{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":59045,"title":"8 : Find the Solving vector","description":"The Puzzle 8 is a variant of 15 ( Fifteen ). Fifteen is a slider puzzle, also a matlab function, with the goal being to create the matrix [1 2 3 4;5 6 7 8;9 10 11 12;13 14 15 0] where 0 is a hole.\r\nGiven a matrix m [3,3] and a matrix vset [n,k] of n possible solutions of up to length k determine which solution is valid. Return a vector [1,k] that produces [1 2 3;4 5 6;7 8 0]\r\nMovement is of the Zero-0. 3-Up, 0-Down, 1-Left, 2-Right, 4 is Not used/SKIP\r\nSome potential solutions may cause faults so try/catch may be required\r\nThe deepest solutions of 8 is 31 single moves. Solving this will be the next 8 challenge.\r\n[867;254;301] and [647;850;321] have 29 solutions each of length 31\r\nThe Puzzle 8 cases are readily created using a 15 board.","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: 243px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 121.5px; transform-origin: 407px 121.5px; vertical-align: baseline; \"\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: 101.5px 8px; transform-origin: 101.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Puzzle 8 is a variant of 15 ( \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/15_Puzzle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eFifteen\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: 252px 8px; transform-origin: 252px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ). Fifteen is a slider puzzle, also a matlab function, with the goal being to create the matrix [1 2 3 4;5 6 7 8;9 10 11 12;13 14 15 0] where 0 is a hole.\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: 371.5px 8px; transform-origin: 371.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a matrix m [3,3] and a matrix vset [n,k] of n possible solutions of up to length k determine which solution is valid. Return a vector [1,k] that produces [1 2 3;4 5 6;7 8 0]\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: 241px 8px; transform-origin: 241px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMovement is of the Zero-0. 3-Up, 0-Down, 1-Left, 2-Right, 4 is Not used/SKIP\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: 224px 8px; transform-origin: 224px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSome potential solutions may cause faults so try/catch may be required\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: 272.5px 8px; transform-origin: 272.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe deepest solutions of 8 is 31 single moves. Solving this will be the next 8 challenge.\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: 218.5px 8px; transform-origin: 218.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e[867;254;301] and [647;850;321] have 29 solutions each of length 31\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: 180px 8px; transform-origin: 180px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Puzzle 8 cases are readily created using a 15 board.