{"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":1771,"title":"Polygonal numbers","description":"The task of \u003chttp://www.mathworks.co.uk/matlabcentral/cody/problems/5 Problem 5\u003e is to calculate triangular numbers. By playing with dots we can produce also square numbers like:\r\n\r\n                                 * * * *\r\n                     * * *       * * * *\r\n           * *       * * *       * * * *\r\n1: *    4: * *    9: * * *   16: * * * *\r\n\r\nor hexagonal numbers:\r\n\r\n                                          * * * *\r\n                                         *       *\r\n                         * * *          * * * *   *\r\n                        *     *        * *     *   *\r\n            * *        * * *   *        * * *   * * \r\n           *   *        *   * *          *   * * *\r\n1: *    6:  * *    15:   * * *       28:  * * * *\r\n\r\n\u0026nbsp\r\n\r\nAccording to those rules we can create \u003chttp://en.wikipedia.org/wiki/Polygonal_number polygonal numbers\u003e for all regular polygons.\r\n\r\n\u0026nbsp\r\n\r\nYour task: given _S_ and _N_ *calculate _N_-th _S_-gonal numbers* _P(S,N)_ \r\n\r\n\u0026nbsp\r\n\r\nExamples:\r\n\r\n# _P(4, 3)_ returns _[9]_    because 3-rd square number is 9,\r\n# _P(3, 1:5)_ returns _[1, 3, 6, 10, 15]_   first 5 triangular numbers,\r\n# _P(3:6, 4)_ returns _[10, 16, 22, 28]_   4-th triangular, square, pentagonal and hexagonal numbers,\r\n# _P([3, 4], [1; 2])_ returns _[1, 1; 3, 4]_.\r\n\r\nsee the test suite for more hints","description_html":"\u003cp\u003eThe task of \u003ca href = \"http://www.mathworks.co.uk/matlabcentral/cody/problems/5\"\u003eProblem 5\u003c/a\u003e is to calculate triangular numbers. By playing with dots we can produce also square numbers like:\u003c/p\u003e\u003cpre\u003e                                 * * * *\r\n                     * * *       * * * *\r\n           * *       * * *       * * * *\r\n1: *    4: * *    9: * * *   16: * * * *\u003c/pre\u003e\u003cp\u003eor hexagonal numbers:\u003c/p\u003e\u003cpre\u003e                                          * * * *\r\n                                         *       *\r\n                         * * *          * * * *   *\r\n                        *     *        * *     *   *\r\n            * *        * * *   *        * * *   * * \r\n           *   *        *   * *          *   * * *\r\n1: *    6:  * *    15:   * * *       28:  * * * *\u003c/pre\u003e\u003cp\u003e\u0026nbsp\u003c/p\u003e\u003cp\u003eAccording to those rules we can create \u003ca href = \"http://en.wikipedia.org/wiki/Polygonal_number\"\u003epolygonal numbers\u003c/a\u003e for all regular polygons.\u003c/p\u003e\u003cp\u003e\u0026nbsp\u003c/p\u003e\u003cp\u003eYour task: given \u003ci\u003eS\u003c/i\u003e and \u003ci\u003eN\u003c/i\u003e \u003cb\u003ecalculate \u003ci\u003eN\u003c/i\u003e-th \u003ci\u003eS\u003c/i\u003e-gonal numbers\u003c/b\u003e \u003ci\u003eP(S,N)\u003c/i\u003e\u003c/p\u003e\u003cp\u003e\u0026nbsp\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003col\u003e\u003cli\u003e\u003ci\u003eP(4, 3)\u003c/i\u003e returns \u003ci\u003e[9]\u003c/i\u003e    because 3-rd square number is 9,\u003c/li\u003e\u003cli\u003e\u003ci\u003eP(3, 1:5)\u003c/i\u003e returns \u003ci\u003e[1, 3, 6, 10, 15]\u003c/i\u003e   first 5 triangular numbers,\u003c/li\u003e\u003cli\u003e\u003ci\u003eP(3:6, 4)\u003c/i\u003e returns \u003ci\u003e[10, 16, 22, 28]\u003c/i\u003e   4-th triangular, square, pentagonal and hexagonal numbers,\u003c/li\u003e\u003cli\u003e\u003ci\u003eP([3, 4], [1; 2])\u003c/i\u003e returns \u003ci\u003e[1, 1; 3, 4]\u003c/i\u003e.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003esee the test suite for more hints\u003c/p\u003e","function_template":"function y = P(s,n)\r\n  y = s*n;\r\nend","test_suite":"%%\r\nassert(P(4,3)==9)\r\n%%\r\ns=3;\r\nn=1:5;\r\ny_correct=[1 3 6 10 15];\r\nassert(isequal(P(s,n),y_correct))\r\n%%\r\ns=3:6;\r\nn=4;\r\nY_correct=[10 16 22 28];\r\nassert(isequal(P(s,n),Y_correct))\r\n%%\r\ns=randi([3 1000],1,10);\r\nn=1;\r\ny_correct=ones(1,10);\r\nassert(isequal(P(s,n),y_correct))\r\n%%\r\ns=randi(1000,1,10)+2;\r\nn=5;\r\ny_correct=10*s-15;\r\nassert(isequal(P(s,n),y_correct))\r\n%%\r\ns=[5 6 7]';\r\nn=[2 8 9];\r\ny_correct=[5 92 117;6 120 153;7 148 189];\r\nassert(isequal(P(s,n),y_correct))\r\n%%\r\n% for M.Z.\r\ns=[5 6 7]';\r\nn=[2 8 9];\r\ny_correct=[5 92 117;6 120 153;7 148 189];\r\nassert(isequal(P(flipud(s),n),flipud(y_correct)))\r\n%%\r\ns=randi([3,1000]);\r\nn=randi([3,1000]);\r\nassert(P(s+1,n+1)-P(s,n+1)==P(3,n))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":4,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":138,"test_suite_updated_at":"2016-10-15T05:56:15.000Z","rescore_all_solutions":true,"group_id":8,"created_at":"2013-08-02T13:16:29.000Z","updated_at":"2026-02-16T10:32:51.000Z","published_at":"2013-08-02T23:34:24.000Z","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\":[],\"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\u003eThe task of\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://www.mathworks.co.uk/matlabcentral/cody/problems/5\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is to calculate triangular numbers. By playing with dots we can produce