16 17 18;\r\n           1 2 3   5 6 7 8 9    11 12 13 14 15    17 18;\r\n           1 2 3 4   6 7 8 9 10    12 13 14 15 16    18;\r\n           1 2 3 4 5   7 8 9 10 11    13 14 15 16 17   ];\r\n\r\nmov2t1=randi(18); \r\nmov2t2=move_map(mov2t1,randi(15));% Avoid complementary moves\r\n\r\n\r\nr1=rubik_rot(mov2t1,r); % Create Challenge Cube: First Turn\r\nr1=rubik_rot(mov2t2,r1); % Create Challenge Cube: Second Turn\r\n\r\n\r\nmov_vec=rubik_solve(r1);\r\n\r\nfor i=1:length(mov_vec) % Perform moves to see if it solves\r\n r1=rubik_rot(mov_vec(i),r1);\r\nend\r\n\r\nassert(isequal(length(mov_vec),2), [sprintf('Exp_moves=2 Exp Mov=[%i %i]  moves=[',cmov(mov2t2),cmov(mov2t1))  sprintf('%i ',mov_vec(:)) sprintf(']\\n')])\r\n\r\nassert(isequal(r1,r),sprintf('Exp Mov=[%i %i]  moves=[%i %i]\\n',cmov(mov2t2),cmov(mov2t1),mov_vec(:)))\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2020-09-29T16:49:36.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2012-08-09T16:34:10.000Z","updated_at":"2020-09-29T16:50:43.000Z","published_at":"2012-08-09T20:21:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face/Vector numbering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice. The loaded function r_new=rubick_rot(mov,r) implements moves 1-18: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Input: (rubik)\\n\\nrubik: row vector of size 54\\n(The cube started [L=0,U=1,F=2,D=3,B=4,R=5] and then received one or two face moves.\\n\\nOutput: mov (A row vector of one or two of values {1:18})\\n mov: is a vector values 1:18 representing the moves in order to fix the cube: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the cube was randomized by [1 9] UD', the one and only 2 move answer is [3 7] DU' which are the complements in reverse order.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMinimum moves is also required. Scramble by 13(U2) should return a [13], not [1 1] or [7 7]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVerifications will be by executing your move vector against the provided rubik and checking number of moves.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function rubik_rot(mov,r) is available for usage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the next incremental solution step: Move optimization.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAdditional Challenges will be solving the cube at even deeper depths for time and minimizing face moves utilized. This depth does not justify a time check.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://kociemba.org/cube.htm\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCube Theory: 20-moves Any 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ZuqzojI4DcF+fnDDbdOqaioKHfuqNiyRbsOnbjXx668BRKWD2/fqKlitx49u3ZRYQ2UVYzue4vKeTfav4xr0LlDuxYtWnbs1LlLn5H3/SLjAh5PH6yqzJ1QVu7cSWXx32dKhz2/BSs/dtOCEcoqKh3atm7RUqmzsnKf8QsCUlGQE3Ni62Lldu2UVbood+rQd/Tsx16feR+rGoCVnhzj7eXp5e3j9+mTr4+Pp5dXdCLnBuV9CQv29fPz8fEuPLgWcSmZolbpxEWFe3p6+vj4fvr0ycfby9vXPymDBZtykxO8PD08PT0CQqN/FG7I+xwa4OHp5evr98nPj7slv8DQrCL19iXUn5Pi6e2TlsdP6VSvOBY/Cc2DJSFYoaGhEnYn5zNJnvP+5s1ba2trCYWEhIT8l4Clf+GCtqVlVctpS0s9S0t9wQttcQt3rYGlpa4EQk5bWR03MnJycoqICImICBa7+Pp6ampu//xZfCHctdevXzEw0JXsTkKcnN4d1zY6Y2itbWApZtG3NDS1PGtoeVpfTAmnDSzPGFgamVqKfQ/65y6Q69y579XVq1rc1NUvqKufU1f/UPVri4uLurqxuvoNgTTxJHhMm2Y9cqSSYovWrdtKUpSUWsvLN2jbtp3YEtq2ba+g0KJx48Zt2ogvpE2bNi1bNr+4f9QH82nvjdTFKYbqTqbqZ7aqO2iru5qoiyfExVj9ub661mb1NyZMoBgSXM3nEuTlQSRGuU9kJdaFpcs5oreSSXAhkiYVokiiKAlKINEOySRw5RaRjmQSwol6ee4jWBCMxSpG7NoT08j/KMFcXCHnKEWH9kykPDOBQDEknJcXH6x7RJb/BlhvJJPgRFSbekt8I2lEhyQW8lLinyRXigZ/kAysgvN0Yhb5HpMIrHhd2jeVsniwiAokE5NCdFDib/OC6LxkErKlaBAPFg8WDxYPVnUHy4BwlqBXXmVhMawEWPqClvrf1XBFtxRD5YJV+rMKhZgUeXW6pSp/BFZtLFyHfX9CSjKwVIZB1xAbFqJGFcGSqov1B2BlhfPnBcUcurpYO7fyYLXvjUMnMLpLmcqeI2BiwaRyd1QxWDXqYubvrKWlMTRGlNTLNcDivwT3pY9x/X4AVh0FrN/HGhtro2+Hovo6WLEVJudgYQELTr4R1Nr+CCyOp2uT4G2Mp1NKeprrzksj4XkO/lbwOQFrecZWBWBx7R+shrcu7vQpbMnEXlGHryWT8GwmQ8dIBFjcqbtL4GOMTxascO0fjmIYcWdNmuLZdlbjZ4CbKkymUflgSaH7UDxwQ1Yu4t5DRgKwZBqgcJv1T3aoW1Ww5PDrJpw+jRMnWDmohXTguUFlwJJrhHVHEC1IZtmlXtJ29hbEJOGqCY7pIToF1w6U/nJlwJKug/OP4PIaxw/AzhF5udiuweplG+PmG7x/jGMHcf8F8nKwarRIsBq0x/NQ3LfG4UNw+4SMMEzqLjilANdkuNzG0SPQOomTB6HaqkKwGAStECnYTOuzrlAz6Unj/k5kxyHABO8Pwt8OD0cydIxFgMWRYTUKhTNY7stZ9+tJ4cku5CTAzxBuxshMh+cWISvfg8W193yODF+8PwY3LbifhMMgAYhNEeqFiKt4exRf/FEQg/tD2W2UA5ZsA9x8h1NbccAIkU6QlQCsZSfg9wRmd+F3E3UkM4XtJiAtBbMHVgassWvh8hCLfoVHOHZNFVbWagXvdNjsFr4duRIFuRjToXywZOth7C9oUEuoYB4H46szmtREzQYYNwZ1pAXwKcAtCv73UVdaBFgtMWG0UOM37IqoAtifEpxqBpcYbB1daVPImZi3Voi+iU+v8PksA4vr/gu/IAd4OwPaxApDSkakKWTWqi6CnBCgi5hguC+DDsFMBSlp8FyH04SThHu7kR+Fq4pMeLlgeTxF4FEcJ3ZtsSk0bYI7v7A2nBADBSRn4asRe2v+PVhSMmjQgL1YeQxxzuKD1aIPIhMxZwA0LyBAQrBkYPYCoU/RULpSGqseasuAmsM9AruLwFIcwlTeqiIya7SBRyyOLa6EjyUFw5eI9IBi7W+dhWueCHyGBjKV8LEa430yHugVgRWN7SMrBxbXfzbjkZWAm13h/hRfBGBx/fraBJlOrL+1BT2tW6GPxTW4vwMZ7rDqjNgIfFyGMxyao5AFOKixs0xLdWNvX41iosoH6wmCjkNLIE2vlO9V+NpEcKthkYi2ZpXmFTjv604j9r24YEnD0BGPjNgfrNZd+EsGVrthSMjHgTlVct7rdIDH5xKNVb8rIgGr7cK38r3wKR6mm38MllxreMfhoc63v0TjrgjPwIU9pb1QkWB1FOiXnTOFpvB9PLyewoxzs4wwpIdosJimkUOQMwIPMpXg4yLUWFxf+rrhiykerWDOjb8FHk4QWrHvwWK93gaJMXjB2coWSIhiGotD06IfMoCPqxiapwiWw5ihdJtXEVgZAfA1h78lHo4Vemml7bX5QORydnYVI+/8/xNYQ5bgawi61Wevj9nB7xqkJQBrmy2yg9BMShKwOMXzhxYy8vDgNi5ewhNnpGfj7Nofg7X8LLg/5Qldvq3/xwZ5SRioVIlRoRTM3iDeA+0aCFXd9CXYuQu79+DaC6QmY91UEWBxfeywFSkfYC7N+t7bCREnWSVX/F2R/QUBxni1A952yMvGa41Ctr4FS1cKrjfw2UJgv1oh7ivcFjONpSuDt+eQl4FwroNsEeWKvAK8n1E+WBw3N6bg7Q447YHnRWSnwfcfGEgJzxoJlOgHB+QE42ILdhv/L2DVVoRzNC7vR8fO6Nod554i9CF6qaBebXHAqtcREdkw21zVcMO3YAnKmJnQ3IWd2zBiElwjcGjuD8AaOhepgNaKb+unrGIaaPuMSoUb/tQCZ4YXDBSh2Z8g6jkaSn0HllGhG5SKjxtgoQyb7gjyQJQlbDrCsAb8PRFpJDSFp6TwyQWJD2EizTnUZcDi+vjKXORk4elYWHbF5QlMdflqwkJJOAK4MwfOu/B+C+wmIz1LoNVEhBuKAxOc7nx0AEjDlWZCT4vD1HEfkI+nwwoHEBWCtV5bTLCa9ca7ILg5w8UFzi6ISUZWMtxffDv0ryRYK7WRF4N+imKCNa3865THIjMf4ztVBFZ/DaTlw2LvtyGXscuZN3Lmr0rFsX7bBc5AbJwh8vv9ZYwcL7T6HixuzGX7CxICEeuMOBfEuiIrHTmxiL4Da86a3kLiTdbGRMCWmyNS3+NcjW/B4shz2IRkf8Q4MY85zosNcTPCEW7K0cOw0BP4TJzndOU35MfgeuvynXcjEn6WqUBfXp2NAuBWG9aYu/zuekaV8yIhVT8Aa/kRxL4TK0Aqjdp1UK8eK3J1oX0PgfZoKAdp6SqDVacFXCLx2KgCvkUGSFvCLRz/jC0ak8iiZXPh67qKuOcPr6uQkxEJVo+x+BIP/Y3ffuCAWYhNxv5llQqQztyMjCSsGlv2704JLRsWeX5t4RSFe2dRs3znXQYmdWBSD6b1YFgPfq74og+jWqz/7m9lOuOGIhvQmXZCQhwCDpRvCo1lYVKXSTCWg1l35mNxfpV+DZjUhmULJorj0qQzoj4jwlToOX0DFqtpDGslxhCnnHTk4PkA6e9hVpvV2C1FTiZeT2d3ckag0kTEsWpjjwFu28E3HMjG7duwNSj+gxIn8n72Eb44VDlAWlhmbWdxl5m9qhR57zoRN+zh8IRZq2Bn3LbH6imgGjB/gDeOuHYTHkFwfoBuDUUGSOsowV2QeHz7Oq7egJ097l7B6E6o1w6BgvDYjcu4ztXfht0FDGxfPlhth4NlHSfC1ga3bjEhV02gWAPTtsDXG7du4Pot+IXjzZ0i36vcUaFhUeG68JM3ogwYPWwA2AIB75AdhYDriA9FzB3YNCqMcJbjvBdKYGHx9khOgedKRoBRKwS9RMQ9BNkhPghfr+F8fSbh+wApV3lpPGI9EHYLgdcR7YkkV9j1ZFCaqQpiY+kIsEHQLQTbIfgyLtXHuXLAqoHpS/H3Jqz+HUuXYeMmrFmKRhKApTYGGqNEBVp/AFafkVgyvapTOoo9sWEzNv6FZUux6k9s2YwxfQQ9rYZNf+PvvzF/4vcasAxYtRpAYy6WL8e6v7BxA/sNNq9DtxasftZCVr/+L2wQ1G9cjY7NygerUVss/Q3LVrCWhY3XLYOCnMDVm87uavNmLFT/5i9O9JQOR8atybjTv8Q2cTrs4Qq824Kns2EsJZxOqSDyzi6sj/tzcL2jELWLQ/BmM979DcexzCYaFM3SlBt5vzgMb7fg7Sa8+g3nagsnl861wuNf8XQ5Xm/AG65sxJu1sK4NM36usBpNQuuXneYrnqTTKQpiVWYSWpeEaqkQF53vJgornivUKftxhQJ1yhYjfhKaz274CbMbnhFdlrgrbIncJJPwkUiO1CS+kVwiLYmFOEn+k0jRMH+OicsEK7GKJbtWZz6Fcl7URXGF2FLmOTo2k3BBIFAMCRfl6YG8vANRVYsj0VGifwQvHMQtnM7bSnRaAiHchWeJalEnCe6isFwnWi7Zt3EUoLlNkLMt9u9xV4q6G/9G97eTw99ilc10dzutHkGmq+j+P2IKubeVrv1Fy4aQ3VYmUAwJDzTl6aK8vJUge71KxVZA1Wqii1W/trjYEP1BtIfogrgSuE/fT1ST2kpwF4XFmGiO4GuJLYH7EppEqyQQYiOwpJ2PzCLb1WS1QsxiuYoWDqATC8h2lZgSbP4go6U0S43M/xBTwsV1/2lTeEGwGkISCR/+HVOY/W+YwneS/yTSNOwTZwqvEKzFKlbMFOrOp2DO0b4krpALlFFoCguNqRgSLkkAlsO/4byb/kTO+4F/w3k3l9x5d9vLOb9FkcmqFkMqMKfjnPN+lGAmrhBTitehvZzzfo6EIdOqFnN+VMiPCvmc9/9psAwFESP9UjEt3bJFTzRYhuW1LJ33rFsqh72COFZpIQal2hffjOEPweoxCBrTMXa4qKmYH4BVuz4Gj8SUKYKijkmjUbemWGDJYthYTJvG7kS6CmDJNsLkqZiqDpVW38obMQEaGujf7cdgNWmP6TMwdQIU6papb92DSVAfh4a1fgyWSj9M18D4kaj93b13H4jp0zB1Cto2+RFYLNupFewm4FJH4RTN5aG4MxW3pwiL3Thc6VbYspwpnfNtcGu8sOWdabimWhJPN6yNmxNxdzoudyqZQi53EtqmB+wmCoSo4646LrYVYsRdZdsXd6bDfhxMpYXolwNWjaawdISPF1zcEJMCeyMo1KkyWG0HIigF/j5wdYXbBzjfRruGVQarXkuWYR4SwLIkvsbhljaa16kMWGOW4aMvPrrCNwDx0Vgxqoj2Fjj/AJ+D4OKKmK/Q2VJ6YqcMWFKy2KAF309wc0XoZwS5YVQbgWddE1tOIyQCbi4I/QKP5+jVUCRYNRpC1w7+Xuz2oxPwxBbtigCVrYWjFoiOgKsLPHxw6WhxAoUIsHRkWGYgChB6Qjjr52KN+A+Ic0OcK2LdkJWG2BuFrHwLlp4gpyU3GXGC9txVvruZEKZy2iHgGVL9EOuOrBg4/V7+JHShEDd7NjUZ6yIU8nquQG/VgtN5pIUgxgVpMYi6AZtmIvKxFNRgpIOOTQWZ4WvYjKvWb1UGq81AhMVjUHuJTOEOGyT4QUVwJ10ns1SVP9V/DJYUVu3EJsEinFoNYe+BjEB0Fszy7rRBShBUBTkO8zazb7aob/lg1WiMw9pQF2RQKfZCSDI8brLc9lotoHUGEwWLc9oORkwGLmiKBKt5F+gaoVcLYV5XDooSVqWgaY70UPxSmDtaC926QEZKNFhc/9mvQYovIgMRcUaoJwyLZnh0OD46ISmNpW7qlmcKOSYeHkP8C6Et0y+a0tGTwUcHZHrCuj5LTHh6miU03lYRnfP+DMGnBbntVDQRzrn5rfHRADdU2Ky29S8sg/TDahEZpFKlklukGyIIuHtEHLBCotFHUSKwDF8gwFE4ey3VAknA+umV0Vil06cWHGUAjWjP1j74pMNkQ9GphnANK41FWY1Vds7d4BVifNG6DmOidF7oXV+8My1tosuAVfqH5D7OKRnPzrHXTXsgAdCcWjkfiw2y2iAhBq+m44MjvuiUnhZkhevFpydQEA3b2uUv/yoEK+4xa6ld5GBxLc91YVmEbouFaxINWiM5Fx+Xi05NforAYzgh+MTi2UZj6ZIZTE7OV85M7RexSqfMgohBSAMOL6m6KRyMr1nYsw6z52Dc0AoWJ1YEVq/p+JKCc9sxdBSsXsDZHkoNq+q8H7zKErXb1EbLwSxrb/3IkvUZt93w1rz41kQ679LyeBSAj9eFi3OKy+AFiIrHpimVct4bdEdcAQzXsdcjViIrHP27YLwG5s/DsD4VgsX1lpMt4u1Zb3m/F+a8l3G/GiAxHQGaIp13BtZxpAfj3mw4zMHl9owMDoWLY5FdAMdBAp3H4SKPz18QfJK1L3/51zPEOcJ+Fu7NgFXDEofMqChb0H4FslLwaNSPct65svcC8iLRW7HKYDVXwaUHcP/A3BnOv3hqg1ZiOe/Df2XaNScf4W/Qo0lVR4WNVPEVuLBXYEu5nzEds/qW6BsbV3jcKPapRYI14Fem8zYXASTfD69c4eqG/AJcPfZN+o1IsNbrAckYIlhtNu5v5Obg/Uu8coKbFxISoL22WO2VBYvrMNuxyIiHvTKzNb7O34LF9e7dbeA04I32wp7+HixOu9xajKj3iHFGvA9y4uG8ikm+PIfdh30PdqGJwDIG+yLCuHyNxYH47ADLYo11RlIwWyT5aLgw0+bCSHzm6j3Zz+TxpzBRoiKwhi9niWr75kkabug7BZHpsNhcZbBUxsHFBzZamLMAr/zh9xb921ceLNl6uOSESBe0lxeClZOFRf1KslyvcHzYFvdo+WA16wjvBLw5B7niVC0FzJqHuXOxUwtpGTDYVnrcXD5YfTXYyrOzfwrfTtiG7ESsmCh8u+oUkIr+LcsDy7ApQjzgtZF5NmcLF1OcKklxYaqiPsL9EX1RML6jitYVFsYUdKXxjPu8DNi3ge0U5OXjTm8hWLq1ERaEsLPla6xC61koxKAJyyDNCYB1PQYcN1y9Ow935sJZFznpcPmjwsUUnBlKBaz2/jtxrEvv4X2j3Fw/kWDJNsbTADzQEdqq2q3wOhb3tSoJllQtGNghKxIjVYrGJAM4lYH9s0ryZJ944MHZisIN8m3xKhxBz6FUr/yvtf08CmKh1qIisLqMYUtVb5wp+fbDl7GVob2L4iBdRrJhyaL+5ea8T2ap5UmeiOEGdO7IzEBeMiLvClfCcN18fS5r8HBgacNUUYCUk2naho0jXv+C8/3YBz8fV6SxmiA6EZ80RYJlXGqV4pXpyAfs27HGxUGsUwTnW+CMhKWoRD+V4QhPgem2fydAKtsM3jG4cbBqGqtRR4QnQm91SY2RMz5YVwosWRy9gARfDO5QZsnoq2jcPS1821QVUdnYPlUkWHItcN8T7vfQXK7UTSmhW9tSYFmxAXjv5iLBajcI/vG4dLyMk6k0ANncAHe88O3ULUxj9WtR3iqdc01xczxuT2VxJvvpCPuEODvYjYWZnDDLz/sV0p4WZYeKBsugKC7KOe9X5nG+Be73hF4zxMUhYJdwLbX1GOTn4clwkWAVoqwnWKXzlFN7MbCpB7O2uNBauGL2tACsgjBY1ioPrBaqiMhHuj/mTcWsuZg3D3OmQr6Kqcm7TKC/FzM1MHsuHFwR4YSuzaq4d0NtnLZHXjx2r2GBzsOmSEvE75MqE27YZMjMvcVRTJzMbp8rAwXrg8ZvQHomTm3GdIFpdbeHgojFFLINYesi2PphDSZPEwiZizYNWRr7pwiYHcWUqdA8i8xsnNtWWhGXAatJN/imMR910UzMms2EzJ2OxrXZuEHrNvLCsXYxVv2DuHSY7hYRxyoxYYJu8/NCpI5wtQJnmGwnCXa1n8f6VdSUDtfMrAP8HfBqMe7PxJNNSE1gC5qNpNhVD/YgNwNO6+HwG+IiEWnBFpAZlpvzPgEht/B4Ou5p4O0pZsudljAJF6YiIxIfd+POFDjrITcNbqtFmELOs7lxHdeuw+Ee7t9n5bY12khXDaweo2B+DQ8f4IEj9I6iXVNxRoW1G+P3Lbj7AI7cYOQ6pvYvN/j+PVibtXD9KlvpUHj73NV/zxH6VZN+hb0DHjpC9zAU5UVG3usr4ex5XLuGO3eLhNyBem8mfOhYXLJnX8vhJn6fjVqinfc2g3D9Oq6W+iEdLkC5seCbKWCvNu4/wP272DwHNaQqt43RSy24LC8Zpt1dgwAjWDUoNfgvdzGFHO6uQvg9RDgi4g6eL2ZUFTpk+tJwWIvw+/j8AB+2sEx2w/Ii72wtdTO8OIjPj5iQ8Ou4M1S4NY1hLdxagEA7RDxAmB0cRwhDrPxcYXWahDYom/NuKPVtrrooU6hXVL6Z0TMqe8qgwikdvSJ7qvfd3g3f1/Ng8dkNP112gyORtcRdYS7xrsnODKw+/0Wb2w76uF+QXmcqVjFhWepas+nTcQGd4gkxp0R92j+Ncs4XrX6uarGQpwx5+XSiqpZsIjuBvsmp+rXFJYvIkOiJQJp4EnIEWqI29RSQkS5BiSbaK7iRDAnu5QGRieBriSchkyhJiga820VZppSuJ1bRpTQTOqxB7oco21hMIVmG9OU0aU6hBCMmUAwJGSbydFhefo8g8bxKZT/RIiINQdrlHnEL15PTiJYJpIkngfv0lUSy1EKCuygs24hGS3AjhfeylGg60T4Jfg9NIqVVo2jfdNqjLm6ZTmO70dqxTOWIJ2HvNPpnEo1SoZ3iSjg8VwJT+FiQsS6h8bAS2DIJc95rU99/I+f9mMRC3gpWUki4/GuIz2HBuqvzYhVztnhLey4FnSLYiCvEitKMmdpj2evmYkmw4Z133nnnU5N5sHiweLD+H8AyKidq9W2lKLC+WUXzveQfgmVUCSFGlQFLVraCPKqqzBXKQkZaArCkUENWDLBkZCr42MqCJVujOLezXH+oUmB980NKSQnuTVC4U2V3Dasw8m4oVaY7dQU1JrLCeUOjCrMbjKQE2yrLsO2yjKW/XaNhWIlNQZgQacHlAjlMYFmqDKmksjywZDBxJd64wsMTEQFYN0PUDkQ/AksGizbjgw88PRAYgt/HVRks6RpYdRCe/vDyxXsH9OtU2W2MVHDYmE2sBQTjsS2UFcrk0mzYj0/BmKv6A7B6jYHFLXh5ICQE546iUVm2ZVvjhQ8iPmFyD9FgyWD0Itx7AQ8PfAnBtqXCBJvBS+HtLSyenvD0RbAn+ravEKyzhKdHkfEF3tuEEBjWwL3VbF+rBE8ke7MMdAMRYOkTbq9BchgSvZHohUQf+B8SCtEXbNT+9jTSvGDXtSSsX24+1hsDpAYLJHiz8nZhSUoFS57piehPSHbCjbaict4HwNkL6+ahd1/stWUz4ep9qg6WDDYbsn0NV82EWh9MnIVZY6oIlhT+NgDisHIG+g3BxZeIdkObBpWZK9xljHvWGNYPv0xFUDwC76KpYPdT5RF47oWYL2w38lUDKgKrRiNcfQ79A+jXC0vWseyS6weLN91jH8H9MLExyMzEwgEiwVLojtd+2DgPfXpjnxGbL94i2LdSvjkGDsKAAaz06YPD15EbgU6NRIOlxw3ThiM5GmnJwpx3rkfvrEVeKl4tgFVfPD/MtqN8Mqr8BwgUpianeODKQFwegKuDYNtOqKsuTkR0IFsKwYly6FuyLExUanLkJdj0w9WBrFgplCgzjnuPe8iIRm4kbndmjcsBq2ZdNCheDNMUscDhRVUGq/0wpADrJ4rvY9VtBb9YWBZtny2ngsQ8/D2tMhqrUaOS83/osLUtwwX5MxNWYu9qtO0D7yj8ObgisKRl0agUw9auiPOFYlH+TO9piArH7GWISMPigSLBqimHBvVKfkivDDwx/u72m+JjIs5tqdAU6tZA4Ef47sXHB8Kcd64jXeyR5sjSSrW5t/IsKd5zPXtrXGHO+5lSc4KcXnHciNe/4cIgZCXhXp+Kln8Jc96Ps5z3byYcuVO3ViLdCw/XICsC9p1EgFW6dJuInDz8OrzKYC08xh6P0UgKdeqhXl1xwGrSCWFxOFZqr8+H0bDeWFXnfS2n9eLRu5Q1bNgVn+Lw56BKO+81cdEFwS/QWFaYIfg0BDoL0HoA4vKwaEClnPca3J9JJq4e+LZ+9m7kJ2JoO9FgsR25dyDLB+YN4PlGmJrMNNYa5Gfi2RiGy6NDyI2BnXL5e5AW5rwnvIVpfbYZqWGpBav6AtSsBiMnpRJgPUeYIfRr41wdhmbxogz9pmwxnZMGbGcjL7pCsJQHY4cmjpzG5xic+UMc533fRcR7w9QUHz7ALwDP7dBHqWpgSTfEPW98fYVebdG0KUbPRVgWbh2qGliN8C4K763KZKY36V41sJQGcWTCuGiP5JVa+OyGJpxSHo+4XCwaWCmwxq5lpnB+WfsrUw9PAvHUuLRrXxYstvSvAxKj8HYqy8fydcFnnaKelsb9jSy3OD0SqR643YUhYiICrHvbWdZUggcSPyH6Hts+tPSmflZDkF0JsJwvse2W492RHIogA9gqCDcEfGWIpIeMsKu//Qis3hNhYgxdU3iF4/UtDOxUdbAuIP0zdq1A504YMBrOX/DhGupJVc157zwML7yQGofQYDx/iJBEWFZNY60xZMmZk3qUVYVVAksK596zhQJtBM9CUOwH/wjM7SpItxqG6BzM7PZjsOq3hnsiXluhnkzZ7b4Xsfze+RWs0tGTgvNlhJ8TPu7G6y3CjzOACp+O5GyKZA94mSM9Gj5HYSZb/vIvlonaCDZdYduFbToa8Aa5/risIHTVKwkW2+ejJS50g00XXJuCmHAk3mIcWw1DcgSut8NRwoW5yPuK662Ydbao2BQ27gC3VHhcKndgWBFY262Q+LpkVfmCE+wPq2eLKocbatZDh45QVkbdxviQiANLKg/WzL9QkI9t3z2IrgpgSWG/FXv8RPHQb78dM6x7tmHvXuhbIz0Pt8wx95eKwJJpALuPiH6PTvLfLva3ckHoI8iLimNxlFiNYYouxBRvd8NpPxt3pDjh3QaY1YfTBWR9gI08Y+7KDGTlwX9n+bsmGxcNAPUEzplZV7ZG5s1kIUaVBKt4MUVhfvPNJezGLjfGx5fI/4x3/7AnVnjfRH4aPunDYVh5qcmyNcq81XqATA/UqyJYUzRZTnSHor0N/tBDYhA6y4sfIO3LfZMUjOtSSbDGLkdKHg79Xt4Svy4MrNX9fwzWRh1kJ2DOkJKayX9ATw+m52BkiKuO7BEEz+yxZoZIsGo0gOUjpvBUW303vBnD9rEufFqdSLAse8Bdlz2m0O8cfEyRGIt0b3gdho0iM8Ouy5ga47qcc6jdHyHlMVMhBuVprEKHvfDF+f5s/cXLsUKMOOAsBzKwHHoKk56NRTzypDhUdkawMpuTcrkp7q2Blz58udszRMhzFGQi/CqeTC5vO+5Ja2BvBtXOaNaMZfJy395Ks8qmsGVffMmHxTa0UEDPkfichOuHy00sFg1WbUyZBZXWUGiOPpMQloobp8vdoeR7sIbOQ0IBzPeiaWM0b44WLSAvGObWqsteq4xEYCK2TWCn6smJWAldAysOs4ct/KWBhg3YVS2aQ67sysjWI9mnzBYdx6pRH3p3kB/NltI3asyENG+KGtLCJOnTd5Hqj/Z1Koy8GxXtanxWsAbGm/OxTgpWM0sh0BcZbrjSHsYKuDweaVnlP0CAbXbVAs/WwLYVTBVwXgX+Tkh5DSt5gQNXn529OBG56ey5S0bNca5mOXs3cFRZ98LTJTivwITYDkdsFCKMWLxUr+gOOcV5YT7yY4WmsBwfizMVtnfxJQohwUiOheEu4d7kVQ2QTvqdrbL/Go7oKFifKHc/jwrBqondFkiIRmg4W++mvxt1ZSoVIJWCyWP2qISgQAQFIzQUkV9wWDC4HLkOkdwP8gVJKcyqfAnHllkict47wDUUWakICEBwMMIi8MUP88tGKJQnIiwJ8/uJBKvzBGTksAdB+PkjJJQJ+fQSqoLs/yac1owULoyu7JQOB433S4QVbQpi0x+BT5Adg5QwZHxG4Cmcr1PokpcD1sebyOTMaAiyotlDKy+3Exo1R02kfUXaF+SmMl8lPRxPh5SzSocZ5d4Ic0JGBJKD2fYhvsdKnjZQPAi4uhiZIT8KN7TpABUVtG4p0ZROo+ZQVkF7JTHnCqVroUNn5mC1UqjSlE5jBbRWYr5Z586sKHeGgmBpfp3GTFinjlBqhXYdWX2T+iLiWDXQvCVat0bHTkIh3CBEvuzfl2xttFT8Ro2V1VhyaKWE1m2KJHRGp3aoJfjrqFGbnaolXcW5QvNmON+ghDMDWfbApgvKsG5VstVHuc67vjRsOsNWGbbtS8IN7CFQTVmlTQdYtmKiuNfmcuXvNsMsaV3YqgjaKwmXE35zeyZ1YNkSprL8YopqPgltVOqBKD+chC5uKUpC6bOi5gq//7jvd4f778pukDzRL1Owv7iEQt4Idj6WNNHvfz1t5qHkvyKRhYAMSSS4ENUgVaIoQd662CWIaBdRrAQS4gTLAAwlEBJD9IWon5dkYOE8nZ5JAZKBlaJLB9UpTxKwXObPd5o2rarlw8yZ+sOGHR4w4OOsWWJcXlhcNTT2qqlZjh7tpqEhnoQPMzSsRo1p0VSuRYvmkhwKCgp169Zt2bJlC3EFcdc2btxYXl6+hfi3wi5t2qTOxX2/uJnPcDKaJk4xnOZiprFpruqNY+Pdzk0XT4iz6fTHOlP+1Oj+1nQ6J1AMCS7m80nv4sXTVlZVLtbWp83MtE1NtbkXYlwuKNy1p0xMTpubnxZbiLXNMaNLLq69Y2IoOlr8EhREu3ZRbKz4EuLiyM6ODA0lEsJ9C2fnvse0L2sbWp82sBK3WJ/WMT6tb8FeiC3BwOqUjpG2uBL0zl0kM1NTQ339qhYDfX0jQ0OuGFT92m+EGBoYSCDB4Iy2RVhYP4AkKZmZdPQoSSjkzRuysZFUSGjooDNnLAwN9bhfVrxiYKBvZMR6RmwJhcWYEyLutWbnTOncuXMG1fgw1Na2CAhQk7A7U1Lo4EFJmXjxgs6fl1SIv/8A7hsZGupX504x4KDiweLB4sHiweLB+g+ClZtFb+7Qork0ex7pXaGcUqcC3tAfC2jWLNq4h8JTKgIrM4VszpLGDJq3lG69/rb7H1+ibXvpa9IPwEqKokPbaOZM+nU9uYZ9KyQ5jLavJ83jFJfNg1UdwDLbRW1USHMPbVxGckTLj1KuoP71FWpcj5aspb17aXhXaj+EwpJEgJVOf8+krgNp9176XYNkZcjwufBUVDCtmUQ1iOSU6OPnisBKj6RJ3WjUTPZxUwZQg3bkVLb94YVE0tRMlQJTebB+frAKyPUF+X8Vvj06n6gZeSSw1yt705A/hfUJntSqFp1/Wz5Y+an07BHFZwje5tAUFRr6q1D4rt9pymq6dJYUVcj7a0VgpX6lp0+ETOeGkhLRTuuSs953SFmVDm2njv0oJJ0Hq7r5WDcPEcmTcwx7vWMKdZxAifmC0IA1NWhAz4Ir5WMt7k/DllGBAKwMAW0Bt0mh4w/AKlPiqVMd2mNbBG4SqauS5iV6YUpKPXmwqiFYq4ZR27GUXiCwYj40nlNa42m3Jg0cQDrXBKyIAKsgh4IC6dMn0t9NnfqRo0+Zs143KgVWZioF+JOfB/01n9SmUXCR5bXeTR2GUBbH/SlqxYNV7cDyuEG1pOjM7ZKaq0eoTm1SbEydh9PbTxU577khNKA7tWtHdWrR4AUUniAOWG4OpNyO2rYhkqLVhyhJ4KQn+FLntnTNg722O0NKvSgihwer+oAV5UHKDUhjK+UV+V5G20mxC9m7UmwEbZhO9ZrRfS/RpjCP4mLZ/Iy/Ew1qTj3GU2R2lcHixqexMRQbR89sqKUszTvAxK6dRP1nkm8A+frQ2a3UXJkcXSghjQerOoAV60cDWtPA34QeFRujBVCLGqTnWNQmn8Z2oUl7K+VjPT9LVIcelbKG3jcZWD6RVYhjHV9MdbtQegr9PpO6qFCnjtSpMzVvQjI1SbEtXXjBg/XTg5UaThO709h1Rbqq0N0JptYy9OfZojZhpNqcfj1TPlhRwaRnQTGZwlHh9qkk34k+xZc0CLlHLVUoMKEisLxekvEtyha8zo6hcR2p5zzKLqD0NEpIYCUxiS4epda9yCOKsnN5sH56sLZOJu4YpUHLf6UFC2j+fDr/UOAyHyH5RjRxFi1dQn1VqN9YCkkoH6yUCJo+hDr0pBXLaOIgUmhDZo+Ep86fogWLaOJgFoKaMI2WrCK38PLBCn1DXVrT0HG0bBn170hdB9OLgG/V2JWj1KAThWTyPlZ1AOvlPbKyImND0tMjfX3278siX8rnHRnoka4OXbhFybkVOe/ZaXTHgs7qkKEZ+UWUEn6fXW5oQtZWZKhP+ucoNEGkKUwMIVsT0tEhMxtKzCjHPoZ50/U7lJrLg1Xdwg38XCEPFg8WD9ZPBlZoqKRgZWT8C4l+r1//W4l+lgYGPFj/abB0dS3u3FF79YopDLGLoyOtXElv39LLl2JKePeOdHVpxw6Gl9i3wV174UJXLa3CvFoerP8oWPr6FubmamZmzAyJXQwNac4csrAQXwJ3LUfVqlUSCeGKllbHEyf0jIyMeLD+w2CdPm3x5YukprCggOtRSa2YiwtdviypkMjIwWfOWPE+Fu+88847DxYPFg8WDxYP1s8IVnYyPXlEj55SUFSZ+rw0evGEHj4iv6gfgxUVRg8c6ckLikktU/81hB7cp2dvKCHzx2B5uTMhL5yEqaSF899+nvT8KT16JCjPKDaFB6s6gPX8GvXrSQOGU6/OVK89XX5aNH/iShP7UHtVGt6fGrahS08rAsvmMHXtQMPGkEor6jyIXCKFE9LH/qEePWjUGGrVhHqPIb9okWDlpdOBpdS+C40eQ83r0fgVFFWY0JdGQzpQy840YiQNGUJDxtErfx6snx+sArp4hoyuUVYupSXSfDWq3Z3CMgi5NFeV+sym+FSWJnVqFcm1pdDU8sHKTaITmnT3DeUWUKw3dW1A6v+wdNPsSDqgSc8+Un4BBb8hRVkau7Ekh+IbsBICaNdW8opgjT3sSJpI20FwKpX6tiXtW5SXRzk5lJNbksjKg1VtfCy7wyyV6m0sZfuSgiyZPhPWpwWTchMyeFwpH2vNCFKbTfnf58IPoPbjKaUyPlY29alHf5sUgdWG9B/wPlZ1BuvoQpLvQVF5lO5DzaToxN2iUwmk1om2mlcEFqdRcnPJ8wl1bUeHvwtQ5cfTkLY0aXMJcN+DVVBAeblMQdrpU4uO9NBHCJZqc1q8nRwcyOERpeXxYFU3sBL9SKkmrTwleJtF68aQvDIZW9HFC7RlCclI0xYz0TnvYTRhOA0aQPVq0vi/yhH+0JBIhq59qMh593hEQwdR/54sP2yPVVF9JmmupQnjacIE6tyc+o4j53AerGoEVib91odaD6bPRYlQGfG0ZyX16U0DBtOR46Tang5fFb1KJ40e3aeHj8noALVqRr/uoYyCkrPRH6hjDZq3v4x7VE4+ViTdv0ePn9De36h5Czp+rZT8wgafaWwnGrqixFHjwfq5wcqi7eok34GcI8o3kcm+1L4RXXGrlI91eTtJN6DXRYsQEwJpoAINWUyJeVWIY20aR43VKLHg2/rz/1D9HhTPg1UNwMqnI8uonSp5xpZxd0q3ObSIdXNsnojU5ETyKbXVgi0HVkN6J6jJ/EyTutLEVT8OkMZ8poCYkrcbxlHTAZQE5nWVvmrlCOo5U5gaz4P1U4Nlto35NIt3kK0VmZuT6Tly9qf8XDr8N500IovztHEJyTegG84i41jRPtRbmRZsIEsLOr2P5ImW7GHrSzPjaH4/Nsw8YUxWFmRmSucv0Jek8sFyu0HNlGifFhOydSnJyNBpe1Z/15gWrhHkMpjTunlUvw099uV9rOoA1qktNG4ijR1Dw4bS0KE0YCAZCgaDN3SpXz8aNJDmrSSvkAoj73n06T39Oo4GDqLBo8ngGmUVCHPYf5tNEybSqBFM+OCBNGIqOYeVD1Z+Fj25QFO4EcAgGqVO912F9XHhbOgwYBC7fOZS8ozgR4XVMNzAzxXyYPFg8WD9ZGAFBkoKVloaHTokKRMvX7L0UQmFBATwYP0cYJ05Y+Hurla4l7XYJTiY9uyhwj29xRZib08mJhLdBlfc3Pppa5+v5inv/xVgGRpaHD+uduAASVI0NWnMGLZQhzOI4kngrl2+nGbMoMOHxb8NTmtu2KB09Ki2sbExD9ZP4WOxNAEJSnw869TcXPElcNc+eUKWlhIJ4YrAx+KXf/E+Vqny6tW/4GMFBvI+Fj8q5EeFPFg8WDxY/w5YSYlsA6qC71fTp7K9qbLzKgVWQjwlpXxXny+oT60UWHlZ7ONSyttqJj9buEsWn0FaPcCKCWZzc63bUitFmrCk1LqJfLp5llTakJIS9R1F9z9WBJbXK5o7gRSVSLEdrdhJMUXbhLo8oqkjqZUStepAm45ScoVgPb5Mg9WodRtSVKbj1my2seSJTtdpVC92k4qKtN2UB6s6gGW8nSYvoncfyPkhqcrRkJXCFTL39ahGLTK4Qe7utHka1WxB7pEi9nlPorUzaNUe+uBODmbsKQRrDQWLf6Jo6RT6+xh9+EjXT7PHCOy9IhKspACaOoiOWbGP09vK5sUvuxQBZ0byNWinATv19hlZOlBeAQ/WTw5WAUt6KX5rvY3qdqQoQYbWmHY0a7+wPucLqSrQP1YiwMopYwFXDKV+s5nBKsii5FIWcHoPGv+nSLByMiiteJ/tNOopR5uMBbmpcdS7Mf2uzftY1dl5Xz+FVNSZDUr1oeY1Sfdh0alcmtWXftn2Y+c9J4at1pq791t3LSWUurektbqVct6/OFEDOTIS7DfpdYvkWpFzFCXHs12ZM3N4sKoLWNlkY0KHDtPS6aQyij4INs2OeEmNG5C9e6lnCwyl/guEuHwPVl4cnTxMhw/ShEE0bCnFFnV/xhc6tJ8OHaARfWnK+pIlOuWCFeHNWh7YSV070Wot4eOiHI2pviKtXU9qyqTYgnoMpIcePFjVAqwsOr6L5i2gmROpZVvaY8gW0oQ9o0YN6I5nqUVdw2nQUpFg5X6lP5fR4iU0dgi17Uy2RaouLYiWLaIli2lEP2rfm269qQisACf6dSEt+ZX6dKB+I+iVYHPb+8ZUQ47WHiRPL/LyoF/Hknxv+prFg1WtTKHNfpIiuuVNKW7URJaMnpSYwjl9acTGSsSxMunvcVSvLfnEl11tkUxLB1KznhSe/mNTmBpCv7Sm7rOY0npiSvKdySdZeMrvAdUlsvfmwfq5wSrIp5z8kh6N/0jNiI7dJCSTcn1ab1yyrrB3K9oiwnnPyyuzPPWFDktHfuLH6kt7Wjd3U60m5BYhwnkv6zydWEK1O1MCpzsfU436dM+vKK5xi2rL0LNQHqyfG6z8dFq9mE5epahY+hJIa8dTvVbkLthhQWctNexAb30oNopOrKDmbcg3rnywPnvR7IV05TUlJtAnVxrVgVQnszU5we9p1gK660qJ8SzQ1VuBhi6klLzywXK6QeoryNmPCXG2I6VaNL/wI5JpYkcauISCvlKoD03uRb3mUwbvY/38ptDekPp0o169SVWFeo+kR0WB0OwE2rKAlDpSn17UZTA99BQZIM1JojOapKxIan2pczuasJi8BQt+MmPoyAbq0IbVd2hHM1ZTSLJIHyslgv6cQV07k5oatW5Ff+4retQFKPAdDVGhLqrUrSONW0afYnjnvZr4WFmJFBpCoWGU+d06vi/hFBxKyTk/ntJJjqTgEAr/+t08zxcKCaGIyEpN6UR/Zo2/xHxbn5tGYSEUFvFtFIMHq3o47/wkNA+W+GAFBf0sOe+Wlnw+1n8LWGfOWHi6qyXFkSTlcyh77KqEQu7dJiN9SYW4vu976pR5Nd+N+78CrPPmFsNGqzVoSI2biV8aNSW5utRYQQIhCiTfkOrKSyakGTVsWmv/vgPVvFOqP1iGBoYWRha99qrRJqK/JSjriYYSbZNAAnftIqKJRNslELKJemr2MTcwNzDgNdZ/HCxDC7XjanSQJCq7icYSHZdAAnftGqKZkgnZTwO1BloaW+rziyl+CrCOqtFeon0SlJ1EY4gOSyCBu/YPIg3JhOyhAUcHcDqYB4sHiwfrfwesPUQ7BE7PNsGLwlN7Bd7PtrJl14/A2lvUck+pmp2lhO+pBFi7BY23U8lNapZ3DzxYPzVYe0lqT93hl9YbupoYu+hvuj6xzi5B9x9uv+OVkbGLcWExctbXfnty+YVBrI8r0lhN1j7ROv3m+JAzdRkfXM0OmeG2C/VcTE3dDNZcmlhHs4gtUWDtJnmtXvten9J6sq7NESnWeBcpnBqk+VLH1M1E5/WunqcbC++BB+unBmuH1MonNtGJHtoPt2s5Xc8ryNC7O1uK0xaHWq24t3vf0z17nuzZ/Wjn/ldmWYDds4VMkYgCaxsNvnYMgmPD+Was+zWl1W/rJGVEWb46cPDZ+YTMjMvPVtbUFKiicsHazwmR2vTuIROR5jbwpDT3cQpnJjknfn7kYbTNYe/7pOSoSIduR+SEdPJg/bxg7akx0mKa8olatJVos9Rhb4+smFut95Q1hRto0NVjuVlBo0/JM0u0vzywNEnu2ID3iaEnX578lJqxngNrG9U/OcovI//igxksurGRpjlaIytk7OmGjLlywdpBHc1XhSS673lpExf3pp+WNPdBzbUHTDHrw8zoBmpluCQbeXtt+7Ab4MH62X2snQLvR5NFhra4vsuOvt5yd5H+2F/YRtE+LsP1406ZHaJ9rG203e2du8cBRd3JQVn463xTTlr/K9vTClJnnZVlZnE31dWelVqQtM6mJ/u478Hi2uxtbf810vSeusrlY6lJLv1OSLPKPQLEudv7h+R0pqUgW9NKlQerOoC1v3anMz37nVWbe+eEV6z7WtshJU7MPtapahf2Ij9hqUlrYXd+D5YmKZv/FZcZ9Mvxug315oRlF6wXgKXhaJCX5ax6QKD/dlOtY8MCCvK07cYzLfg9WNtptqNNfOy9lttpoJ1BejFYe6n+sbZqOmqDjCZZB7g9dD/R8oAsbwp/flPIuVMdzAPehyaFpOYVJETfHX6mRWnvmHY2Mg0ODQsxbbSz1DCtNFis75VufA42c1CnddRQf3ZIVsEqEznOcs1/bJOX9rzTfsGFe0j2mJpnbp6e/USmgb4BS5PkT4/1Sg5ZadKGE6J282xaolOPQwJFtZMG3zwSmhQalhwLZOrdnyO3q+hOeLB+7jiWlMwBWZl9Uk2P9bYICshL8xzK+VK7hQApmS6Nz8eBy2q0o7w41n5mRqfds8hIc51m0Kufdv/JV//5kl1w0m5Mx31NZz8wKsh1739IqLFqHx8dipwjN0Z9CxZ3dld9LV/3sFCLwad799fu/9uTK+mpnkvNByodrs/GrQdkauyXkdpdb9Ktg9zNWD1aILWdB+unDzcIHSzu9VZS1FucAhy5NIj1PQfNdql/Prhlx91vvV+6JAT1DVi7aOmLqzHJgX7xAf4J/qEp0bkF4EaCRvdmDbj4VxZy5urIMJdfk+qdXZiZn/SHZZdvfSxO8oF2xn7vviQFfkrw54R8Tk8pyM+KSQ765+IAzrUSRtf2sxGAXtDnxAjbppo8WD8zWHtI6kjbP+5u6nuiIW1hYC15chkFiXMMFAXBAmqoPTEyHxb3pjOvaL/oyPteVmQ4paIppWSyKCwLG84rcEqlwalRPhm4+mQJBwRtrfW389OUuBddD9Zk6vB7H4sJkWJCdkoNszfkfKz+J2SkdlA/21//sB1eOFfd8NRojzS8dNlWs5B7HqyfFCzm+jTX9f4YlfjJwffOgzDXpOwEk/tzaxY6MTuk1zs9RabfiBN1y8S7KwiQ7qTW55ZH5WOLRVOBeyQzye5YYnbyqwDHxyHuiWlB6y1VhCOACiLvO2jE3fN5qe6DtKQ5ddX/ws6vqfGvQ57c9nXwT4kNDLs6+GR9oaXmwfqpTeFO2RG2i7c7bt/msHmkjqIwBMr0R+0xFxbNshggrVnpucI9VOd4p/lXV3TXqi00ndtJxXDiFscdO++uVT3VsMRRqwCsPdRcZ+jSS9ObHpRit8EpTq3eax22bbu/fc3lKfX2EB95ry7Ou8CJ+UdQdpU1eTuojM9emUnoPWXnCvcLQ1Cs7K70JPSusnOFu4skbOcnoasXWHx2Aw/WvwCWlhrrziMSFK5TxxFpSSCBu3Yt0WzJhByiwacGWxlb8WD9BGCZWKhtUqPFREslKAuJ+hAtl0DCCiJ1QX7zCgmE/EpdVnYxOmtkaGTIg/UTgLVOjWYRzZWgzCTqQbRAAgkLBMnNAyQTMoc6Leqkr63Pg/UzmUJJyt4iUyi2BO7aP4nxLYmQgzTo1CA+55133nnnnQeLB4sH618Aa3dRyGrXd0GpwvqdlQZrZ6nE+dJxqZ2VBqswTX7nd0JKT2vyYFUDsDRJ7rjyNNtZM23Ue5xsXEKAJskcaD7eWmPWhZmjDHuQqLSZMoDKqhqNmmg+utXRGiWNt1Njre6jTQfJ75cpqRQFFptzbDDEbOIYk371D1Dp9J6aB5uOOD95pFHvOvv5tJmfH6ydUiMv/eMeH/Hp64dPibHxKZ7LzHoyrbCLWuuPf/I1MCLB1+2rd3J2vO3zVbV3VwjWTmpmsCA2H0DWGvMmVJjbrll75u2DfikJGYmuA4+UmnMUBdY2Gmt3Mg/ISXw5QEuainNZ/6GZD8wLgPjoe90OEz9X+HODxeZbaq58cOSvSyNYhtOutteikqJDzZswy1XnlH9wWJh5M46PLTTm+uFsZC/WV2K4lJvzzhnN3c2tQ3xeBD36nJ7Oct65Nnsa7HB68jXmiaX3k4R41wGH6/wALE2qc2Koe3zYHf83SXGvhRmkgvpmZ6d6J4XdCXSLjHrUlQerOphCKeHE3D6Wl7L81T0k3G/PvJwmV6JSXrlsoc0snaatyeKkgvxfDUSDtY0mORh/ibzR3Xi6f2Y+y3nn2uyX62c+uu0+2a62+5ISvQYcqRAs5kLJ7fNweu22q8+Vw0kJ70ty3nc21AvwvPN69cjbJlExz7vwYFUPH2uvcNK3+ZlfnsXEXX+5RnYnUxLDr+2Ly447e3/eCKPZtyNCHjhryu8ucm6+AWs31T0+1C89ZZNZ+wZnNcKywXLeNUvWmva/eiw50fMHYO2gHhYb4zOChx2R7n1dtyTnfQcNuXQoMcW9216a5Hg5LpYHq1qAJVibevLj3eehz4LSMkOCz7XdL0uF+VhbaPY9I85jyimAr//ZFrup/MUUbKFY7f0e7z28jtT4m5oaLgjLKlhn3qh04x+DxbIh2t6JibRyVKcNNNhe///auxKopq40fNkHIQFE1IJVkQEB10pFnVpGxwWlrq2jjrS2StHRqVTbgoCBJC8hhC0gm0CIZS0VBBUBZVHQTkEFwo4sAkFAtkCAAGURXt/LIosgDJw5J3hezj0n79zk/Xnn5Dv//9/7f/f7ezqyN7igqJJ2WpPV3uoVtxVcBAcfxHBbM/SoGLAkH1jIBYTbzDI9GPLZV7G2pR2tuRWBH1JkEQe2NdKmoqPc5/7pQze+z2lvLK6MMHAWnxQdTU22B+vDrF51FvydLoXEzUX+R2v6hs8z8SMUlymBhUZeOfP0yOraXxbaAcSI8S1vPu/pehqSsytYZSUWV3jjbND5fSk3Wloe6pLE2yIYsCQ6FBLEm1U/AKOwywMwbB2iLwWtK+rti0jaJ6Qsq3rtqewdjkg5KKJnjQXWdzlPBvvqHnMyHtVmPGuq6BuCq1ue+Sabv4mGxkJgOc8boWSNBhYyCenENze3dz7PqEGMpBe2Nw695ufXp52OPpbc2NTcXpjOycioffS8gzs42MmuT/+GpSdcdWLAkkhgEYEUVXW1r4GcUHXjB/BRuD0CLKtgHQWvg73wH9bXDdBDzNZIsNNKb+WlZllOACwi0PJav4O1c2+omSlrt3mCU9PA8LXko0ae2kL+J2LB8BcKrz1vtSMaXifQbkAPSiga+m3eeX23GWIkePfF3+/2dpdZRe1Z4aa52m/TruumZqF7TYNNSbkZvI78MxG7ltNxqB3MY0kusCCdKE7tb8XXTv365fkkYmVPV0G5zwdEKUBaGlRd1cnPtb5j8eWNU34l/+3pKfun3xJRDBqXvI/yeQv8jrXC8AWmIkr4JCpsDDlsEXOSkpMGD7Y53T339a+Hl9EF8fTt5P2K2MglYHwnCO4pWuck3oIXz+9Pu93bkaXzhp2MAUtyQ6ED0PLY4vwsLLEyMbEyySXpqDpRRrjIl6cu+S49IKkyMaEyMTrP18Rr4Ug5ZdKdd6DubRJYGPuZv0DlwRFnmeGPWE4oj497fiuhIjGhJGirlxr60TtKOgSgH3Y2KsdNx1lqzJkzAtgUbR36lLqECrCT0BIPLPIoV2E3VsLKYew8YXq1QuJYI+OM200lYzT6pyect8dqhXMleRcfDJyY8jDhR+9mNxAnun2cnSnZDcRpzGPAkixguRgBaNbitjsAoM/CAnLvvwVMVPrsxG1dMXFbCQFWQIgRxQjdZLKfxUAWdybCYstMB3LvKQD2z86ILTAiGf3s/7P/HH+9F8BihhidNAKfArB9FgNBlbbAac3YAnLvxwDoC5jvMzayDWjt1PJ08wwMDMSAJRmhkIKenZr5cBTrvM/Ywmid9xkbgcBmdwHn3Q8LhRKSvDtOlFZPf9gJknfqLCxQxcn7bIw4AGMalrxL8qoQ47xjwPp/bTc4CLX5pjf/bu2G0d8ni2cc/hdgjfu+w9hBxIA1J4CF8kWlVCA1NUhVlgBG2MCCygkeUkXm5Qhj/+nJGwjIk3BqEF6OJDUiK0KQn48YJyuNYc2/U21GiayKJyvLiGak55FwqpCKCqSiCqmqQjg5kjQGrDlQ0lnsuZlRkJrXyC5oLkot9lxFxwsdgwKkaZcZW9icx24uTC3xXeWMm6IzBXIXbX1CQ0lpC/t4oEBzm6iwLdzyRkUmYrykpcD74bf4KTnvdmBF0Mmc1rL8qtA1rtKoEZo+qyKvoImd25jLbmKz6+/t9VmC0WYkG1iogqisTdadtHzXLZ5/NQ46Udk39CyPrGAnEAUtzWvvzDwUsEHXe1dcE5dTHTh/MgapiO4nf+nJvbaetr7BAZRBagsU6UZ3a564JJrr0HQskoMGYfh60hcy7xBeQyPvoqia8mY+r5/3ZKMQWM5G+d091+KP6LnrGfqsWuWti6fIYad0JD8UymjQBdVlB5Q+cDYrFeYla18BSlf3NA4PQlEbUM6MDVjOsuwY6j0ZoDlpyxNbsDzYsq6z8EiM5fPuASsBNVmWgtNwUhIdS3TUSuK21XL8VYU09gmBdRnsu8eqqI85EO/R3vb0YxGwNuR0tdgKCTzCkiWWY82NHEvYFAkB0BV1Zs3Lmsqryj+BxYFHeuCOC0wd0X9JW/O0o9/7lrGoBvy2BqmDxq2mpoikfaqeZpx+2OoN511MQ5CGdFK4bfkllHmTtTxB8jn3HVXdHeeZSw1iGN1CzrsAWNldXFrUtvlE9QVUZdGuPQYsSQcWqlis8XWCnUu6c2xNYVXdzY9c1RAwyTmvz+TDpc/dljnhcETc/nh61+sh5j2z8UQ/sbs6lBzewk1ZRgALrp2o7Ru+IOylM8oVGYT8pw+GKdHGIgvjgIXujSk4FecXlFDlfgSfCMRtRcCirbnf0t7IK2c35ZVySzyST6uTMNqM5AMLuaBo2vwWcLMwKuFFNq+7ihZ/WFFQv1sbeq6wva6Z/7K6rSzlRVp7/x/ucRN5LAKYz/hHflu1hb8mOAdw3geq+4Yt/GVQFyj2iLKkFXeaefXVARqO4kA2Dlj2YF2kTQ330RoSqkKz9iaDz8vSFy4qyXLqrlrLGSuWuWt/fpvOHYAj0o5J22HAkvxQKBRoQHMp+dPp0TDMNw9YKmwJgXdeuvbqurVu+gsZnxR1D1iHCDSPyeMbCJzJegwPVrs/hJwf0nzZcbzXww8K/b4NN0GDLKrwruFTXtzf9funHrgRNzZO552oGfeqlc995JRKdX5AC63I7e9riMhy2euvDQijdsJ+Ata5WX80xix2FHW7wIAlocCSIsspkqRFfsgGaPp+1QXD1KhNaNZlL4QF2nbrQHLkcF+OIU1+glM6DsAk2oqZHRiSFxbGDo0pf9z9GmbX3LG7aSYQi1dzKc7k8/N3XV00RixkHOcd0jh9H2LmsELzw8NyQ+/VlQ32c1NKw48H66MU5zdwtAZQUTGvLhRrICDZwEIbCOgFlaRdublXGVLScFvN4nCGurI3us4DJM0jN46soCsrUXA7ogmtAwPMhM+lJ+v+ZS9WNb4IlH0O1w/CZwJkwI9Aiqh2OScFHqozD9aVISqq0FVUaDg5SGqyA6siI9+DdXHeA525K8kokrZEWnwTvlmJoqREUTaNI/MG+6DYbVJY9y9JD4UExX/Fu+dzq+o6XzbwG/I4sYeR6IMu3D5wKsx8xa+v7ax/0com3f5CwW4aO+9XgGbg8dz2hrMsdcTnLfY5mM1raezilHErOB2cl10NL5vSdvmoT8F5twebbjM4r+5vQJJ3O/C3iEuCx6tFnqSaW+QYu1/GHlObmRM5li1QpmkZMAwMPPRwRPCmFaAMpKaPTDIMNZ3moZGRNK2SjiykvMxVR4WCKhbJktFrXXfdlR4rBcNgpbu2MiQzaYdVsZG/UBdouyxRIIt+C0/70IChr88wRHs22b6nRWgmk/m+AUu4lSVonjPmVIyjeNJhbFeBKQ9TEEZ1LCeIEzXhIEyyKny7kk2Y6PHGPcn7AiwEVCAkJAR5C56bL1YwK5IVacIwwdPweOdZDDIevw+Pd5+FBeReKzz+xOyMOOG3M7ZHXo9kBs/VfwR5IXBCQPUnAs8Qbn2QZ+cAAAAASUVORK5CYII=\",\"relationship\":null},{\"partUri\":\"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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":879,"title":"Perform Rubik's Cube Moves","description":"A standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face numbering.\r\n\r\nThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\r\n\r\nMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice. The F move would map 19 to 25,..., 7 goes to 18,..., and 23 is unchanged.\r\n\r\nThe moves X( R ), Y(U), and Z(F) rotate the entire cube with its associated face.\r\nX would map 23 to 14. (19:27) moves to (10:18). Only contents of 5 and 50 are unchanged There are also X' and X2 moves.\r\n\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/cube_small.gif\u003e\u003e\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/Cube_Map28_200.png\u003e\u003e\r\n\r\n\u003c\u003chttp://mathworks.com/matlabcentral/images/surf.gif\u003e\u003e\r\n\r\n\r\n  \r\n  \r\n  Input: (mov,rubik)\r\n  mov: is an integer 1:27 representing the moves in order: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2XYZX'Y'Z'X2Y2Z2\r\n  rubik: row vector of size 54\r\n  (A normal cube would have values 0:5 in locations 1:54,\r\n  The test input is generally numbered 1:54 to check that each tile is correctly remapped. A normal cube with 6 values may be used in testing)\r\n\r\n  Output: rubik vector of the input cubes values remapped based upon mov\r\n\r\nAll 27 moves are enumerated in the test suite\r\n\r\nFollow-up Challenges will be solving the cube at various move depths for time and actual face moves required.\r\n \r\nNote: Images inserted/linked to my free google web page. Used a gif and a png.\r\n\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003eA standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face numbering.\u003c/p\u003e\u003cp\u003eThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\u003c/p\u003e\u003cp\u003eMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice. The F move would map 19 to 25,..., 7 goes to 18,..., and 23 is unchanged.\u003c/p\u003e\u003cp\u003eThe moves X( R ), Y(U), and Z(F) rotate the entire cube with its associated face.\r\nX would map 23 to 14. (19:27) moves to (10:18). Only contents of 5 and 50 are unchanged There are also X' and X2 moves.\u003c/p\u003e\u003cimg src=\"https://sites.google.com/site/razapor/matlab_cody/cube_small.gif\"\u003e\u003cimg src=\"https://sites.google.com/site/razapor/matlab_cody/Cube_Map28_200.png\"\u003e\u003cimg src=\"http://mathworks.com/matlabcentral/images/surf.gif\"\u003e\u003cpre class=\"language-matlab\"\u003eInput: (mov,rubik)\r\nmov: is an integer 1:27 representing the moves in order: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2XYZX'Y'Z'X2Y2Z2\r\nrubik: row vector of size 54\r\n(A normal cube would have values 0:5 in locations 1:54,\r\nThe test input is generally numbered 1:54 to check that each tile is correctly remapped. A normal cube with 6 values may be used in testing)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eOutput: rubik vector of the input cubes values remapped based upon mov\r\n\u003c/pre\u003e\u003cp\u003eAll 27 moves are enumerated in the test suite\u003c/p\u003e\u003cp\u003eFollow-up Challenges will be solving the cube at various move depths for time and actual face moves required.\u003c/p\u003e\u003cp\u003eNote: Images inserted/linked to my free google web page. Used a gif and a png.\u003c/p\u003e","function_template":"function r = rubik_rot(mov,r)\r\n  r=r;\r\nend","test_suite":"%%\r\n% Single move cases\r\nmov=1; % U\r\nr=1:54;\r\nr_exp=[19 2 3 22 5 6 25 8 9 12 15 18 11 14 17 10 13 16 46 20 21 49 23 24 52 26 27 28 29 30 31 32 33 34 35 36 37 38 7 40 41 4 43 44 1 45 47 48 42 50 51 39 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\nmov=7; % U'\r\nr=1:54;\r\nr_exp=[45 2 3 42 5 6 39 8 9 16 13 10 17 14 11 18 15 12 1 20 21 4 23 24 7 26 27 28 29 30 31 32 33 34 35 36 37 38 52 40 41 49 43 44 46 19 47 48 22 50 51 25 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\nmov=13; % U2\r\nr=1:54;\r\nr_exp=[46 2 3 49 5 6 52 8 9 18 17 16 15 14 13 12 11 10 45 20 21 42 23 24 39 26 27 28 29 30 31 32 33 34 35 36 37 38 25 40 41 22 43 44 19 1 47 48 4 50 51 7 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\nmov=19; % X\r\nr=1:54;\r\nr_exp=[7 4 1 8 5 2 9 6 3 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 10 11 12 13 14 15 16 17 18 48 51 54 47 50 53 46 49 52];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\nmov=22; % X'\r\nr=1:54;\r\nr_exp=[3 6 9 2 5 8 1 4 7 37 38 39 40 41 42 43 44 45 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 52 49 46 53 50 47 54 51 48];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\nmov=25; % X2\r\nr=1:54;\r\nr_exp=[9 8 7 6 5 4 3 2 1 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 54 53 52 51 50 49 48 47 46];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\n% Remaining CW Face moves 2-6\r\nmov=2; % F\r\nr=1:54;\r\nr_exp=[1 2 3 4 5 6 28 31 34 10 11 9 13 14 8 16 17 7 21 24 27 20 23 26 19 22 25 48 29 30 47 32 33 46 35 36 37 38 39 40 41 42 43 44 45 12 15 18 49 50 51 52 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=3; % D\r\nr=1:54;\r\nr_exp=[1 2 43 4 5 40 7 8 37 10 11 12 13 14 15 16 17 18 19 20 3 22 23 6 25 26 9 30 33 36 29 32 35 28 31 34 54 38 39 51 41 42 48 44 45 46 47 21 49 50 24 52 53 27];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=4; % L\r\nr=1:54;\r\nr_exp=[3 6 9 2 5 8 1 4 7 37 38 39 13 14 15 16 17 18 10 11 12 22 23 24 25 26 27 19 20 21 31 32 33 34 35 36 28 29 30 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=5; % B\r\nr=1:54;\r\nr_exp=[16 13 10 4 5 6 7 8 9 52 11 12 53 14 15 54 17 18 19 20 21 22 23 24 25 26 27 28 29 1 31 32 2 34 35 3 39 42 45 38 41 44 37 40 43 46 47 48 49 50 51 36 33 30];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=6; % R\r\nr=1:54;\r\nr_exp=[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 25 26 27 19 20 21 22 23 24 34 35 36 28 29 30 31 32 33 43 44 45 37 38 39 40 41 42 16 17 18 48 51 54 47 50 53 46 49 52];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\n% Remaining CCW Face moves 8-12\r\nmov=8; % F'\r\nr=1:54;\r\nr_exp=[1 2 3 4 5 6 18 15 12 10 11 46 13 14 47 16 17 48 25 22 19 26 23 20 27 24 21 7 29 30 8 32 33 9 35 36 37 38 39 40 41 42 43 44 45 34 31 28 49 50 51 52 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=9; % D'\r\nr=1:54;\r\nr_exp=[1 2 21 4 5 24 7 8 27 10 11 12 13 14 15 16 17 18 19 20 48 22 23 51 25 26 54 34 31 28 35 32 29 36 33 30 9 38 39 6 41 42 3 44 45 46 47 43 49 50 40 52 53 37];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=10; % L'\r\nr=1:54;\r\nr_exp=[7 4 1 8 5 2 9 6 3 19 20 21 13 14 15 16 17 18 28 29 30 22 23 24 25 26 27 37 38 39 31 32 33 34 35 36 10 11 12 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=11; % B'\r\nr=1:54;\r\nr_exp=[30 33 36 4 5 6 7 8 9 3 11 12 2 14 15 1 17 18 19 20 21 22 23 24 25 26 27 28 29 54 31 32 53 34 35 52 43 40 37 44 41 38 45 42 39 46 47 48 49 50 51 10 13 16];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=12; % R'\r\nr=1:54;\r\nr_exp=[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 43 44 45 19 20 21 22 23 24 16 17 18 28 29 30 31 32 33 25 26 27 37 38 39 40 41 42 34 35 36 52 49 46 53 50 47 54 51 48];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\n% Remaining Double Face moves 14-18\r\nmov=14; % F2\r\nr=1:54;\r\nr_exp=[1 2 3 4 5 6 48 47 46 10 11 34 13 14 31 16 17 28 