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function v = solve8(m,vset)\r\n% m is 3x3 matrix with 0:8 values\r\n% vset is multiple possible solutions to restore m to [1 2 3;4 5 6;7 8 0]\r\n% Movement is of the 0. 3-U, 0-D, 1-L, 2-R, 4 is Not used/SKIP\r\n% some possible solutions may move the 0 off the board so try/catch may be needed\r\n v=vset(1,:);\r\n for i=1:size(vset,1)\r\n  mf=Eight_SolveA(m,vset(i,:));\r\n  \r\n  %check for valid/return_vector\r\n  \r\n end % i\r\n \r\nend % solve8\r\n\r\n\r\nfunction m=Eight_SolveA(m,svec)\r\n%m [3,3]\r\n%svec [1,n] 3U 0D 1L 2R  Movement of the Zero/Hole, 4 is skip\r\n [zr,zc]=find(m==0);\r\n for i=1:length(svec) \r\n  try\r\n  switch svec(i)  % 1/3 time of if/elseif\r\n   case 3  %U\r\n    m(zr,zc)=m(zr-1,zc);\r\n    zr=zr-1;\r\n   case 0 %D\r\n    m(zr,zc)=m(zr+1,zc);\r\n    zr=zr+1;\r\n   case 1 %L\r\n    m(zr,zc)=m(zr,zc-1);\r\n    zc=zc-1;\r\n   case 2 %R\r\n    m(zr,zc)=m(zr,zc+1);\r\n    zc=zc+1;\r\n   otherwise %4\r\n    return\r\n  end\r\n  m(zr,zc)=0;\r\n  catch\r\n   return;\r\n  end\r\n end % i  svec(i)\r\nend %Eight_SolveA\r\n","test_suite":"%%\r\nvalid=1;\r\nm=[1 2 3;4 5 6;7 0 8]; %2\r\nfprintf('Challenge:\\n');\r\nfprintf('%i %i %i\\n',m');fprintf('\\n')\r\nvset=[0 4;2 4;1 1];\r\n\r\nsvec = solve8(m,vset);\r\n\r\nfprintf('Solution: ')\r\nfprintf('%i',svec);fprintf('\\n');\r\n\r\n [zr,zc]=find(m==0);\r\n for i=1:length(svec) \r\n try\r\n  switch svec(i)  % 1/3 time of if/elseif\r\n   case 3  %U\r\n    m(zr,zc)=m(zr-1,zc);\r\n    zr=zr-1;\r\n   case 0 %D\r\n    m(zr,zc)=m(zr+1,zc);\r\n    zr=zr+1;\r\n   case 1 %L\r\n    m(zr,zc)=m(zr,zc-1);\r\n    zc=zc-1;\r\n   case 2 %R\r\n    m(zr,zc)=m(zr,zc+1);\r\n    zc=zc+1;\r\n   otherwise %4\r\n    break;\r\n  end\r\n  m(zr,zc)=0;\r\n catch\r\n  valid=0;\r\n  break;\r\n end\r\n end % i  svec(i)\r\n \r\n if ~isequal(m,[1 2 3;4 5 6;7 8 0])\r\n  valid=0; %\r\n  fprintf('Invalid solution\\n')\r\n end\r\n fprintf('%i %i %i\\n',m');fprintf('\\n')\r\n \r\n assert(valid)\r\n \r\n%%\r\nvalid=1;\r\nm=[3 1 2;4 5 6;7 0 8]; %133201022313200\r\nfprintf('Challenge:\\n');\r\nfprintf('%i %i %i\\n',m');fprintf('\\n')\r\nvset=[2 1 1 3 3 2 0 1 0 2 2 3 1 3 2;\r\n      1 3 3 2 0 3 0 1 0 2 2 3 1 3 2;\r\n      1 3 3 2 0 1 0 2 2 1 2 3 1 3 2;\r\n      1 3 3 2 0 1 0 2 2 3 1 3 2 0 0];\r\n\r\nsvec = solve8(m,vset);\r\n\r\nfprintf('Solution: ')\r\nfprintf('%i',svec);fprintf('\\n');\r\n\r\n [zr,zc]=find(m==0);\r\n for i=1:length(svec) \r\n try\r\n  switch svec(i)  % 1/3 time of if/elseif\r\n   case 3  %U\r\n    m(zr,zc)=m(zr-1,zc);\r\n    zr=zr-1;\r\n   case 0 %D\r\n    m(zr,zc)=m(zr+1,zc);\r\n    zr=zr+1;\r\n   case 1 %L\r\n    m(zr,zc)=m(zr,zc-1);\r\n    zc=zc-1;\r\n   case 2 %R\r\n    m(zr,zc)=m(zr,zc+1);\r\n    zc=zc+1;\r\n   otherwise %4\r\n    break;\r\n  end\r\n  m(zr,zc)=0;\r\n catch\r\n  valid=0;\r\n  break;\r\n