also square numbers like:\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[                                 * * * *\\n                     * * *       * * * *\\n           * *       * * *       * * * *\\n1: *    4: * *    9: * * *   16: * * * *]]\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\u003eor hexagonal numbers:\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[                                          * * * *\\n                                         *       *\\n                         * * *          * * * *   *\\n                        *     *        * *     *   *\\n            * *        * * *   *        * * *   * * \\n           *   *        *   * *          *   * * *\\n1: *    6:  * *    15:   * * *       28:  * * * *]]\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\u003e\u0026amp;nbsp\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\u003eAccording to those rules we can create\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://en.wikipedia.org/wiki/Polygonal_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003epolygonal numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for all regular polygons.\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\u003e\u0026amp;nbsp\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\u003eYour task: given\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecalculate\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-gonal numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP(S,N)\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\u003e\u0026amp;nbsp\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\u003eExamples:\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP(4, 3)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e returns\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[9]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e because 3-rd square number is 9,\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP(3, 1:5)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e returns\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 3, 6, 10, 15]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e first 5 triangular numbers,\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP(3:6, 4)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e returns\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[10, 16, 22, 28]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 4-th triangular, square, pentagonal and hexagonal numbers,\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP([3, 4], [1; 2])\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e returns\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 1; 3, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\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\u003esee the test suite for more hints\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 type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":1771,"title":"Polygonal numbers","description":"The task of \u003chttp://www.mathworks.co.uk/matlabcentral/cody/problems/5 Problem 5\u003e is to calculate triangular numbers. By playing with dots we can produce also square numbers like:\r\n\r\n                                 * * * *\r\n                     * * *       * * * *\r\n           * *       * * *       * * * *\r\n1: *    4: * *    9: * * *   16: * * * *\r\n\r\nor hexagonal numbers:\r\n\r\n                                          * * * *\r\n                                         *       *\r\n                         * * *          * * * *   *\r\n                        *     *        * *     *   *\r\n            * *        * * *   *        * * *   * * \r\n           *   *        *   * *          *   * * *\r\n1: *    6:  * *    15:   * * *       28:  * * * *\r\n\r\n\u0026nbsp\r\n\r\nAccording to those rules we can create \u003chttp://en.wikipedia.org/wiki/Polygonal_number polygonal numbers\u003e for all regular polygons.\r\n\r\n\u0026nbsp\r\n\r\nYour task: given _S_ and _N_ *calculate _N_-th _S_-gonal numbers* _P(S,N)_ \r\n\r\n\u0026nbsp\r\n\r\nExamples:\r\n\r\n# _P(4, 3)_ returns _[9]_    because 3-rd square number is 9,\r\n# _P(3, 1:5)_ returns _[1, 3, 6, 10, 15]_   first 5 triangular numbers,\r\n# _P(3:6, 4)_ returns _[10, 16, 22, 28]_   4-th triangular, square, pentagonal and hexagonal numbers,\r\n# _P([3, 4], [1; 2])_ returns _[1, 1; 3, 4]_.\r\n\r\nsee the test suite for more hints","description_html":"\u003cp\u003eThe task of \u003ca href = \"http://www.mathworks.co.uk/matlabcentral/cody/problems/5\"\u003eProblem 5\u003c/a\u003e is to calculate triangular numbers. By playing with dots we can produce also square numbers like:\u003c/p\u003e\u003cpre\u003e                                 * * * *\r\n                     * * *       * * * *\r\n           * *       * * *       * * * *\r\n1: *    4: * *    9: * * *   16: * * * *\u003c/pre\u003e\u003cp\u003eor hexagonal numbers:\u003c/p\u003e\u003cpre\u003e                                          * * * *\r\n                                         *       *\r\n                         * * *          * * * *   *\r\n                        *     *        * *     *   *\r\n            * *        * * *   *        * * *   * * \r\n           *   *        *   * *          *   * * *\r\n1: *    6:  * *    15:   * * *       28:  * * * *\u003c/pre\u003e\u003cp\u003e\u0026nbsp\u003c/p\u003e\u003cp\u003eAccording to those rules we can create \u003ca href = \"http://en.wikipedia.org/wiki/Polygonal_number\"\u003epolygonal numbers\u003c/a\u003e for all regular polygons.