27 26 25 24 23 22 21 20 19 18 29 30 15 32 33 12 35 36 37 38 39 40 41 42 43 44 45 9 8 7 49 50 51 52 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=15; % D2\r\nr=1:54;\r\nr_exp=[1 2 48 4 5 51 7 8 54 10 11 12 13 14 15 16 17 18 19 20 43 22 23 40 25 26 37 36 35 34 33 32 31 30 29 28 27 38 39 24 41 42 21 44 45 46 47 3 49 50 6 52 53 9];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=16; % L2\r\nr=1:54;\r\nr_exp=[9 8 7 6 5 4 3 2 1 28 29 30 13 14 15 16 17 18 37 38 39 22 23 24 25 26 27 10 11 12 31 32 33 34 35 36 19 20 21 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=17; % B2\r\nr=1:54;\r\nr_exp=[54 53 52 4 5 6 7 8 9 36 11 12 33 14 15 30 17 18 19 20 21 22 23 24 25 26 27 28 29 16 31 32 13 34 35 10 45 44 43 42 41 40 39 38 37 46 47 48 49 50 51 3 2 1];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=18; % R2\r\nr=1:54;\r\nr_exp=[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 34 35 36 19 20 21 22 23 24 43 44 45 28 29 30 31 32 33 16 17 18 37 38 39 40 41 42 25 26 27 54 53 52 51 50 49 48 47 46];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\n% Remaining Cube CW moves 20-21\r\nmov=20; % Y\r\nr=1:54;\r\nr_exp=[19 20 21 22 23 24 25 26 27 12 15 18 11 14 17 10 13 16 46 47 48 49 50 51 52 53 54 34 31 28 35 32 29 36 33 30 9 8 7 6 5 4 3 2 1 45 44 43 42 41 40 39 38 37];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=21; % Z\r\nr=1:54;\r\nr_exp=[30 33 36 29 32 35 28 31 34 3 6 9 2 5 8 1 4 7 21 24 27 20 23 26 19 22 25 48 51 54 47 50 53 46 49 52 43 40 37 44 41 38 45 42 39 12 15 18 11 14 17 10 13 16];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\n% Remaining Cube CCW moves 23-24\r\nmov=23; % Y\r\nr=1:54;\r\nr_exp=[45 44 43 42 41 40 39 38 37 16 13 10 17 14 11 18 15 12 1 2 3 4 5 6 7 8 9 30 33 36 29 32 35 28 31 34 54 53 52 51 50 49 48 47 46 19 20 21 22 23 24 25 26 27];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=24; % Z\r\nr=1:54;\r\nr_exp=[16 13 10 17 14 11 18 15 12 52 49 46 53 50 47 54 51 48 25 22 19 26 23 20 27 24 21 7 4 1 8 5 2 9 6 3 39 42 45 38 41 44 37 40 43 34 31 28 35 32 29 36 33 30];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\n% Remaining Cube Half Rotate moves 26-27\r\nmov=26; % Y\r\nr=1:54;\r\nr_exp=[46 47 48 49 50 51 52 53 54 18 17 16 15 14 13 12 11 10 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 1 2 3 4 5 6 7 8 9];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\nmov=27; % Z\r\nr=1:54;\r\nr_exp=[54 53 52 51 50 49 48 47 46 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 45 44 43 42 41 40 39 38 37 9 8 7 6 5 4 3 2 1];\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\n% Verify that values in the array are returned and not positions\r\nmov=2; % F\r\nr=1:54;\r\nr=r*0; % The simplest Cube - Solid\r\nr_exp=r; \r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n%%\r\n% Perform Sequence of moves and then back\r\nr=1:54;\r\nr_exp=r; \r\nmov=1; % U\r\nr=rubik_rot(mov,r);\r\nmov=2; % F\r\nr=rubik_rot(mov,r);\r\nmov=3; % D\r\nr=rubik_rot(mov,r);\r\nmov=4; % L\r\nr=rubik_rot(mov,r);\r\nmov=5; % B\r\nr=rubik_rot(mov,r);\r\nmov=6; % R\r\nr=rubik_rot(mov,r);\r\nmov=12; % R'\r\nr=rubik_rot(mov,r);\r\nmov=11; % B'\r\nr=rubik_rot(mov,r);\r\nmov=10; % L'\r\nr=rubik_rot(mov,r);\r\nmov=9; % D'\r\nr=rubik_rot(mov,r);\r\nmov=8; % F'\r\nr=rubik_rot(mov,r);\r\nmov=7; % U'\r\n\r\nassert(isequal(rubik_rot(mov,r),r_exp))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-08-05T05:47:50.000Z","updated_at":"2026-03-28T16:32:39.000Z","published_at":"2012-08-05T19:30:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.gif\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/media/image1.png\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId3\",\"target\":\"/media/image2.gif\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face numbering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice. The F move would map 19 to 25,..., 7 goes to 18,..., and 23 is unchanged.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe moves X( R ), Y(U), and Z(F) rotate the entire cube with its associated face. X would map 23 to 14. (19:27) moves to (10:18). Only contents of 5 and 50 are unchanged There are also X' and X2 moves.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Input: (mov,rubik)\\nmov: is an integer 1:27 representing the moves in order: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2XYZX'Y'Z'X2Y2Z2\\nrubik: row vector of size 54\\n(A normal cube would have values 0:5 in locations 1:54,\\nThe test input is generally numbered 1:54 to check that each tile is correctly remapped. A normal cube with 6 values may be used in testing)\\n\\nOutput: rubik vector of the input cubes values remapped based upon mov]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll 27 moves are enumerated in the test suite\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollow-up Challenges will be solving the cube at various move depths for time and actual face moves required.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: Images inserted/linked to my free google web page. Used a gif and a png.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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\"},{\"partUri\":\"/media/image2.gif\",\"contentType\":\"image/gif\",\"content\":\"data:image/gif;base64,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\"}]}"},{"id":882,"title":"Solve Rubik's Cube - One Rotation","description":"A standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face/Vector numbering.\r\n\r\nThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\r\n\r\nMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice.  The loaded function r_new=rubick_rot(mov,r) implements moves 1-18: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2.\r\n\r\n\r\n\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/cube_small.gif\u003e\u003e\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/Cube_Map28_200.png\u003e\u003e\r\n\r\n\u003c\u003chttp://mathworks.com/matlabcentral/images/surf.gif\u003e\u003e\r\n\r\n\r\n  \r\n  \r\n  Input: (rubik)\r\n  \r\n  rubik: row vector of size 54\r\n  (The cube started [L=0,U=1,F=2,D=3,B=4,R=5] and then receives one face move.\r\n\r\n  Output: mov (A single value that solves the cube, 1:18)\r\n   mov: is an integer 1:18 representing the moves in order: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2\r\n\r\nThe function rubik_rot(mov,r) is available for usage\r\n\r\nAdditional Challenges will be solving the cube at even deeper depths for time and minimizing face moves utilized.\r\n\r\n* This easiest Rubik's Cube challenge is solely to whet everyone's appetite.\r\n* \r\n* The superflip will have to wait for a later challenge.\r\n* \u003chttp://kociemba.org/cube.htm Cube Theory: 20-moves Any Cube\u003e \r\n \r\nNote: Images inserted/linked to my free google web page. Used a gif and a png.","description_html":"\u003cp\u003eA standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face/Vector numbering.\u003c/p\u003e\u003cp\u003eThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\u003c/p\u003e\u003cp\u003eMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice.  The loaded function r_new=rubick_rot(mov,r) implements moves 1-18: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2.\u003c/p\u003e\u003cimg src=\"https://sites.google.com/site/razapor/matlab_cody/cube_small.gif\"\u003e\u003cimg src=\"https://sites.google.com/site/razapor/matlab_cody/Cube_Map28_200.png\"\u003e\u003cimg src=\"http://mathworks.com/matlabcentral/images/surf.gif\"\u003e\u003cpre class=\"language-matlab\"\u003eInput: (rubik)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003erubik: row vector of size 54\r\n(The cube started [L=0,U=1,F=2,D=3,B=4,R=5] and then receives one face move.\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eOutput: mov (A single value that solves the cube, 1:18)\r\n mov: is an integer 1:18 representing the moves in order: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2\r\n\u003c/pre\u003e\u003cp\u003eThe function rubik_rot(mov,r) is available for usage\u003c/p\u003e\u003cp\u003eAdditional Challenges will be solving the cube at even deeper depths for time and minimizing face moves utilized.\u003c/p\u003e\u003cul\u003e\u003cli\u003eThis easiest Rubik's Cube challenge is solely to whet everyone's appetite.\u003c/li\u003e\u003cli\u003e\u003c/li\u003e\u003cli\u003eThe superflip will have to wait for a later challenge.\u003c/li\u003e\u003cli\u003e\u003ca href=\"http://kociemba.org/cube.htm\"\u003eCube Theory: 20-moves Any Cube\u003c/a\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eNote: Images inserted/linked to my free google web page. Used a gif and a png.\u003c/p\u003e","function_template":"function mov = rubik_solve(r)\r\n% Single Rubik's Cube Move Solving Challenge\r\n% Available function to check/determine solution : rubik_rot(mov,r)\r\n% out=rubik_rot(mov,r) returns a moved cube array of size 54\r\n% Solved Cube vector\r\n%[000000000111111111222222222333333333444444444555555555]; % with spaces\r\n\r\n  mov=1; % mov is a single value 1-18 for this Challenge\r\nend","test_suite":"%%\r\n% Load function rubik_rot.m\r\ntic\r\n%https://sites.google.com/site/razapor/matlab_cody/rubik_rot.m?attredirects=0\u0026d=1\r\n%urlwrite('http://tinyurl.com/matlab-rubik-rot','rubik_rot.m') ;\r\nurlwrite('https://sites.google.com/site/razapor/matlab_cody/rubik_rot.m','rubik_rot.m') ;\r\nrehash path\r\ntoc\r\n%%\r\n% For mov=1 solution is 7. Need U' to solve U in 1 move\r\nmov_map=[7:12 1:6 13:18]; % Complementary Move\r\n\r\nmov=1; % U\r\nmov_exp1=mov_map(mov);\r\n\r\n% Solved Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\ntic\r\nr=rubik_rot(mov,r); % Create Challenge Cube\r\ntoc\r\nmov=0;\r\nassert(isequal(rubik_solve(r),mov_exp1))\r\ntoc\r\n%%\r\n% For mov=8 solution is 2. Need F to solve F' in 1 move\r\nmov_map=[7:12 1:6 13:18]; % Complementary Move\r\n\r\nmov=8; % F'\r\nmov_exp2=mov_map(mov);\r\n\r\n% Solved Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\n\r\nr=rubik_rot(mov,r); % Create Challenge Cube\r\nmov=0;\r\nassert(isequal(rubik_solve(r),mov_exp2))\r\n%%\r\n% For mov=15 solution is 15. Need D2 to solve D2 in 1 move\r\nmov_map=[7:12 1:6 13:18]; % Complementary Move\r\n\r\nmov=15; % D2\r\nmov_ex3p=mov_map(mov);\r\n\r\n% Solved Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\n\r\nr=rubik_rot(mov,r); % Create Challenge Cube\r\nmov=0;\r\nassert(isequal(rubik_solve(r),mov_ex3p))\r\n%%\r\n% Anti-Hard code solution Test Case #1\r\nmov_map=[7:12 1:6 13:18]; % Complementary Move\r\n\r\nmov=randi(18); % anti-hard code \r\nAmov_exp=mov_map(mov);\r\n\r\n% Solved Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\n\r\nr=rubik_rot(mov,r); % Create Challenge Cube\r\nAmov=mov;\r\nmov=0;\r\nassert(isequal(rubik_solve(r),Amov_exp),sprintf('mov=%i mov_exp=%i Provided answer=%i\\n',Amov,Amov_exp,rubik_solve(r)))\r\n%%\r\n% Anti-Hard code solution Test Case #2\r\nmov_map=[7:12 1:6 13:18]; % Complementary Move\r\n\r\nmov=randi(18); % anti-hard code \r\nmovB_exp=mov_map(mov);\r\n\r\n% Solved Cube Vector\r\nr=[0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5];\r\n\r\nr=rubik_rot(mov,r); % Create Challenge Cube\r\nmovB=mov;\r\nmov=0;\r\nassert(isequal(rubik_solve(r),movB_exp),sprintf('mov=%i mov_exp=%i Provided answer=%i\\n',movB,movB_exp,rubik_solve(r)))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2017-10-16T02:14:45.