end\r\n end % i  svec(i)\r\n \r\n if ~isequal(m,[1 2 3;4 5 6;7 8 0])\r\n  valid=0; %\r\n  fprintf('Invalid solution\\n')\r\n end\r\n fprintf('%i %i %i\\n',m');fprintf('\\n')\r\n \r\n assert(valid)\r\n\r\n \r\n%%\r\nvalid=1;\r\nm=[0 2 3;1 5 6;4 7 8]; %0022\r\nfprintf('Challenge:\\n');\r\nfprintf('%i %i %i\\n',m');fprintf('\\n')\r\nvset=[2 0 0 1 2 4;\r\n      0 0 2 3 4 4;\r\n      0 0 2 2 4 4;\r\n      0 3 2 1 4 4];\r\n\r\nsvec = solve8(m,vset);\r\n\r\nfprintf('Solution: ')\r\nfprintf('%i',svec);fprintf('\\n');\r\n\r\n [zr,zc]=find(m==0);\r\n for i=1:length(svec) \r\n try\r\n  switch svec(i)  % 1/3 time of if/elseif\r\n   case 3  %U\r\n    m(zr,zc)=m(zr-1,zc);\r\n    zr=zr-1;\r\n   case 0 %D\r\n    m(zr,zc)=m(zr+1,zc);\r\n    zr=zr+1;\r\n   case 1 %L\r\n    m(zr,zc)=m(zr,zc-1);\r\n    zc=zc-1;\r\n   case 2 %R\r\n    m(zr,zc)=m(zr,zc+1);\r\n    zc=zc+1;\r\n   otherwise %4\r\n    break;\r\n  end\r\n  m(zr,zc)=0;\r\n catch\r\n  valid=0;\r\n  break;\r\n end\r\n end % i  svec(i)\r\n \r\n if ~isequal(m,[1 2 3;4 5 6;7 8 0])\r\n  valid=0; %\r\n  fprintf('Invalid solution\\n')\r\n end\r\n fprintf('%i %i %i\\n',m');fprintf('\\n')\r\n \r\n assert(valid)\r\n\r\n%%\r\nvalid=1;\r\nm=[2 3 0;1 5 6;4 7 8]; %110022\r\nfprintf('Challenge:\\n');\r\nfprintf('%i %i %i\\n',m');fprintf('\\n')\r\nvset=[1 1 2 0 0 1 2 4;\r\n      1 1 0 0 2 3 3 3;\r\n      1 1 0 0 2 2 4 4;\r\n      1 1 0 3 2 1 2 1];\r\n\r\nsvec = solve8(m,vset);\r\n\r\nfprintf('Solution: ')\r\nfprintf('%i',svec);fprintf('\\n');\r\n\r\n [zr,zc]=find(m==0);\r\n for i=1:length(svec) \r\n try\r\n  switch svec(i)  % 1/3 time of if/elseif\r\n   case 3  %U\r\n    m(zr,zc)=m(zr-1,zc);\r\n    zr=zr-1;\r\n   case 0 %D\r\n    m(zr,zc)=m(zr+1,zc);\r\n    zr=zr+1;\r\n   case 1 %L\r\n    m(zr,zc)=m(zr,zc-1);\r\n    zc=zc-1;\r\n   case 2 %R\r\n    m(zr,zc)=m(zr,zc+1);\r\n    zc=zc+1;\r\n   otherwise %4\r\n    break;\r\n  end\r\n  m(zr,zc)=0;\r\n catch\r\n  valid=0;\r\n  break;\r\n end\r\n end % i  svec(i)\r\n \r\n if ~isequal(m,[1 2 3;4 5 6;7 8 0])\r\n  valid=0; %\r\n  fprintf('Invalid solution\\n')\r\n end\r\n fprintf('%i %i %i\\n',m');fprintf('\\n')\r\n \r\n assert(valid)\r\n\r\n \r\n%%\r\nvalid=1;\r\nm=[2 3 6;1 5 8;4 7 0]; %33110022\r\nfprintf('Challenge:\\n');\r\nfprintf('%i %i %i\\n',m');fprintf('\\n')\r\nvset=[3 3 1 1 2 0 0 1 2;\r\n      3 3 1 1 0 0 2 3 3;\r\n      3 3 1 1 0 3 2 1 2;\r\n      3 3 1 1 0 0 2 2 4;\r\n      3 3 1 1 0 0 2 3 3];\r\n\r\nsvec = solve8(m,vset);\r\n\r\nfprintf('Solution: ')\r\nfprintf('%i',svec);fprintf('\\n');\r\n\r\n [zr,zc]=find(m==0);\r\n for i=1:length(svec) \r\n try\r\n  switch svec(i)  % 1/3 time of if/elseif\r\n   case 3  %U\r\n    m(zr,zc)=m(zr-1,zc);\r\n    zr=zr-1;\r\n   case 0 %D\r\n    m(zr,zc)=m(zr+1,zc);\r\n    zr=zr+1;\r\n   case 1 %L\r\n    m(zr,zc)=m(zr,zc-1);\r\n    zc=zc-1;\r\n   case 2 %R\r\n    m(zr,zc)=m(zr,zc+1);\r\n    zc=zc+1;\r\n   otherwise %4\r\n    break;\r\n  end\r\n  m(zr,zc)=0;\r\n catch\r\n  valid=0;\r\n  