\u003c/p\u003e\u003cp\u003e\u0026nbsp\u003c/p\u003e\u003cp\u003eYour task: given \u003ci\u003eS\u003c/i\u003e and \u003ci\u003eN\u003c/i\u003e \u003cb\u003ecalculate \u003ci\u003eN\u003c/i\u003e-th \u003ci\u003eS\u003c/i\u003e-gonal numbers\u003c/b\u003e \u003ci\u003eP(S,N)\u003c/i\u003e\u003c/p\u003e\u003cp\u003e\u0026nbsp\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003col\u003e\u003cli\u003e\u003ci\u003eP(4, 3)\u003c/i\u003e returns \u003ci\u003e[9]\u003c/i\u003e    because 3-rd square number is 9,\u003c/li\u003e\u003cli\u003e\u003ci\u003eP(3, 1:5)\u003c/i\u003e returns \u003ci\u003e[1, 3, 6, 10, 15]\u003c/i\u003e   first 5 triangular numbers,\u003c/li\u003e\u003cli\u003e\u003ci\u003eP(3:6, 4)\u003c/i\u003e returns \u003ci\u003e[10, 16, 22, 28]\u003c/i\u003e   4-th triangular, square, pentagonal and hexagonal numbers,\u003c/li\u003e\u003cli\u003e\u003ci\u003eP([3, 4], [1; 2])\u003c/i\u003e returns \u003ci\u003e[1, 1; 3, 4]\u003c/i\u003e.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003esee the test suite for more hints\u003c/p\u003e","function_template":"function y = P(s,n)\r\n  y = s*n;\r\nend","test_suite":"%%\r\nassert(P(4,3)==9)\r\n%%\r\ns=3;\r\nn=1:5;\r\ny_correct=[1 3 6 10 15];\r\nassert(isequal(P(s,n),y_correct))\r\n%%\r\ns=3:6;\r\nn=4;\r\nY_correct=[10 16 22 28];\r\nassert(isequal(P(s,n),Y_correct))\r\n%%\r\ns=randi([3 1000],1,10);\r\nn=1;\r\ny_correct=ones(1,10);\r\nassert(isequal(P(s,n),y_correct))\r\n%%\r\ns=randi(1000,1,10)+2;\r\nn=5;\r\ny_correct=10*s-15;\r\nassert(isequal(P(s,n),y_correct))\r\n%%\r\ns=[5 6 7]';\r\nn=[2 8 9];\r\ny_correct=[5 92 117;6 120 153;7 148 189];\r\nassert(isequal(P(s,n),y_correct))\r\n%%\r\n% for M.Z.\r\ns=[5 6 7]';\r\nn=[2 8 9];\r\ny_correct=[5 92 117;6 120 153;7 148 189];\r\nassert(isequal(P(flipud(s),n),flipud(y_correct)))\r\n%%\r\ns=randi([3,1000]);\r\nn=randi([3,1000]);\r\nassert(P(s+1,n+1)-P(s,n+1)==P(3,n))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":4,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":138,"test_suite_updated_at":"2016-10-15T05:56:15.000Z","rescore_all_solutions":true,"group_id":8,"created_at":"2013-08-02T13:16:29.000Z","updated_at":"2026-02-16T10:32:51.000Z","published_at":"2013-08-02T23:34:24.000Z","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\":[],\"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\u003eThe task of\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://www.mathworks.co.uk/matlabcentral/cody/problems/5\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is to calculate triangular numbers. By playing with dots we can produce also square numbers like:\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[                                 * * * *\\n                     * * *       * * * *\\n           * *       * * *       * * * *\\n1: *    4: * *    9: * * *   16: * * * *]]\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\u003eor hexagonal numbers:\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[                                          * * * *\\n                                         *       *\\n                         * * *          * * * *   *\\n                        *     *        * *     *   *\\n            * *        * * *   *        * * *   * * \\n           *   *        *   * *          *   * * *\\n1: *    6:  * *    15:   * * *       28:  * * * *]]\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\u003e\u0026amp;nbsp\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\u003eAccording to those rules we can create\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://en.wikipedia.org/wiki/Polygonal_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003epolygonal numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for all regular polygons.\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\u003e\u0026amp;nbsp\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\u003eYour task: given\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecalculate\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eS\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-gonal numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP(S,N)\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\u003e\u0026amp;nbsp\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\u003eExamples:\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP(4, 3)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e returns\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[9]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e because 3-rd square number is 9,\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP(3, 1:5)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e returns\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1, 3, 6, 10, 15]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e first 5 triangular numbers,\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP(3:6, 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