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-08-05T20:46:31.000Z","updated_at":"2026-03-30T18:55:45.000Z","published_at":"2012-08-05T22:50:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.gif\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/media/image1.png\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId3\",\"target\":\"/media/image2.gif\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA standard Rubik's Cube is shown in 3-D and also unfolded to identify the specific Tile-face/Vector numbering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe faces are White-Up / Red-Left / Blue-Front / Orange-Right / Yellow-Down / Green-Back (ULFRDB)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMoves are denoted as F for clockwise rotation of the Front face. F' is CCW and F2 is F twice. The loaded function r_new=rubick_rot(mov,r) implements moves 1-18: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Input: (rubik)\\n\\nrubik: row vector of size 54\\n(The cube started [L=0,U=1,F=2,D=3,B=4,R=5] and then receives one face move.\\n\\nOutput: mov (A single value that solves the cube, 1:18)\\n mov: is an integer 1:18 representing the moves in order: UFDLBRU'F'D'L'B'R'U2F2D2L2B2R2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function rubik_rot(mov,r) is available for usage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAdditional Challenges will be solving the cube at even deeper depths for time and minimizing face moves utilized.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis easiest Rubik's Cube challenge is solely to whet everyone's appetite.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe superflip will have to wait for a later challenge.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://kociemba.org/cube.htm\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCube Theory: 20-moves Any Cube\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: Images inserted/linked to my free google web page. 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\"},{\"partUri\":\"/media/image2.gif\",\"contentType\":\"image/gif\",\"content\":\"data:image/gif;base64,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\"}]}"},{"id":1123,"title":"Rubik's Cube: 30 Moves or Less : Minimum Moves","description":"This Challenge is to solve a thoroughly scrambled Rubik's cube in the least moves (30 moves max).\r\n\r\nRubik's Cube can be solved in 20 moves or less from any position.  The \u003chttp://kociemba.org/cube.htm Kociemba Two Phase algorithm\u003e can solve the Cube in 30 moves or less.  The basic theory is that any cube can transition to an H-cube by 12 moves using all possible 18 move types.  An H-cube is defined as having no rotations or flips of corners or edges, respectively, and has all middle edges in the middle row. The cube can be solved from any H-cube state in 18 moves or less using only the moves U U' U2 D D' D2 F2 L2 R2 B2. \u003chttp://kociemba.org/math/CubeDefs.htm#faceturns Definitions of Moves / Rotates / Flips for Corners and Edges\u003e. The Two-Phase algorithm typically solves in 24 moves or less.\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/cube_small.gif\u003e\u003e\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/Cube_Map48_200.png\u003e\u003e\r\n\r\nRubik's Cube has 48 faces that are assigned to a vector as in the above figure.\r\nU refers to the White face, F-Blue, L-Red, R-Orange, D-Yellow, and B-Green. Moves (1-6 UFDLBR 7-12 U'F'D'L'B'R' 13-18 U2F2D2L2B2R2) are clockwise looking towards the center, primes are CCW (eq U'), and twos are a half turn of a face.\r\n\r\n  The color to numeric coding is [RWBYGO] [012345]. \r\n  A solved cube is [0000 0000 1111 1111 2222 2222 3333 3333 4444 4444 5555 5555]\r\n\r\n*Input:* Cube\r\n\r\nCube is a 48 long row vector of values 0 thru 5.\r\n  \r\n*Output:* Move_Vector\r\n\r\nMove_Vector is an empty to 30 element vector of values 1:18\r\n\r\n*Constraint:* Solution must be 30 moves or less\r\n\r\n*Scoring:* Minimum number of moves \r\n\r\n\u003chttp://cube20.org/src/ Two Phase Source code\u003e is fairly complex and may require a 500MB database file. Its goal is to find solutions of 20 or less starting with Two Phase.\r\n\r\n\u003chttps://sites.google.com/site/razapor/matlab_cody/Cube30rev001.ppt?attredirects=0\u0026d=1 30 move Cube Solution in Matlab (rought draft)\u003e","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 936.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 468.35px; transform-origin: 407px 468.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 308.633px 7.91667px; transform-origin: 308.633px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis Challenge is to solve a thoroughly scrambled Rubik's cube in the least moves (30 moves max).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 219.95px 7.91667px; transform-origin: 219.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRubik's Cube can be solved in 20 moves or less from any position. The\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://kociemba.org/cube.htm\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eKociemba Two Phase algorithm\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.7px 7.91667px; transform-origin: 63.7px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can solve the Cube in 30 moves or less. The basic theory is that any cube can transition to an H-cube by 12 moves using all possible 18 move types. An H-cube is defined as having no rotations or flips of corners or edges, respectively, and has all middle edges in the middle row. The cube can be solved from any H-cube state in 18 moves or less using only the moves U U' U2 D D' D2 F2 L2 R2 B2.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://kociemba.org/math/CubeDefs.htm#faceturns\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eDefinitions of Moves / Rotates / Flips for Corners and Edges\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 151.317px 7.91667px; transform-origin: 151.317px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The Two-Phase algorithm typically solves in 24 moves or less.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 134.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 67.4667px; text-align: center; transform-origin: 384px 67.4667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.667px 7.91667px; transform-origin: 376.667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRubik's Cube has 48 faces that are assigned to a vector as in the above figure. U refers to the White face, F-Blue, L-Red, R-Orange, D-Yellow, and B-Green. Moves (1-6 UFDLBR 7-12 U'F'D'L'B'R' 13-18 U2F2D2L2B2R2) are clockwise looking towards the center, primes are CCW (eq U'), and twos are a half turn of a face.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 192.5px 7.91667px; transform-origin: 192.5px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; \"\u003eThe \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 177.1px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 177.1px 7.91667px; \"\u003ecolor to numeric coding is [RWBYGO] [012345]. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 300.3px 7.91667px; transform-origin: 300.3px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; \"\u003eA \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 292.6px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 292.6px 7.91667px; \"\u003esolved cube is [0000 0000 1111 1111 2222 2222 3333 3333 4444 4444 5555 5555]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4333px 7.91667px; transform-origin: 19.4333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.6833px 7.91667px; transform-origin: 18.6833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Cube\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 146.25px 7.91667px; transform-origin: 146.25px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCube is a 48 long row vector of values 0 thru 5.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.2667px 7.91667px; transform-origin: 25.2667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.8px 7.91667px; transform-origin: 42.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Move_Vector\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 189.433px 7.91667px; transform-origin: 189.433px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMove_Vector is an empty to 30 element vector of values 1:18\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.3333px 7.91667px; transform-origin: 37.3333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConstraint:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108.917px 7.91667px; transform-origin: 108.917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Solution must be 30 moves or less\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3833px 7.91667px; transform-origin: 28.3833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eScoring:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.35px 7.91667px; transform-origin: 86.35px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Minimum number of moves\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"http://cube20.org/src/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eTwo Phase Source code\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 301.833px 7.91667px; transform-origin: 301.833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is fairly complex and may require a 500MB database file. Its goal is to find solutions of 20 or less starting with Two Phase.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://sites.google.com/site/razapor/matlab_cody/Cube30rev001.ppt?attredirects=0\u0026amp;d=1\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e30 move Cube Solution in Matlab (rought draft)\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [v]=Rubik_Solver(cube)\r\n% moves 1-6 UFDLBR 7-12 U'F;D'L'B'R' 13-18 U2F2D2L2B2R2\r\n% Return v as a numeric row vector of k values in range 1:18\r\n  v=[];\r\nend","test_suite":"%%\r\nfeval(@assignin,'caller','score',30);\r\n%%\r\nvf=[ 17 2 3 20 5 22 7 8 11 13 16 10 15 9 12 14 41 18 19 44 21 46 23 24 25 26 27 28 29 30 31 32 33 34 6 36 4 38 39 1 40 42 43 37 45 35 47 48; \r\n  1 2 3 4 5 25 28 30 9 10 8 12 7 14 15 6 19 21 24 18 23 17 20 22 43 26 27 42 29 41 31 32 33 34 35 36 37 38 39 40 11 13 16 44 45 46 47 48 ;\r\n  1 2 38 4 36 6 7 33 9 10 11 12 13 14 15 16 17 18 3 20 5 22 23 8 27 29 32 26 31 25 28 30 48 34 35 45 37 43 39 40 41 42 19 44 21 46 47 24 ;\r\n  3 5 8 2 7 1 4 6 33 34 35 12 13 14 15 16 9 10 11 20 21 22 23 24 17 18 19 28 29 30 31 32 25 26 27 36 37 38 39 40 41 42 43 44 45 46 47 48 ;\r\n  14 12 9 4 5 6 7 8 46 10 11 47 13 48 15 16 17 18 19 20 21 22 23 24 25 26 1 28 2 30 31 3 35 37 40 34 39 33 36 38 41 42 43 44 45 32 29 27 ;\r\n  1 2 3 4 5 6 7 8 9 10 11 12 13 22 23 24 17 18 19 20 21 30 31 32 25 26 27 28 29 38 39 40 33 34 35 36 37 14 15 16 43 45 48 42 47 41 44 46 ;\r\n  40 2 3 37 5 35 7 8 14 12 9 15 10 16 13 11 1 18 19 4 21 6 23 24 25 26 27 28 29 30 31 32 33 34 46 36 44 38 39 41 17 42 43 20 45 22 47 48 ;\r\n  1 2 3 4 5 16 13 11 9 10 41 12 42 14 15 43 22 20 17 23 18 24 21 19 6 26 27 7 29 8 31 32 33 34 35 36 37 38 39 40 30 28 25 44 45 46 47 48 ;\r\n  1 2 19 4 21 6 7 24 9 10 11 12 13 14 15 16 17 18 43 20 45 22 23 48 30 28 25 31 26 32 29 27 8 34 35 5 37 3 39 40 41 42 38 44 36 46 47 33 ;\r\n  6 4 1 7 2 8 5 3 17 18 19 12 13 14 15 16 25 26 27 20 21 22 23 24 33 34 35 28 29 30 31 32 9 10 11 36 37 38 39 40 41 42 43 44 45 46 47 48 ;\r\n  27 29 32 4 5 6 7 8 3 10 11 2 13 1 15 16 17 18 19 20 21 22 23 24 25 26 48 28 47 30 31 46 38 36 33 39 34 40 37 35 41 42 43 44 45 9 12 14 ;\r\n  1 2 3 4 5 6 7 8 9 10 11 12 13 38 39 40 17 18 19 20 21 14 15 16 25 26 27 28 29 22 23 24 33 34 35 36 37 30 31 32 46 44 41 47 42 48 45 43 ;\r\n  41 2 3 44 5 46 7 8 16 15 14 13 12 11 10 9 40 18 19 37 21 35 23 24 25 26 27 28 29 30 31 32 33 34 22 36 20 38 39 17 1 42 43 4 45 6 47 48 ;\r\n  1 2 3 4 5 43 42 41 9 10 30 12 28 14 15 25 24 23 22 21 20 19 18 17 16 26 27 13 29 11 31 32 33 34 35 36 37 38 39 40 