break;\r\n end\r\n end % i  svec(i)\r\n \r\n if ~isequal(m,[1 2 3;4 5 6;7 8 0])\r\n  valid=0; %\r\n  fprintf('Invalid solution\\n')\r\n end\r\n fprintf('%i %i %i\\n',m');fprintf('\\n')\r\n \r\n assert(valid)\r\n\r\n ","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-10-02T21:40:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-10-02T19:13:59.000Z","updated_at":"2023-10-02T21:40:50.000Z","published_at":"2023-10-02T21:40:50.000Z","restored_at":null,"restored_by":null,"spam":null,"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\u003eThe Puzzle 8 is a variant of 15 ( \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/15_Puzzle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFifteen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ). Fifteen is a slider puzzle, also a matlab function, with the goal being to create the matrix [1 2 3 4;5 6 7 8;9 10 11 12;13 14 15 0] where 0 is a hole.\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\u003eGiven a matrix m [3,3] and a matrix vset [n,k] of n possible solutions of up to length k determine which solution is valid. Return a vector [1,k] that produces [1 2 3;4 5 6;7 8 0]\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\u003eMovement is of the Zero-0. 3-Up, 0-Down, 1-Left, 2-Right, 4 is Not used/SKIP\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\u003eSome potential solutions may cause faults so try/catch may be 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe deepest solutions of 8 is 31 single moves. Solving this will be the next 8 challenge.\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\u003e[867;254;301] and [647;850;321] have 29 solutions each of length 31\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 Puzzle 8 cases are readily created using a 15 board.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":59045,"title":"8 : Find the Solving vector","description":"The Puzzle 8 is a variant of 15 ( Fifteen ). Fifteen is a slider puzzle, also a matlab function, with the goal being to create the matrix [1 2 3 4;5 6 7 8;9 10 11 12;13 14 15 0] where 0 is a hole.\r\nGiven a matrix m [3,3] and a matrix vset [n,k] of n possible solutions of up to length k determine which solution is valid. Return a vector [1,k] that produces [1 2 3;4 5 6;7 8 0]\r\nMovement is of the Zero-0. 3-Up, 0-Down, 1-Left, 2-Right, 4 is Not used/SKIP\r\nSome potential solutions may cause faults so try/catch may be required\r\nThe deepest solutions of 8 is 31 single moves. Solving this will be the next 8 challenge.\r\n[867;254;301] and [647;850;321] have 29 solutions each of length 31\r\nThe Puzzle 8 cases are readily created using a 15 board.","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: 243px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 121.5px; transform-origin: 407px 121.5px; vertical-align: baseline; \"\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: 101.5px 8px; transform-origin: 101.