{"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":59526,"title":"Count paths between corners of a grid that remain on or below the diagonal","description":"Consider motion from the lower left corner of a square grid to the upper right corner. The motion is constrained in two ways: (1) the only legal moves are (0,1), (1,0), and (1,1)—i.e., right, up, and up-and-right between points of the lattice—and (2) the motion must remain on or below the line connecting the starting and finishing corners. For a 2x2 grid, the number of paths is 6, as shown below. \r\nWrite a function to count the legal paths for an x grid. Return the count as a string. Check the last test for banned functions.\r\n","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: 273.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 136.933px; transform-origin: 407px 136.933px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; 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 42px; text-align: left; transform-origin: 384px 42px; 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: 383.125px 8px; transform-origin: 383.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider motion from the lower left corner of a square grid to the upper right corner. The motion is constrained in two ways: (1) the only legal moves are (0,1), (1,0), and (1,1)—i.e., right, up, and up-and-right between points of the lattice—and (2) the motion must remain on or below the line connecting the starting and finishing corners. For a 2x2 grid, the number of paths is 6, as shown below. \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: 144.558px 8px; transform-origin: 144.558px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to count the legal paths for an \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 3.5px 8px; transform-origin: 3.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 202.242px 8px; transform-origin: 202.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e grid. Return the count as a string. Check the last test for banned functions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 129.867px; 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 64.9333px; text-align: left; transform-origin: 384px 64.9333px; 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\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Schroeder(n)\r\n  y = factorial(n);\r\nend","test_suite":"%%\r\nn = 0;\r\ny = Schroeder(n);\r\ny_correct = '1';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 2;\r\ny = Schroeder(n);\r\ny_correct = '6';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 10;\r\ny = Schroeder(n);\r\ny_correct = '1037718';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 17;\r\ny = Schroeder(n);\r\ny_correct = '111818026018';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 23;\r\ny = Schroeder(n);\r\ny_correct = '2832923350929742';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 53;\r\ny = Schroeder(n);\r\ny_correct = '77073779272885977020023254295915628266';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 113;\r\ny = Schroeder(n);\r\ny_correct = '214645018815655382073160317691190772088909088782578589367620531418920165400447421666';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 157;\r\ny = Schroeder(n);\r\ny_correct = '635298195989878453594162293551305562386458118544676764232073734715032717517063580963828995662005206580225562745343802';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 88;\r\ny = Schroeder(n);\r\nyy = Schroeder(str2num(y(1:3)));\r\nyy_correct = '24528665763748049389685052543171711960129970876829498326068598388698578380240132802889284459385709363425133815992875744127843722179914611505186848090410102929094478101446';\r\nassert(isequal(yy,yy_correct))\r\n\r\n%%\r\nfiletext = fileread('Schroeder.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'java') || contains(filetext,'py'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-04T04:53:07.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-01-04T04:42:17.000Z","updated_at":"2024-01-04T04:53:07.000Z","published_at":"2024-01-04T04:53:07.000Z","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\u003eConsider motion from the lower left corner of a square grid to the upper right corner. The motion is constrained in two ways: (1) the only legal moves are (0,1), (1,0), and (1,1)—i.e., right, up, and up-and-right between points of the lattice—and (2) the motion must remain on or below the line connecting the starting and finishing corners. For a 2x2 grid, the number of paths is 6, as shown below. \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\u003eWrite a function to count the legal paths for an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e grid. Return the count as a string. 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paths between corners of a grid that remain on or below the diagonal","description":"Consider motion from the lower left corner of a square grid to the upper right corner. The motion is constrained in two ways: (1) the only legal moves are (0,1), (1,0), and (1,1)—i.e., right, up, and up-and-right between points of the lattice—and (2) the motion must remain on or below the line connecting the starting and finishing corners. For a 2x2 grid, the number of paths is 6, as shown below. \r\nWrite a function to count the legal paths for an x grid. Return the count as a string. Check the last test for banned functions.\r\n","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: 273.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 136.933px; transform-origin: 407px 136.933px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; 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 42px; text-align: left; transform-origin: 384px 42px; 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: 383.125px 8px; transform-origin: 383.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider motion from the lower left corner of a square grid to the upper right corner. The motion is constrained in two ways: (1) the only legal moves are (0,1), (1,0), and (1,1)—i.e., right, up, and up-and-right between points of the lattice—and (2) the motion must remain on or below the line connecting the starting and finishing corners. For a 2x2 grid, the number of paths is 6, as shown below. \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: 144.558px 8px; transform-origin: 144.558px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to count the legal paths for an \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 3.5px 8px; transform-origin: 3.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 202.242px 8px; transform-origin: 202.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e grid. Return the count as a string. Check the last test for banned functions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 129.867px; 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 64.9333px; text-align: left; transform-origin: 384px 64.9333px; 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\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Schroeder(n)\r\n  y = factorial(n);\r\nend","test_suite":"%%\r\nn = 0;\r\ny = Schroeder(n);\r\ny_correct = '1';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 2;\r\ny = Schroeder(n);\r\ny_correct = '6';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 10;\r\ny = Schroeder(n);\r\ny_correct = '1037718';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 17;\r\ny = Schroeder(n);\r\ny_correct = '111818026018';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 23;\r\ny = Schroeder(n);\r\ny_correct = '2832923350929742';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 53;\r\ny = Schroeder(n);\r\ny_correct = '77073779272885977020023254295915628266';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 113;\r\ny = Schroeder(n);\r\ny_correct = '214645018815655382073160317691190772088909088782578589367620531418920165400447421666';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 157;\r\ny = Schroeder(n);\r\ny_correct = '635298195989878453594162293551305562386458118544676764232073734715032717517063580963828995662005206580225562745343802';\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 88;\r\ny = Schroeder(n);\r\nyy = Schroeder(str2num(y(1:3)));\r\nyy_correct = '24528665763748049389685052543171711960129970876829498326068598388698578380240132802889284459385709363425133815992875744127843722179914611505186848090410102929094478101446';\r\nassert(isequal(yy,yy_correct))\r\n\r\n%%\r\nfiletext = fileread('Schroeder.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'java') || contains(filetext,'py'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-04T04:53:07.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-01-04T04:42:17.000Z","updated_at":"2024-01-04T04:53:07.000Z","published_at":"2024-01-04T04:53:07.000Z","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\u003eConsider motion from the lower left corner of a square grid to the upper right corner. The motion is constrained in two ways: (1) the only legal moves are (0,1), (1,0), and (1,1)—i.e., right, up, and up-and-right between points of the lattice—and (2) the motion must remain on or below the line connecting the starting and finishing corners. For a 2x2 grid, the number of paths is 6, as shown below. \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\u003eWrite a function to count the legal paths for an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e grid. Return the count as a string. Check the last test for banned functions.\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"157\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"971\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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