8 7 6 44 45 46 47 48 ;\r\n  1 2 43 4 45 6 7 48 9 10 11 12 13 14 15 16 17 18 38 20 36 22 23 33 32 31 30 29 28 27 26 25 24 34 35 21 37 19 39 40 41 42 3 44 5 46 47 8 ;\r\n  8 7 6 5 4 3 2 1 25 26 27 12 13 14 15 16 33 34 35 20 21 22 23 24 9 10 11 28 29 30 31 32 17 18 19 36 37 38 39 40 41 42 43 44 45 46 47 48 ;\r\n  48 47 46 4 5 6 7 8 32 10 11 29 13 27 15 16 17 18 19 20 21 22 23 24 25 26 14 28 12 30 31 9 40 39 38 37 36 35 34 33 41 42 43 44 45 3 2 1 ; \r\n  1 2 3 4 5 6 7 8 9 10 11 12 13 30 31 32 17 18 19 20 21 38 39 40 25 26 27 28 29 14 15 16 33 34 35 36 37 22 23 24 48 47 46 45 44 43 42 41 ];\r\n\r\n cube_orig=[zeros(1,8) ones(1,8) ones(1,8)*2 ones(1,8)*3 ones(1,8)*4 ones(1,8)*5]; \r\n tsum=0;\r\n Lbest=30;\r\n for cube_sets=1:4\r\n  if cube_sets==2,tsum=0;end\r\n encode=randi(18,1,80);\r\n fprintf('Encode: ');fprintf('%i ',encode);fprintf('\\n')\r\n r=cube_orig;\r\n for i= encode\r\n  r=r(vf(i,:));\r\n end\r\n encode=[]; % anti-shortcut\r\n encode_str='';\r\n cube=r;\r\n fprintf('%i',r);fprintf('\\n')\r\n\r\n% Time function\r\n ta=clock;\r\n [v]=Rubik_Solver(cube);\r\n t1=etime(clock,ta)*1000; % time in msec\r\n tsum=tsum+t1;\r\n Lv=length(v);\r\n assert(Lv\u003c=30)\r\n \r\n fprintf('Time: %.0f msec  Total Time %.0f\\n',t1,tsum)\r\n \r\n fprintf('Solution length %i\\n',length(v))\r\n fprintf('%i ',v);fprintf('\\n')\r\n \r\n r=cube;\r\n for i=v\r\n  r=r(vf(i,:));\r\n end\r\n \r\n fprintf('Solved Cube\\n');fprintf('%i',r);fprintf('\\n')\r\n\r\n tf=isequal(r,cube_orig);\r\n fprintf('Solved %i Moves %i \\n\\n\\n\\n',tf, Lv)\r\n assert(tf)\r\n assert(~isequal(1,2))\r\n if Lv\u003cLbest,Lbest=Lv;end\r\n \r\n end % cubesets\r\n\r\n %msiz=mtree('Rubik_Solver.m','-file').count\r\n\r\nfeval(  @assignin,'caller','score',min( 30,Lv )  );","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-12-17T02:11:05.000Z","updated_at":"2025-12-20T07:40:07.000Z","published_at":"2012-12-25T05:15:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to solve a thoroughly scrambled Rubik's cube in the least moves (30 moves max).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRubik's Cube can be solved in 20 moves or less from any position. The\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://kociemba.org/cube.htm\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKociemba Two Phase algorithm\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e can solve the Cube in 30 moves or less. The basic theory is that any cube can transition to an H-cube by 12 moves using all possible 18 move types. An H-cube is defined as having no rotations or flips of corners or edges, respectively, and has all middle edges in the middle row. The cube can be solved from any H-cube state in 18 moves or less using only the moves U U' U2 D D' D2 F2 L2 R2 B2.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://kociemba.org/math/CubeDefs.htm#faceturns\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eDefinitions of Moves / Rotates / Flips for Corners and Edges\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The Two-Phase algorithm typically solves in 24 moves or less.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRubik's Cube has 48 faces that are assigned to a vector as in the above figure. U refers to the White face, F-Blue, L-Red, R-Orange, D-Yellow, and B-Green. Moves (1-6 UFDLBR 7-12 U'F'D'L'B'R' 13-18 U2F2D2L2B2R2) are clockwise looking towards the center, primes are CCW (eq U'), and twos are a half turn of a face.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[The color to numeric coding is [RWBYGO] [012345]. \\nA solved cube is [0000 0000 1111 1111 2222 2222 3333 3333 4444 4444 5555 5555]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Cube\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCube is a 48 long row vector of values 0 thru 5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Move_Vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMove_Vector is an empty to 30 element vector of values 1:18\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConstraint:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Solution must be 30 moves or less\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Minimum number of moves\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://cube20.org/src/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTwo Phase Source code\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is fairly complex and may require a 500MB database file. Its goal is to find solutions of 20 or less starting with Two Phase.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/Cube30rev001.ppt?attredirects=0\u0026amp;d=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e30 move Cube Solution in Matlab (rought 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1137,"title":"Rubik's Cube: 30 Moves or Less : Cody Size","description":"This Challenge is to solve a thoroughly scrambled Rubik's cube with smallest code (30 moves max).\r\n\r\nRubik's Cube can be solved in 20 moves or less from any position.  The \u003chttp://kociemba.org/cube.htm Kociemba Two Phase algorithm\u003e can solve the Cube in 30 moves or less.  The basic theory is that any cube can transition to an H-cube by 12 moves using all possible 18 move types.  An H-cube is defined as having no rotations or flips of corners or edges, respectively, and has all middle edges in the middle row. The cube can be solved from any H-cube state in 18 moves or less using only the moves U U' U2 D D' D2 F2 L2 R2 B2. \u003chttp://kociemba.org/math/CubeDefs.htm#faceturns Definitions of Moves / Rotates / Flips for Corners and Edges\u003e. The Two-Phase algorithm typically solves in 24 moves or less.\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/cube_small.gif\u003e\u003e\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/Cube_Map48_200.png\u003e\u003e\r\n\r\nRubik's Cube has 48 faces that are assigned to a vector as in the above figure.\r\nU refers to the White face, F-Blue, L-Red, R-Orange, D-Yellow, and B-Green. Moves (1-6 UFDLBR 7-12 U'F'D'L'B'R' 13-18 U2F2D2L2B2R2) are clockwise looking towards the center, primes are CCW (eq U'), and twos are a half turn of a face.\r\n\r\n  The color to numeric coding is [RWBYGO] [012345]. \r\n  A solved cube is [0000 0000 1111 1111 2222 2222 3333 3333 4444 4444 5555 5555]\r\n\r\n*Input:* Cube\r\n\r\nCube is a 48 long row vector of values 0 thru 5.\r\n  \r\n*Output:* Move_Vector\r\n\r\nMove_Vector is an empty to 30 element vector of values 1:18\r\n\r\n*Constraint:* Solution must be 30 moves or less\r\n\r\n*Scoring:* Cody Size \r\n\r\n\u003chttp://cube20.org/src/ Two Phase Source code\u003e is fairly complex and may require a 500MB database file. Its goal is to find solutions of 20 or less starting with Two Phase.\r\n\r\n\u003chttps://sites.google.com/site/razapor/matlab_cody/Cube30rev001.ppt?attredirects=0\u0026d=1 30 move Cube Solution in Matlab (rought draft)\u003e","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 936.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 468.35px; transform-origin: 407px 468.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 309.417px 7.91667px; transform-origin: 309.417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis Challenge is to solve a thoroughly scrambled Rubik's cube with smallest code (30 moves max).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 219.95px 7.91667px; transform-origin: 219.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRubik's Cube can be solved in 20 moves or less from any position. The\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://kociemba.org/cube.htm\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eKociemba Two Phase algorithm\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.7px 7.91667px; transform-origin: 63.7px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can solve the Cube in 30 moves or less. The basic theory is that any cube can transition to an H-cube by 12 moves using all possible 18 move types. An H-cube is defined as having no rotations or flips of corners or edges, respectively, and has all middle edges in the middle row. The cube can be solved from any H-cube state in 18 moves or less using only the moves U U' U2 D D' D2 F2 L2 R2 B2.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://kociemba.org/math/CubeDefs.htm#faceturns\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eDefinitions of Moves / Rotates / Flips for Corners and Edges\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 151.317px 7.91667px; transform-origin: 151.317px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The Two-Phase algorithm typically solves in 24 moves or less.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 134.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 67.4667px; text-align: center; transform-origin: 384px 67.4667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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/qlFWJ6GZ4bh2wRMteODJVxZGFhE/ulmCsS3PwrC8hhkS6EL9dazDTEW4GKjdoDFwrB49FqJ4/WwqqLtYMngmdd41xdnL0JvX/R2xVkT2xS8j1gsEqxfTPFKoLi3ssIOsQa/UMVvN2B1MY5V5edLq2JcGR4xav1WeApTerea3xgsokbPr8Xyt3gE8MwKrKloqH5eT3TdrBWwiHwvFqbGY/wmdAVMTeVj4SlauTlYxMmvL+Cr7Y0VZDDxNab7YtgijPPFOFcMm9gQ13csWMusMfEBqgBOXEmCNaWtYMkhuU91CZ47grZ2eJYKKbbO/gfAYuHt17hjmVi3Iv8JvuLgAz+q+TbEqhwcXP/8oIiRRM9o3sqtCCq0li8AFslKL8xKxYgF6EwEzn+Q1X9Oo+ExUBywiCjqhjUWPMDDRKMijSmpmGJHKYhWbgIWEU4FDsakUAySaqTgLYfvqNpJOoJP7TCJqp37s/lsdSBYOl/g+0LcPZcKwLdjdSXOH4TSsm0D63IyPvJHuboGLCQGky7VvaUP1jh9LKvGiUPEuBUZDLiHeYk4Upv6zzBEbmnjFqsUg3a3eCuNFVrLFwCLqKFHoVh0i3zU8pfFsG1YU4lhg/CQrLhgEUwEf4GcQoyYS5YK7Ilp6ZjmRp5MKt8UrtwELOIyIoPxyQ481KVOwZ3E1EceU5Ix05/8FqIlc5XBNzFYeAn9eM8WHQfW18uxiHheSMQk4utzySe00ny0Xtm2GMvnIb46zQ+AiWR9AcueonKXdoIV9Bg/3kZWq7cijU7nsSoTvxlWN37xG/ln+evohhgrqxL3LxN9K1Lo9GcjBVHKTcFiU01CQhRWZSPnHRYnY1kutY42H5+s5LcKrYJFdFjnlmNlBRYnYnEKFqdidTVyKzDhMCY8wspM4cp+AmCRlyGPb4iTs8gzeQq1ZVhwB4MU8AXxl3Ga/4RIsBV1Aauf4uEuVCPXKlgL9iAnATXb/lQoI0eG/1raqCSP87bRarGIGMSRvKVh1GOEtDo+yMTLzuJ3hZ8uQA4Hv9ZslDloJlYhWv7c+q1YHcWiZBzXX6DzGoSplRhQ10TN2421xTi5l8hbmbsCcxNx/ICm39VcWViMJYUByhikicHaeFi+abtCEOAEGGaK7y/yA2ehXeEhOTLMJxSCNTCwB7+9CSA+Fa3cPMYKUMFgrUYKh6lvvOmINVl4XJ3sT73VMSMTU5z5nIkGSxpXGaK7M16NIgcqDrHR2RYHsGgOV3+zHmuq8Ju2PxXKD8DobEyLQTtrDH+FWXE4to84YP2wCtnuGHoVa6rx/CF0c26oXdfzWJOKg+RbuZVfLck/4+i7uP8AOe7lewh/X0KFWaZYW4NnvNEjhOxPXTaJvBWZnuTYRGw4X8GbjYZUe61v0UiZzF9V3yg3Dt7ZVHfmQ4VKf1L/h39SkRBbGm8bYqwzpj3BknSM98Vbs/iNVvPgnadAtF5e8piagam2JJQ+IpSFgsUWoeA3ALOysTgGn1pj5issjcMzfVqNsSiwfH3Q0R4t96ObB7ra0Qer3xdobor9aI28K+uisR36sNF6N2ooivlUSIDl74vOjmhpiU5u5AMlHyw5XGeKv89ovfGdvAjt7NDWnhyjJ6qfTYD1E/+jr2aj+yE85IFzv27pVuR1cJcFOjjwFerB+nphI+WWwBIcnwz9AqNMMZQaH+eBFe+Dz+wxxhrj/fH2D8LBajSCL403t+PNGY3mhZootzyl00SBON9fFyPtMI6NT3djoCIJHzNXKGGT0OzGk3FeAjN07gLzdy1PQns2m1tsrtzyJHQTBZ+6qUZ34HPJgMW4Gxh3w/8nsOar4Qkg42t6KRRc9CHJjnj0pasQRBYnRAgp+pdxRA0i1dQiAOil55Sd9ixAJF2FSKr4NkqKtsJ1AGX4EuARwGNJv5XVk5TjLCDCiGZ6bg7bpsPZdRBpTFOBKEgUJ0QIKdqXEWmhBgVqavkA9FI1gDXAUwAOXQUOVdyakqKtkAKgCtMBCqjGS7JvZc8sVaIryXehmap9wHoBPDUFjjtNBaIgUZwQIaRoX0aBN9MVdsIYi+iDDtFNIVSMZUP1R/QUAsjiZIwV0o7LCGLAYoJ3JnhnwGLAYsDqYM87zzbjTuWz/y2wmnjem4yl8S6mdbBkVPD37eRkzsEDOFr3v6gNavSf7U2OT5PJlRyxXq+PMjQ973zr4Qx0YyPbC6dP7PBbEel5H4m2LmT+3nW0PO9EziEVvLUdX/vh4814SKZhcLLjwBL0vJPTQbzRf2986UYlV3xmh/f0yQCrpblCOV2MSMSHl9DKAaNSEDNw2oj/EixXV3IBQxZizHFxwBLqeSfSbwewqhiPeKHnIcz9gHoTOvJWRHjexyzE9EK8GELeUA4XH4eifJs870RD5aeLHxMx4xLGOGLee0xxJ+uS3ZFgNfG8ezcByxWfe2ApYvbx1sBS7otLZqMS9VpjKOYhXnP9j/uPnlMwvxK3zqLteZdWw1dl6LOV//bIdbxxsANvRaTnfTJOG8s/Z/5uMv/7vm30vB/ui1dnk1V4EPCCPmIlXqyb/e0gsJp73gW7QhfikqZgeSU+mMXvDcWKsaSU8FEhRgWh1H8K1oEzWPgCdaRpe96J+4jKxdO2dYspHuARw3/pVkR53r/8DaurcFbfNnre2XUGc6KCT88gDVJXRvCn8DoCLKGed3bjCUSiQS5/gUHSYiz/EmwqKhCdV/+XLZbSUMxB9DJop+d90nLMLMBTbDRxwAtHsY/Mv3QrTbztiqqoqYZ9xuGNF3jVR7BvF9vzXl+jYWux4jUeZfFrtCPAEup5Zwv0kgFDsQzxhUHD/LRYYDlfwIp0HKn1X4Jl4IUEWUOV2r+YYl/d/sVmy/6lW2nubd/GxoIszCzEigxcOoWu592XekaLv4CvzcR1N9AAS6jn3UsALKLvu0PVznGltthm5hmTlbD52//yGV26Bz4vxsuObR1uaA6W21+YGY+TPsHh3+CHXHTb1PG3IszbTrRY2lqooYn2p8n/3TXTaXneCaquWWBxLAYrNNToPw6WcM+7FGlw5dPfA3OKMcWxUVPaClgz1pE2XkeD/3jwZ/4O4okIvx/cTrCGLcSqSlxYJ2PoiZUJIldC/zO3IsrzLjCkE1uFt1zb7nkn2omL68jn3ojljdqwfxYskZ73exhKdb5kX0zVzsXBYoM1cSkWc9FM/78eVZTHW6n47ETDkgq6nvfx1FKIZXVLIfZ4YVkcqkp34K0I8bxL4TfzcWR3/lvdcViMGLi7TZ53GbIK/1yKVVx8rE8+kblBB3aFwj3vVIvFwy4tFbNPNIx3tAJWzzHkoFHFB3RzQCcX9PBslzW5PWBNXEWtb5/ZppH35p73cX0QVPHME6zJRi9XdPfGjBzc93MH3oooz/s2H6zMRbYnOntgajEmP8BhGiKCd6Ged+LxPmQMOWhU8wFfOuBzF4z3E8uaTBssoZ53NkXzn1Tt3JnZMObeClg6I9DiAFpZows16v0fgjV5EVrsaGG7mzZ53rvIo/5GZPugjxd+N6ljb0WI573O2z5lPnr6orcP7lqFirJiTOkIOtPJka0RGH2AdLu/oEa9OxosUZ534kouLMLoHegv3XR/JWauUCI97+xmk3Re/9YkdBPPu7ewXbsYsBh3A+Nu+H8D1kI1PENVKr10Elx+haSDQNJJT+EoWZwQIaToX8ZxNfBWU3Oh/j9oJB+ABQCmAO50Fdyp4gsoKdoKNgAsGALgSiXJvpVZw1m+y8gGg17yWQoLRoPpHHDXp6lAFCSKEyKEFO3L8F6hBilqaknU3xqNlE39X94FeE9X4T1V3JSSoq3wHECF3GA9mbK/S/atbJ2uku9Mdkb0UvZBEou7u+C9LU0FoiBRnBAhpGhfRspBpivsbF3hPDU8TkVI9NJRcPmZWv4VSFchkFr+9TPVmdK+jBAGLCZ4Z4J3BiwGLAasjve8e7TR896yY92b1j7vgns3eIsJlpwyrjVCXzY6WePntDzvfT5DC1v+ruq+HjhtJJ3aUOuP5g7o442OVjhYtU1gCfW8fz0XPf3QwxmH9W/lVkTvxi5cWXzPOy8Nn4j2LrheT3AWVGzPu68y3jXCV34YuYXcq9inLfu88xzr1wzwhQu+dCdTvAf+NbKlXZOF7vNO6Bzuj1EO5Cbvz6zwuKoYe5BK98Rbr/DlHbS1xYdvsPoDTujfZrC+WYflVXjIm5wXogfWwImYysEHl9DKDiNeY0kijutHe593Iu3ywsoSDPFAv4vkzQ2QFXkronZjF6Usvue9fr/zE9HkPFv8eVRoq+f9UE9Me4W5d8jNP3MT8a2A806cfd7JzbQVMDkB8yPwmYNYYDXf553cjnsiFnEo670dZr7GqkQ824/fbrXkef9pDiry/u6GYgGi5xY6YOXFo6Y8/f5j/3nMus+/DHldTKtAu3W0Pe+6k0knrIkef6HGzcfovrYN+7yv+7bVHeTF8rzzN/49gNH3MPgGvg0T3FRVbM/7tTl1nvelWJWMoUotOUiF7NIuT6IZsxYdxOsKmysQfeKT81h2n/zUmcBaF4sr8Ok68kxxYywZNXwjsAjh3wTLMBiLX6EuNfndewwW1uD2+bQ979+uIzesnFz31vkEvvpTsBtqZZ93nmO9xR3kxfW8dxuDKXm46Es0/hNTr7YIVgued2+qMTszFysSWwJL6D7vTcDyarvnnSgVEYyVrzCYRYIVPAYrajB8vhiLKWTlUUsLNbTQKhiTo4Xu0ShWV+jHRhd7/GooHbA0huGd1xh7Fbdvwzsv8YStUFeWmEa/MXpk7RpM5b91CMXcCMEtblvZ511wl3YR2+aK63n3DsPbAeQLmystgtWC591PnvRIBWrhy+MYZ9zwKyZi7vPe0BUexJeOeH5oA1tiet7JAGsYfniNeVfx4TZMe4mJtvy1X62ANW4JJmVg+gfyxxiCdgtdoiNW8H7QAcMeklVquoiWbeYnsgMjjtwXOHt0u6zJChgaidwc9HJDZzf8yMGUm62DpTAY35Q03aW9TWA1UZjwG2a/xpFUWbswTAkT/KWn5p73FHw4Dx0JsCjP+xkNskkg6vXMEizKwLIsLE/FiyMb7FBC93nPv0vuku0qjckpmGxHZtYH7y8cMYWqnUeLhMdYPM/7uxAMkGpQ4D2fEr3hnz8RfzDkUf4CL40mc3zFabG0tVFJHWf+julleNO3+UrRNjyjW53E8kTs3cZdk/VMMfk1bl6I6t3xgB/mFODuH9vjeZdXxnV7STPWvv14/hZGhgr+vQi5la4D8cJjjLuHQ7RogtVEQbovPsslA/kFc3Dez/jXC8x7SW6b20NFmOc96iy5Ee9tPbw6H6P9sLYaY9bj6UEkWIfkSWdpgAreMiWD+sujhawrJJg4+hWW1uA7J7w8D28sx9xczAvDi2P47RDvN3CIFH2SDL2PyFLbijbzvMecw5RQvDyXr5D7N177liT1qgkWvcb7CzGwOz7xw7ICDP+xteBdVhblBLZTNzuLmIm92mH0W+9CthV9WW0AS04dU6vQcUNDjt0N/HhFcOFwy2ANW0T+hI/wH8SQxTuRdYG8iFsZ9g1+JDofF+wirnLTW+kxmHyoveDaoMDqj+ZWaGqKFhZotA8fvMWiJLQxwU+1m7dYMnhzKz7Zh1H7MNIYX/+F3BpMdMW/x1MNSRey4SGtUYPINuPFVn6j1QSs0HH4xAajTDDaAqMOYGEhciLx9gL++BPPnuoCeJuqHd4asiZgEZdxYwvG7G9QKIrAR6sxpBsWEtH6BjJKI+Aj/o25gcVXWvsBgSm/473L+PVwlJPDqYsxH/GyU9u6wi4s3GiI4/qiggJOXoyZXPQzbGNXKIsX4skecHw/lFfAsbPxYw0eNROnxVJURVVFnLQKy0pwwSCy2ZWVQqXe+NvPqKOOyuq44SDGnG/8/N/4Vvp9iSnFGH4K1RVRRQ27dkUVZUpZpamyvKzIW/E8g4/+JPd65imoNxuGI7rC1LAWYyzeEChR96eprvC0Bhkpn/8dP1zG88PJlTO3dpIjHxc/Eb4SWtAS6CqHyalkR0aonZmFd/UxSBkPK+J5ovnlYrwhv7ERGrw3USCCLS9ZTIrHshd4rh/6K+DZ2Vhcg2/MWmuxWH3w4HHMysKUFPIX4QLNsatCG2OsLriTjRkfMPU9GShYbhIcrhG3K9QdjiduYl4eJidjLu8y5MQBi1y4l41pH7CgAD+kYUYSLiLCMzX8MwpzP+KHLIy9g2NaHCDd6EFGDqlJmPiO/D/IzUOP/WT+Vp+mykvGCb8VxU/xdT5mpPIVMnIwjN3khzPR4hzGnmvxqbB+0OHccjKiOqdOtlIBffD5cfJtSRoWvSRHLFt1kJK+dTl8F4vvLEiF49PwQyyWpWPxeyxLwehNZNzd8nbcggq8cawjwzHxJlbkkQt4ynPwlTkGyomxElpKilz5RvyhaWiQr2mMvBOlNLUoBRVRsX/rwbuUHGpqt3wZQlusbl1RS5O8OS2itDa/XWEpkkpEUmytV1dQQnV11NQk40xt7UYtllDl5rciJY2qjRWat1jEt6goiTdXSP7GhBoeqlvN5yFFLuAJ6YoBqm1Y/kXEZAEKfFJ9FcniwV0xSKXRvFDLc4X1CjwRbznqZy8IEeJxVaphAoCZK5Qkz7sPNN3736eZ37xlsHwEdmNnC/w+hfiT0E3OFxRhM5PQjLuBcTeIDdZ0gCJq4+FCWqkWwJbyopbQVSihittSUrQVUv93wIrR04uaM4deips3z3DUqL++/TZm7lx6CkRBojghQkjRVrj9/ffd1VWUVVXU6B7q6uoKCgoqKvQViIMoTogQUrQVpGRZmxYNfR2yIIo9h16KC5pn+Muov6y/jfGbS0+BKEgUJ0QIKdqXEXNYD7yPH3cJDqaZQkKc2WyXw4fpKxDp8GFSJCSEtoKd76nbd2aVl0NhIc1UWwu2tvD8OZSU0FQgChLFCRFCip5CURH576mz2xzdT7p4B9NNIc7ubBevw+1QCCaKkyLeIbQVvP2Pg7+/v3c7Dh8fH+92H+0UcXEJjo6eiwjtSS4ukJTULgWiOCHSzsv4++/Nbm4SXyMEVO0FqzMcBFhRUXP+V8Da5OYWIOk1woDFgMWAxYDFgPWfg1VbA1eOwrrVsHk33I9tyL97AbZtg82bYdMG2GUNeVUtgZWVBJY7wcAAHAKgpLIh//kt2Loe1hmA21EobxGswgzYs4M8094fSgUUsByCXWDNWthlDImFDFiSAhYXNv8II78GQ1P4fiyAFATe539k/BN0HQrbDVsHKz4MBujCb+tJhjQBvvwZCqn8UGtQ6QYrN8L2DdBbDaZvhGrRYBktg1m/wM5N0FMWvloOlbz8Ylg+CfoOh50mMOsLYPWB+wkMWJIAVm0lxD6DolLqbRn8NAL6/gAV1Efbf4SftovVFWYmQULd2+hgIA7/h4BVMEYVNvrx8x8GgRILnucLB6umAt7FQQ1P4RgoyMPddPK191bQ/hxSOdRp1bB2Mnz+E9QyYElYjFUL+p/BiJ/4FbxzHnxnAJxqyMuDaq64MdazU9BFCk48JV8bzgPdz+DZR0AOLB4N4/T5yLYcYwWZgGJfSConXy8eBnN3Nnx0yghY/SGjigFLosB6dx9YAFan+G9t1oGMIvTtB920YIuduGBtmwMaoyG3lnpbCbsWkg2YijrMXA0cbksx1qsnsG0rLJsNGv3gdAS/BZ3aB1a7NpxzzR1YGhDHYcCSILBKYdFw6P8dFNTlVJSRbVVBISRFw4DeYHeudbAeBZIYeV7nv024DdNGw9wV8MdC0NYC26OtgLVlE2xaB/01YPpySKskuZykC2sEwXIDxR6QUMqAJTlg7Z4NKn3habrwdmjdIpi8shWw3tyErgBr7Plvy1NhSDfYWIfFGScAWTgV03pXmHIfNADWeZGvZ/eHOTsad4X94CPTFUoKWJa/guoACE8WOWK0/Af4YUNLYL17CP1VYKlVQ07MMVBWhOi6aL06Hz5RBMOjwsGqrYaK6rq3xTCBBT/uIl/v+BH6zqx7QkQwmQejFvNDQAaszg6W62by98dPh5OPZjnZkJND1lxWLLgHQmY+FBXDy9sw5DMIeykSrI9P4VNtskkrKoeifMjKgvIayHkKXaVhkTEUcKCUA0EW5FaCf8ULBysjChYug4+5UFIEHtsBpCHwIZn/8i9QALA/BdW1cD0IVLqA9zVmuEESwKp8D59pgoImfPoJ9O0LvXWh1yC4lgg1GaA/HXrpQJ8+0E0bAsNaCt4PG5KhVe8BMHAAKaKlATv2k/n3TsHng6FbT+jdAwaMhMMXRcdYlWC2Anr2Ir+x3wg4/HfDR+fY0E8DeumCdn9wCmUGSCUELG4tFBVCQQHZUNWnSqpXqimF3GzIzoa8fOC2ONxQUUoqEJE+rzhRhFNSF2mVkW+JVFrWypRObRXk5kBWszORC6VUK5hfClxmSkcix7GYuUIGLAYsBiwGrI4C69KlLe00+jFg/YNHsIfHHKJSaScfH1iwAExNwd2dpgJRkChOiBBS9BRcXcHREWxsfmOzDzNgdYrDzS342rU5aWlkm0EvEZE4gcXdu/D+PU0FoiBRnBAhpOgpJCfDu3dw7Ng6Dw+mK2S6ws7neWfAYsBigncGLAYsBiz++HspZGdBbn5T3xWRqsogh/gor9EYaUeARejn5VGDq+VCzi8vhtJyBiyJAuv6MZjxJej2AlVVmL8WsgT85q+uw8wvQEcHtLuD17WOBetiAHTrDj11oPsgCL3TaLbntCd0k4XVBxiwJAisYjCYBy4noJwL4adBFWCxeZ2b6j70lodVtlBQDG9fwq0XHQhWbRHsM4DwRKgohm2zQLY3JFETO5WZoDcF+g6A3hrwiwkDluSAxa2FKoEmas1XoDUVynivp8DYn/+lGIu4jOoK/uvEC6DIgiuUhycnHhx8oaYaNkyH+TsZsCQ0eK8FvVEwSo+agf4Ig5TB/hK5hCErC8rK/r3gPcAIFPtBUmmjzFWTGLAkFixBz3tBDKiyYPYvMH0saGnC2JkQk9axYAnxvDNg/S+A1djzXhANyjIwex2k5EAFBxZ/A58tarBudhBYgp73VKbF+t8Aq4nnnRMPmsrgdY//9oQRyGnxA+qO7gp5nncDdwYsyQdLiOedA+O1YIs//63/DlAfBlm1HfZU2Nzz3hijP6bAAgYsyQKruee9sobMP7gS1AdC+DsozYVJo2CVfQfGWKI871xquWx5Pvw6AWZtBE4VFHEYsCQBLKGe98tx1INhFqz5ETQ1oEd3WGbEH4PoqK5QhOe9KA5GDgJdXeiqBdrdQEcbluxklthLyDiWKM87+WkV5FE5VVUdPtwg1PNOtFhEZnYO5BdAfj454VPItFiSN47FTEIzYDFgMX6sznUwDlIGrA46GM87AxbTFTKrdBiwmOCdAYsBiwGLAYsBS3LBau55541M1g+Z5uWR+xlxWwCLC4W55FNecWNnem05tbNILpTX0vW8i1BmwOrsYAn1vPPmUnrpkvM8/ftDVzXoMR0Ka4SDVZIOhmthSD/o3g26DYRjt+p2U34DSyaDTlfQ6grT9CGtsM2ed1HKDFidHixRnvcafouVm0v60JfPhjH6IrvCu4EwXx9eZ0JJAayfAqABjzIBS2ByPxivBxnFUJgIXw2Ar/5os+e9uXJ4OgOWJIAl1PNe2rjHqSmDSWMh5IFIsKoryR+I4zvWL5KbsHk/gA83gaUIV1P4+Y+PgZIWRGe2zfPeXNnlCgOWxAXvdZ732sb5iVfhqwXAES94f3oSpKTgQiK8OkPyEZHDz8+PBUVVCI2i6XmvVz4Zw4AlaWA12ee9Pln8Ansd27bPexFC8WvoIwsL9kJhMXDywWMn2d6wb9H0vDfdQZ4BS2LAarbPOy+VJsKnqvDnA7HAarLP+51QGKgDOj1hwGDQXwKySnDiCU3PexNlBiyJAUvUPu+H94BsL3hf0jpYTfZ55y+N55AjBUXlkH4DNNTgQTodz7tQZQYsCQBL5D7v+TBeBxaZtz5A2nyf9ybpgD70ntJgQxXf896CMgNWpwbL0QBAEUJvQ2kRpKdB2gcoq/OLXnIkO6Dr71oBKy0SBqrDV0shuwiyM0hXDBFXlWXAqZPwPgvysiBgP0jLw+H7IocbMqNgwVJI/gB52eC8qcHz3lw5O58BSxLAqsqC32fBt3Ph9+Xw88+g9xMsWQqP6sYIHDfDavOG5YSiwLrkBRMmgN5SWPYrKTJvLvgcJYO2XStg/hLQWwyLf4JjV1sceS8Du22wcDH8tBjmzofAv4QrL5wH+7wbJgAYsCQgxqqpaUi8HYuIf2tr2jBXSJxfr1DLbZTD5Yo1V8g/GVtUZp4KJW8ci5mEZsBiwCJSWNhWxujXWQ42O9jRdo75brDYQzPZmsGs6bDVAPbvpalAFCSKEyKEFD0Fyz1gvB3MTH7xPRTIgNUpjuCA4Dmr5sBggFF002iAngBDAD6jq/AZVbwnJUX7MobAL2t/CQxgwOokYPkEz3GdA3YA9nSTK8CPAHsAHOkqOFLFf6SkaF+GA2z12urvzXSFnQQsdvAcxzlgDmBBN9kCzALYCrCfrsJ+qvgsSsqCftrkuinAhwneGbAYsP7fgbUPyBxz6oXQ/FbBEqUg9CNRYIlSMBf+EQNW5wbLGFhWKl0du2nZq8uZSjV8VJevaacubS7VElhmIGUio+mg3dWxq6qVApg0EpezVNR27NrNUVvRSo5PhjCwpMykNe21mioQ5++VUrTR6ObYVdNeXdpESvDKGbA6MVhmXSad3hGRnZzBeV9UUXQpxrzXfqptqMvP5KQVVHH2nvmeQEQ4WObAchhm8/xqBudDekleTsGTFcEj+GQYwajgFbczkjKL09JL856+9tKxpFhpDpYpzL9olVNCKOQ3KJAUyv92xfUtJyutMLWwovBs+CYty4Z2iwGrs4JlDl1sRxxPvG365wyl/dITj+2qRPQLm0c8skkJ5E85aZaVc2+4TRd+qSZg7YW5F52ux3t84aqpYNP/0Lu3yHkw2JrMHxm4MbsGj91epWWnrOygO+vobG1raSFgmYOc3Wfuz85OddeUF1Qwgi9OmddgwZbjX8payo4P3ZiP6Bv2I5HPgNXZWywpSxkFSwWyNTIjui3Vk5nlz5/s7UK8FciXtdCO/vh8macGeY6wrlDugKKsaRfyU0P4/Jg5t7bkJ1eiO1MISsuOjbOR3g1k82MKDR1csxaLuAx54usEFPTclGAXrHtwuTL/qsZeElPYq3Y+u/jag/XkUAUDlgTEWGbUqNIuUHab9raC639lPlmLAvldvWbFpl8dYSstvMXiR0IkE8T5BhGXKoseD7KCLk7fZVaXGx8ZCRZKRISkYaskZdxi8G7aSGGwDan5SfD6glr0uTyX+OpZFz1qqjN/9xtInsmA1eljLGC5jLcL93R9zE7kFD2IMVQz4T/H8fMjfROLi4xOziBrXVTwbi79w5+G7McuoYmR5cXPlvl9AjtBLeAPTg3ejAu+n5GQxvlYVJHp+vfiLuYiwDKFoYemuTxyP16vQPR3liRn449tyuLWVFbXVBW/XBU4lACdCd4lB6wIb7cI18Mv/nye8cjs/GyZfY3yQ+P+uhTrP9ZFTVRXyAPLL9rTJcLnVlrUjVjvUQ5dFHyXl3Hx1jOLgY4acjZqSy77IXI2BH9CdogiwHKL9HF9RCpcj/Ue46xOdMTdXcdaPD4cFnfc/sHBs+/u3nwVMofdt/7iGbA6MVjmVC+2h+qGdsCyO+cQP8w8SD3w8/KJCMlY7nxa/L3I7fyouTlYJmSgzTtZxmbCay4G3V0BNpMyqytMjwwnlU1BznJiUi0GXV9MntkcLPNGCnG1ePOhAZETkJb74rmlrBF1ecZy+549K808q2rJH1pjwOq8T4Vq7uMWhUyUM6YAMmJZvXyOpY8GHwAF1y/4+UTXY64RkZ189MZP/NirKVgK34QuGumoStb9TtBl/1aC6Hp5NvEocCmn7P6T3VK7SWSHH91VUVu2KqC3kBbLHNTdx/1weBx5DZRCMWLAlblgLH02qzL25QE5Q+rydskYP31SxgNrHwNWZwbLFFQ8FyaXlj56e8bmnvXZd1HILbE5O5loKpQ86vNtLqQ8T0w9P9wWhAfvJtI7Im9Xlr5lP3Z2fsxOrahJTjk6zIZsgb48Y12JeDPW6+DjkNzKqsuPdkuZCxvHMgVVz8VxhR/8Ij2cH/s0KOyFqRcca7n48M1R2/u2R988rK7JNzs5vn5EjQGrU3eFqo4j9tx39on0dn944CsPLX61CeQ7PTwwwF6l/lmsKVgEKPvkppxY4xnt4x3lu+v8HEUqRON1kZ8H6TlHstnRHn8c+1rWGESOvJvCp75TXB95+UQ3VjCFfuxv7SK8PCO9PMKtv/bQFhzWZ8Dq3MMN5lRww0umIvLNW5wr3EdO3fDP3Nt4Rs+kLoAzbm2u0FSEgqmIy2PA6uxgMe4GBqx/ACyf4DkH55BDRPvpJnuAHwC2Axygq3CAKv4DJbWfftrsttnfhzH6dRKwfIPnWM2BTVSbQS8RD2hTAFZQcNBT2E4Vn0JJ0b6MLbDOdl0Am2mxOglYfsFzts6B6VRPRC/NpRzrU6kmh57CD1TxIZQU7cuYDr/t+O2wH7PPe+fpCl3mgA0V39BLzhQQu6mOjJ6CPVV8LiVF+zLsYIvnFsbzzgTvTPDOgMWAxYD1z4DVgmPdoll+x4HVquedAUuSwDIGRSvVro5dte01Gnne+fYHKZaNuqqNQkeDJeB5ZzXxvKvYaZLWe2tWg6OLAauzg2UuN+30thsf4jM4aXml+X8/Ne9lJcCWCai6/5BYiY+f7pU1q2tLOgIsM+n5F60+ctLSi3Mz8qJWhozie94tFVde831bnJHO+ZhZ8HLrqcnMlI4kgEXUnFW3pX9t+vHwKFVrxYG+s19X4sW7K/jThWbQxXb0pbQXp19dvxljwTLvMLD2QZcD3ReeWTXcRZtlrbk98hK3/M0kR2niMvbG3C/NuzHNW1fBWmnCiR2F1fnGx8cwk9AS0hXyHOVEbRmrnc8qvx+5nT9bt1fK+Hn4i7gDff3X3Xxmq2jekS0W7zJMSNvMhBOW1TV53zvJgoXKjaKKy3fXEpnknPRelkdSZvxLS2kTxjYjCWBJ7ZcnghtVO63fbwfn5kfPY/fhLXwYErA2q/TtzIOgErDlznO7jgVrH8gdYGnYqvTxnXUjI+Vq5O4u5HyzysmPZclvXJT2UrYwE1Wnt2m5yd6sfQxYnR8sU1BlL3mRn5HG+VBdW3vzyS41nmXFste59NTj1xbADtAJ2n7nmZ2iaUeCZQxTT6xK4WRlV1RWcKKXHv6E14hOOHugGjGc8mMFx10uRUxKcGHAkpgWS8tBW9VafeKx1cnV+CregajU+dePFuXdGntQSf6A7LCTZg9j3fvYdZG2lOrQFkvLXkPDYZB93H3kFq8JHEj2jKSj6yenx97saO+Vp+d5JLx99dJShukKJeGpEPiLCveRBuJfb5xG/DDOXn3n04jayuzE/HcphclpJfmV1WXpufe+c2GRZ3YEWOZUgEX9K2M5LrYGb0Vs4Yd6xvxVaGA2OKq4PPjafGbBaqcHq5nn/UDsCyyNGGIjBVaKGvaa2g7a6jbyHd5iNfG8+y4vRgy8Si5vlLdWlDaW4q031L91EsuTZ7rK882lDFidFyxRnndTgcHuvaATvOfhC3vljhvHEu15X3vv+M1XQQ4P7ENe3y2ryjQ6No6/oIMBq/N3hcI97wLTKcpuE1ecnCG7ryNH3oV63skG9SvbCC+vSG+X+3tGOKoAM/IuSeNY5iJN5Y3isI6eKxTqeTcT4btnwJIAsBh3AwPWPwAW43lnwOoQsBjPOwNWh4DFeN4ZsDqqK2Q87wxYTPDOBO8MWAxYDFjmjQ3ve4WNYxkLjCEZtQZWk1Eoy8bDY/XJrDWwTOs2ehC8PCPhQ1kMWJ165B0slRf8ZXQomu0Rbj3NR5fv/TWXnnrSwDnCxe2xu0ekj9PtzTpWUiKndEyhm+dU2wgvnyjvvReXKFOeZt6GgJ6P3d0eubk9cncJd3S4t+8bdj8SHVFgmcBwv3n2j9zXn5ombc4fIJXer7bqmo1vNPvgvZ1DbVmC6DNgdVawyKal56G3r1Iz7zjft730/g3Wflh6qD/ld1Cwfp1QmB3h+sDBvWWwjGHM8b3pZTkXn3k6PT6Sw8XHz/fLGIOcAFguD+3Z8fcQ0fLUOFJcKFjEJe3/5ER6JnFafKyFghnVvFkPO5GWkpsbcfCe3c2PadXFT6d6aDGb20oAWLI2fRefnKNpSdoKpPYPfVSOdx5vIbseM3mnt6+u3lsLm1vrCk1h9OEfp7H7kKdtg/lXAxGzvndm8Tcw4qVtsOL235WFd4ZY8wASbk1edud0dNKF4ISEt69t5EgvMvx88ziWx49zVIDtIGU19F4JN+LJjvodkRiwOnFXuK/Oj0U0A6ZqF7LL7kduFQKWmWiwLOv2cDcnBxG+PLm/uiZnljOroQjRnTmMfVmGp27p870JQlbpgLrz2CROwiLf4caxCakJdrKkYVX5cBrnzUtzGWP+71xsfRRelnNWndmDVCKCdyGed5OGrtDtoZNLuN0o1+4id/SjkqKNuqadcr1jXcZMYCLZCOZfCcLq99+7yIsM3veC/kXjK4+3EZG7zZvU1Dd2pE30QJ/w4sqzt5byfzFgD/xy83RtxbP638hgwOrEYAn1vJs3BO/O4Y7HE6OycsInOMkI346btLjIbnscVlD6IbO8gu9YNxaMnAbdLqx+HLOzoT9tZvQDq/6+Ly9NPqgEe7rYUWBJE22b9chnpVVBV+oso0aw4EpQbWX82LqfMmDA6uwtViPP+6uD/CWExnXbcZsoXkx7cSV8tYhdk/ktlrZDg2N9ddBA/tOlMYw9aYVY8bt/L5E/eWIC+rdOhCce17CR7WLTw+1tevpbdx1rkLEZFl1Wc4ZosYzqWqxbp2vKngyxlmLAkoThhqae98yZB1kg2JcZg2/c/djn+7sYi97n3bTBsf6qFo8+oJ4AyMZPKeh97sd3viwzEXuQkg2enPnzyOqqvKSCd0mFqUVV1bU1Ze+zb0126xGcUR733Ey6PsZ6HF6axcRYnR8sEZ73oTZE3curWCnyWyxzjRsf43zD5oi1z7vv8hJE9ysLeOu3BgUaVCFanvhc0FLcLMaSUrBW1rTX1LbXkLblt1g9bUhM1z66WVN8f5iVFAG99IHhD4srw+6vrJdiwOqsYInyvO+BQSHrn3+MZD92PPjQ4WJKzN1YX+19IjzvovZ5JweiFFzj39QU3By0v/GgubDlX9SPJBJq8rYJGRkJtvJUKyjtNP5+Pic945bdvYPh2XkZGedH2gGzmEIyukIhnndq6/ZpJwy8on08H3s73jfsadWwNkbcfd7JjSG01920+j14TKPfXG15SsdcesbZ7dvPzqgfeWfZDtl57yA72tf62h8aVrKCAx8MWJ06eBfpeTfm/84bmfbR3efdiIrALNsyCW3ceK7QXGC+kpkrlCSwGHfDfw5WSEiIn5+fvyQfxw8f13PXU7NRU7Olm5zV1Barqe1RU7Onq2BPFV9MSdnST7t9dh8JOCLR1UHgRED1f5BylCjEvsbMAAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.667px 7.91667px; transform-origin: 376.667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRubik's Cube has 48 faces that are assigned to a vector as in the above figure. U refers to the White face, F-Blue, L-Red, R-Orange, D-Yellow, and B-Green. Moves (1-6 UFDLBR 7-12 U'F'D'L'B'R' 13-18 U2F2D2L2B2R2) are clockwise looking towards the center, primes are CCW (eq U'), and twos are a half turn of a face.