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Puzzle 8 is a variant of 15 ( \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/15_Puzzle\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eFifteen\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: 252px 8px; transform-origin: 252px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ). Fifteen is a slider puzzle, also a matlab function, with the goal being to create the matrix [1 2 3 4;5 6 7 8;9 10 11 12;13 14 15 0] where 0 is a hole.\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: 371.5px 8px; transform-origin: 371.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a matrix m [3,3] and a matrix vset [n,k] of n possible solutions of up to length k determine which solution is valid. Return a vector [1,k] that produces [1 2 3;4 5 6;7 8 0]\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: 241px 8px; transform-origin: 241px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMovement is of the Zero-0. 3-Up, 0-Down, 1-Left, 2-Right, 4 is Not used/SKIP\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: 224px 8px; transform-origin: 224px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSome potential solutions may cause faults so try/catch may be required\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: 272.5px 8px; transform-origin: 272.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe deepest solutions of 8 is 31 single moves. Solving this will be the next 8 challenge.\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: 218.5px 8px; transform-origin: 218.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e[867;254;301] and [647;850;321] have 29 solutions each of length 31\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: 180px 8px; transform-origin: 180px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Puzzle 8 cases are readily created using a 15 board.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function v = solve8(m,vset)\r\n% m is 3x3 matrix with 0:8 values\r\n% vset is multiple possible solutions to restore m to [1 2 3;4 5 6;7 8 0]\r\n% Movement is of the 0. 3-U, 0-D, 1-L, 2-R, 4 is Not used/SKIP\r\n% some possible solutions may move the 0 off the board so try/catch may be needed\r\n v=vset(1,:);\r\n for i=1:size(vset,1)\r\n  mf=Eight_SolveA(m,vset(i,:));\r\n  \r\n  %check for valid/return_vector\r\n  \r\n end % i\r\n \r\nend % solve8\r\n\r\n\r\nfunction m=Eight_SolveA(m,svec)\r\n%m [3,3]\r\n%svec [1,n] 3U 0D 1L 2R  Movement of the Zero/Hole, 4 is skip\r\n [zr,zc]=find(m==0);\r\n for i=1:length(svec) \r\n  try\r\n  switch svec(i)  % 1/3 time of if/elseif\r\n   case 3  %U\r\n    m(zr,zc)=m(zr-1,zc);\r\n    zr=zr-1;\r\n   case 0 %D\r\n    m(zr,zc)=m(zr+1,zc);\r\n    zr=zr+1;\r\n   case 1 %L\r\n    m(zr,zc)=m(zr,zc-1);\r\n    zc=zc-1;\r\n   case 2 %R\r\n    m(zr,zc)=m(zr,zc+1);\r\n    zc=zc+1;\r\n   otherwise %4\r\n    return\r\n  end\r\n  m(zr,zc)=0;\r\n  catch\r\n   return;\r\n  end\r\n end % i  svec(i)\r\nend %Eight_SolveA\r\n","test_suite":"%%\r\nvalid=1;\r\nm=[1 2 3;4 5 6;7 0 8]; %2\r\nfprintf('Challenge:\\n');\r\nfprintf('%i %i %i\\n',m');fprintf('\\n')\r\nvset=[0 4;2 4;1 1];\r\n\r\nsvec = solve8(m,vset);\r\n\r\nfprintf('Solution: ')\r\nfprintf('%i',svec);fprintf('\\n');\r\n\r\n [zr,zc]=find(m==0);\r\n for i=1:length(svec) \r\n try\r\n  switch svec(i)  % 1/3 time of if/elseif\r\n   case 3  %U\r\n    m(zr,zc)=m(zr-1,zc);\r\n    zr=zr-1;\r\n   case 0 %D\r\n    m(zr,zc)=m(zr+1,zc);\r\n    zr=zr+1;\r\n   case 1 %L\r\n    m(zr,zc)=m(zr,zc-1);\r\n    zc=zc-1;\r\n   case 2 %R\r\n    m(zr,zc)=m(zr,zc+1);\r\n    zc=zc+1;\r\n   otherwise %4\r\n    break;\r\n  end\r\n  m(zr,zc)=0;\r\n catch\r\n  valid=0;\r\n  break;\r\n end\r\n end % i  svec(i)\r\n \r\n if ~isequal(m,[1 2 3;4 5 6;7 8 0])\r\n  valid=0; %\r\n  fprintf('Invalid solution\\n')\r\n end\r\n fprintf('%i %i %i\\n',m');fprintf('\\n')\r\n \r\n assert(valid)\r\n \r\n%%\r\nvalid=1;\r\nm=[3 1 2;4 5 6;7 0 8]; %133201022313200\r\nfprintf('Challenge:\\n');\r\nfprintf('%i %i %i\\n',m');fprintf('\\n')\r\nvset=[2 1 1 3 3 2 0 1 0 2 2 3 1 3 2;\r\n      1 3 3 2 0 3 0 1 0 2 2 3 1 3 2;\r\n      1 3 3 2 0 1 0 2 2 1 2 3 1 3 2;\r\n      1 3 3 2 0 1 0 2 2 3 1 3 2 0 0];\r\n\r\nsvec = solve8(m,vset);\r\n\r\nfprintf('Solution: ')\r\nfprintf('%i',svec);fprintf('\\n');\r\n\r\n [zr,zc]=find(m==0);\r\n for i=1:length(svec) \r\n try\r\n  switch svec(i)  % 1/3 time of if/elseif\r\n   case 3  %U\r\n    m(zr,zc)=m(zr-1,zc);\r\n    zr=zr-1;\r\n   case 0 %D\r\n    m(zr,zc)=m(zr+1,zc);\r\n    zr=zr+1;\r\n   case 1 %L\r\n    m(zr,zc)=m(zr,zc-1);\r\n    zc=zc-1;\r\n   case 2 %R\r\n    m(zr,zc)=m(zr,zc+1);\r\n    zc=zc+1;\r\n   otherwise %4\r\n    break;\r\n  end\r\n  m(zr,zc)=0;\r\n catch\r\n  valid=0;\r\n  break;\r\n end\r\n end % i  svec(i)\r\n \r\n if ~isequal(m,[1 2 3;4 5 6;7 8 0])\r\n  valid=0; %\r\n  fprintf('Invalid solution\\n')\r\n end\r\n fprintf('%i %i %i\\n',m');fprintf('\\n')\r\n \r\n assert(valid)\r\n\r\n \r\n%%\r\nvalid=1;\r\nm=[0 2 3;1 5 6;4 7 8]; %0022\r\nfprintf('Challenge:\\n');\r\nfprintf('%i %i %i\\n',m');fprintf('\\n')\r\nvset=[2 0 0 1 2 4;\r\n      0 0 2 3 4 4;\r\n      0 0 2 2 4 4;\r\n      0 3 2 1 4 4];\r\n\r\nsvec = solve8(m,vset);\r\n\r\nfprintf('Solution: ')\r\nfprintf('%i',svec);fprintf('\\n');\r\n\r\n [zr,zc]=find(m==0);\r\n for i=1:length(svec) \r\n try\r\n  switch svec(i)  % 1/3 time of if/elseif\r\n   case 3  %U\r\n    m(zr,zc)=m(zr-1,zc);\r\n    zr=zr-1;\r\n   case 0 %D\r\n    m(zr,zc)=m(zr+1,zc);\r\n    zr=zr+1;\r\n   case 1 %L\r\n    m(zr,zc)=m(zr,zc-1);\r\n    zc=zc-1;\r\n   case 2 %R\r\n    m(zr,zc)=m(zr,zc+1);\r\n    zc=zc+1;\r\n   otherwise %4\r\n    break;\r\n  end\r\n  m(zr,zc)=0;\r\n catch\r\n  valid=0;\r\n  break;\r\n end\r\n end % i  svec(i)\r\n \r\n if ~isequal(m,[1 2 3;4 5 6;7 8 0])\r\n  valid=0; %\r\n  fprintf('Invalid solution\\n')\r\n end\r\n fprintf('%i %i %i\\n',m');fprintf('\\n')\r\n \r\n