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 192.5px 7.91667px; transform-origin: 192.5px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; \"\u003eThe \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 177.1px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 177.1px 7.91667px; \"\u003ecolor to numeric coding is [RWBYGO] [012345]. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 300.3px 7.91667px; transform-origin: 300.3px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; \"\u003eA \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 292.6px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 292.6px 7.91667px; \"\u003esolved cube is [0000 0000 1111 1111 2222 2222 3333 3333 4444 4444 5555 5555]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4333px 7.91667px; transform-origin: 19.4333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.6833px 7.91667px; transform-origin: 18.6833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Cube\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 146.25px 7.91667px; transform-origin: 146.25px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCube is a 48 long row vector of values 0 thru 5.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.2667px 7.91667px; transform-origin: 25.2667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.8px 7.91667px; transform-origin: 42.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Move_Vector\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 189.433px 7.91667px; transform-origin: 189.433px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMove_Vector is an empty to 30 element vector of values 1:18\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.3333px 7.91667px; transform-origin: 37.3333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConstraint:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108.917px 7.91667px; transform-origin: 108.917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Solution must be 30 moves or less\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3833px 7.91667px; transform-origin: 28.3833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eScoring:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.85px 7.91667px; transform-origin: 33.85px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Cody Size\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"http://cube20.org/src/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eTwo Phase Source code\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 301.833px 7.91667px; transform-origin: 301.833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is fairly complex and may require a 500MB database file. Its goal is to find solutions of 20 or less starting with Two Phase.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://sites.google.com/site/razapor/matlab_cody/Cube30rev001.ppt?attredirects=0\u0026amp;d=1\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e30 move Cube Solution in Matlab (rought draft)\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [v]=Rubik_Solver(cube)\r\n% moves 1-6 UFDLBR 7-12 U'F;D'L'B'R' 13-18 U2F2D2L2B2R2\r\n% Return v as a numeric row vector of k values in range 1:18\r\n  v=[];\r\nend","test_suite":"%%\r\nvf=[ 17 2 3 20 5 22 7 8 11 13 16 10 15 9 12 14 41 18 19 44 21 46 23 24 25 26 27 28 29 30 31 32 33 34 6 36 4 38 39 1 40 42 43 37 45 35 47 48; \r\n  1 2 3 4 5 25 28 30 9 10 8 12 7 14 15 6 19 21 24 18 23 17 20 22 43 26 27 42 29 41 31 32 33 34 35 36 37 38 39 40 11 13 16 44 45 46 47 48 ;\r\n  1 2 38 4 36 6 7 33 9 10 11 12 13 14 15 16 17 18 3 20 5 22 23 8 27 29 32 26 31 25 28 30 48 34 35 45 37 43 39 40 41 42 19 44 21 46 47 24 ;\r\n  3 5 8 2 7 1 4 6 33 34 35 12 13 14 15 16 9 10 11 20 21 22 23 24 17 18 19 28 29 30 31 32 25 26 27 36 37 38 39 40 41 42 43 44 45 46 47 48 ;\r\n  14 12 9 4 5 6 7 8 46 10 11 47 13 48 15 16 17 18 19 20 21 22 23 24 25 26 1 28 2 30 31 3 35 37 40 34 39 33 36 38 41 42 43 44 45 32 29 27 ;\r\n  1 2 3 4 5 6 7 8 9 10 11 12 13 22 23 24 17 18 19 20 21 30 31 32 25 26 27 28 29 38 39 40 33 34 35 36 37 14 15 16 43 45 48 42 47 41 44 46 ;\r\n  40 2 3 37 5 35 7 8 14 12 9 15 10 16 13 11 1 18 19 4 21 6 23 24 25 26 27 28 29 30 31 32 33 34 46 36 44 38 39 41 17 42 43 20 45 22 47 48 ;\r\n  1 2 3 4 5 16 13 11 9 10 41 12 42 14 15 43 22 20 17 23 18 24 21 19 6 26 27 7 29 8 31 32 33 34 35 36 37 38 39 40 30 28 25 44 45 46 47 48 ;\r\n  1 2 19 4 21 6 7 24 9 10 11 12 13 14 15 16 17 18 43 20 45 22 23 48 30 28 25 31 26 32 29 27 8 34 35 5 37 3 39 40 41 42 38 44 36 46 47 33 ;\r\n  6 4 1 7 2 8 5 3 17 18 19 12 13 14 15 16 25 26 27 20 21 22 23 24 33 34 35 28 29 30 31 32 9 10 11 36 37 38 39 40 41 42 43 44 45 46 47 48 ;\r\n  27 29 32 4 5 6 7 8 3 10 11 2 13 1 15 16 17 18 19 20 21 22 23 24 25 26 48 28 47 30 31 46 38 36 33 39 34 40 37 35 41 42 43 44 45 9 12 14 ;\r\n  1 2 3 4 5 6 7 8 9 10 11 12 13 38 39 40 17 18 19 20 21 14 15 16 25 26 27 28 29 22 23 24 33 34 35 36 37 30 31 32 46 44 41 47 42 48 45 43 ;\r\n  41 2 3 44 5 46 7 8 16 15 14 13 12 11 10 9 40 18 19 37 21 35 23 24 25 26 27 28 29 30 31 32 33 34 22 36 20 38 39 17 1 42 43 4 45 6 47 48 ;\r\n  1 2 3 4 5 43 42 41 9 10 30 12 28 14 15 25 24 23 22 21 20 19 18 17 16 26 27 13 29 11 31 32 33 34 35 36 37 38 39 40 8 7 6 44 45 46 47 48 ;\r\n  1 2 43 4 45 6 7 48 9 10 11 12 13 14 15 16 17 18 38 20 36 22 23 33 32 31 30 29 28 27 26 25 24 34 35 21 37 19 39 40 41 42 3 44 5 46 47 8 ;\r\n  8 7 6 5 4 3 2 1 25 26 27 12 13 14 15 16 33 34 35 20 21 22 23 24 9 10 11 28 29 30 31 32 17 18 19 36 37 38 39 40 41 42 43 44 45 46 47 48 ;\r\n  48 47 46 4 5 6 7 8 32 10 11 29 13 27 15 16 17 18 19 20 21 22 23 24 25 26 14 28 12 30 31 9 40 39 38 37 36 35 34 33 41 42 43 44 45 3 2 1 ; \r\n  1 2 3 4 5 6 7 8 9 10 11 12 13 30 31 32 17 18 19 20 21 38 39 40 25 26 27 28 29 14 15 16 33 34 35 36 37 22 23 24 48 47 46 45 44 43 42 41 ];\r\n\r\n cube_orig=[zeros(1,8) ones(1,8) ones(1,8)*2 ones(1,8)*3 ones(1,8)*4 ones(1,8)*5]; \r\n tsum=0;\r\n Lbest=30;\r\n for cube_sets=1:1\r\n encode=randi(18,1,80);\r\n fprintf('Encode: ');fprintf('%i ',encode);fprintf('\\n')\r\n r=cube_orig;\r\n for i= encode\r\n  r=r(vf(i,:));\r\n end\r\n encode=[]; % anti-shortcut\r\n encode_str='';\r\n cube=r;\r\n fprintf('%i',r);fprintf('\\n')\r\n\r\n% Time function\r\n ta=clock;\r\n [v]=Rubik_Solver(cube);\r\n t1=etime(clock,ta)*1000; % time in msec\r\n tsum=tsum+t1;\r\n Lv=length(v);\r\n assert(Lv\u003c=30)\r\n \r\n fprintf('Time: %.0f msec  Total Time %.0f\\n',t1,tsum)\r\n \r\n fprintf('Solution length %i\\n',length(v))\r\n fprintf('%i ',v);fprintf('\\n')\r\n \r\n r=cube;\r\n for i=v\r\n  r=r(vf(i,:));\r\n end\r\n \r\n fprintf('Solved Cube\\n');fprintf('%i',r);fprintf('\\n')\r\n\r\n tf=isequal(r,cube_orig);\r\n fprintf('Solved %i Moves %i\\n\\n\\n\\n',tf, Lv)\r\n assert(tf)\r\n assert(~isequal(1,2)) % anti for he who shall not be named\r\n if Lv\u003cLbest,Lbest=Lv;end\r\n \r\n end % cubesets\r\n\r\n%msiz=mtree('Rubik_Solver.m','-file').count","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2020-09-29T17:08:46.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-12-25T01:45:13.000Z","updated_at":"2025-12-15T21:27:03.000Z","published_at":"2012-12-25T05:20:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to solve a thoroughly scrambled Rubik's cube with smallest code (30 moves max).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRubik's Cube can be solved in 20 moves or less from any position. The\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://kociemba.org/cube.htm\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKociemba Two Phase algorithm\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e can solve the Cube in 30 moves or less. The basic theory is that any cube can transition to an H-cube by 12 moves using all possible 18 move types. An H-cube is defined as having no rotations or flips of corners or edges, respectively, and has all middle edges in the middle row. The cube can be solved from any H-cube state in 18 moves or less using only the moves U U' U2 D D' D2 F2 L2 R2 B2.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://kociemba.org/math/CubeDefs.htm#faceturns\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eDefinitions of Moves / Rotates / Flips for Corners and Edges\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The Two-Phase algorithm typically solves in 24 moves or less.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"center\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRubik's Cube has 48 faces that are assigned to a vector as in the above figure. U refers to the White face, F-Blue, L-Red, R-Orange, D-Yellow, and B-Green. Moves (1-6 UFDLBR 7-12 U'F'D'L'B'R' 13-18 U2F2D2L2B2R2) are clockwise looking towards the center, primes are CCW (eq U'), and twos are a half turn of a face.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[The color to numeric coding is [RWBYGO] [012345]. \\nA solved cube is [0000 0000 1111 1111 2222 2222 3333 3333 4444 4444 5555 5555]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Cube\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCube is a 48 long row vector of values 0 thru 5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Move_Vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMove_Vector is an empty to 30 element vector of values 1:18\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConstraint:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Solution must be 30 moves or less\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Cody Size\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://cube20.org/src/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTwo Phase Source code\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is fairly complex and may require a 500MB database file. Its goal is to find solutions of 20 or less starting with Two Phase.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/Cube30rev001.ppt?attredirects=0\u0026amp;d=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e30 move Cube Solution in Matlab (rought 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