assert(valid)\r\n\r\n%%\r\nvalid=1;\r\nm=[2 3 0;1 5 6;4 7 8]; %110022\r\nfprintf('Challenge:\\n');\r\nfprintf('%i %i %i\\n',m');fprintf('\\n')\r\nvset=[1 1 2 0 0 1 2 4;\r\n      1 1 0 0 2 3 3 3;\r\n      1 1 0 0 2 2 4 4;\r\n      1 1 0 3 2 1 2 1];\r\n\r\nsvec = solve8(m,vset);\r\n\r\nfprintf('Solution: ')\r\nfprintf('%i',svec);fprintf('\\n');\r\n\r\n [zr,zc]=find(m==0);\r\n for i=1:length(svec) \r\n try\r\n  switch svec(i)  % 1/3 time of if/elseif\r\n   case 3  %U\r\n    m(zr,zc)=m(zr-1,zc);\r\n    zr=zr-1;\r\n   case 0 %D\r\n    m(zr,zc)=m(zr+1,zc);\r\n    zr=zr+1;\r\n   case 1 %L\r\n    m(zr,zc)=m(zr,zc-1);\r\n    zc=zc-1;\r\n   case 2 %R\r\n    m(zr,zc)=m(zr,zc+1);\r\n    zc=zc+1;\r\n   otherwise %4\r\n    break;\r\n  end\r\n  m(zr,zc)=0;\r\n catch\r\n  valid=0;\r\n  break;\r\n end\r\n end % i  svec(i)\r\n \r\n if ~isequal(m,[1 2 3;4 5 6;7 8 0])\r\n  valid=0; %\r\n  fprintf('Invalid solution\\n')\r\n end\r\n fprintf('%i %i %i\\n',m');fprintf('\\n')\r\n \r\n assert(valid)\r\n\r\n \r\n%%\r\nvalid=1;\r\nm=[2 3 6;1 5 8;4 7 0]; %33110022\r\nfprintf('Challenge:\\n');\r\nfprintf('%i %i %i\\n',m');fprintf('\\n')\r\nvset=[3 3 1 1 2 0 0 1 2;\r\n      3 3 1 1 0 0 2 3 3;\r\n      3 3 1 1 0 3 2 1 2;\r\n      3 3 1 1 0 0 2 2 4;\r\n      3 3 1 1 0 0 2 3 3];\r\n\r\nsvec = solve8(m,vset);\r\n\r\nfprintf('Solution: ')\r\nfprintf('%i',svec);fprintf('\\n');\r\n\r\n [zr,zc]=find(m==0);\r\n for i=1:length(svec) \r\n try\r\n  switch svec(i)  % 1/3 time of if/elseif\r\n   case 3  %U\r\n    m(zr,zc)=m(zr-1,zc);\r\n    zr=zr-1;\r\n   case 0 %D\r\n    m(zr,zc)=m(zr+1,zc);\r\n    zr=zr+1;\r\n   case 1 %L\r\n    m(zr,zc)=m(zr,zc-1);\r\n    zc=zc-1;\r\n   case 2 %R\r\n    m(zr,zc)=m(zr,zc+1);\r\n    zc=zc+1;\r\n   otherwise %4\r\n    break;\r\n  end\r\n  m(zr,zc)=0;\r\n catch\r\n  valid=0;\r\n  break;\r\n end\r\n end % i  svec(i)\r\n \r\n if ~isequal(m,[1 2 3;4 5 6;7 8 0])\r\n  valid=0; %\r\n  fprintf('Invalid solution\\n')\r\n end\r\n fprintf('%i %i %i\\n',m');fprintf('\\n')\r\n \r\n assert(valid)\r\n\r\n ","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-10-02T21:40:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-10-02T19:13:59.000Z","updated_at":"2023-10-02T21:40:50.000Z","published_at":"2023-10-02T21:40:50.000Z","restored_at":null,"restored_by":null,"spam":null,"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\u003eThe Puzzle 8 is a variant of 15 ( \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/15_Puzzle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eFifteen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ). Fifteen is a slider puzzle, also a matlab function, with the goal being to create the matrix [1 2 3 4;5 6 7 8;9 10 11 12;13 14 15 0] where 0 is a hole.\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\u003eGiven a matrix m [3,3] and a matrix vset [n,k] of n possible solutions of up to length k determine which solution is valid. 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