{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","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":"2026-04-16T00:00:00.000Z","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":2085,"title":"Sudoku Solver - Standard 9x9","description":"Solve a Standard 9x9 \u003chttp://en.wikipedia.org/wiki/Sudoku Sudoku\u003e. Values 1 thru 9 occur in each row, column, and the nine non-overlapping 3x3 matrices starting at the top left corner. \u003chttp://www.free-sudoku.com/sudoku.php?dchoix=evil Sudoku practice site\u003e.\r\n\r\n*Input:* m, a 9x9 matrix of values 0 thru 9. Unknowns are 0s.\r\n\r\n*Output:* mout, a 9x9 matrix of values 1 thru 9 that satisfy Sudoku rules.\r\n\r\n*Scoring:* Time (msec) to solve the Hard Sudoku\r\n\r\n*Example:*\r\n\r\n  m         mout\r\n  390701506 398721546\r\n  042890701 542896731\r\n  106540890 176543892\r\n  820600150 829674153\r\n  400138009 457138269\r\n  031002087 631952487\r\n  065087304 965287314\r\n  703065920 713465928\r\n  204309075 284319675\r\n\r\n*Sudoku Variations:*\r\n\r\nFuture challenges will involve the Sudoku variations Diagonal, Arrow(Sums), Inequality, Irregular, and others as they present themselves.\r\n\r\n*Algorithm Spoiler:*\r\nSudoku's can be readily solved using minimal choice recursion with consistency check. A key step is an index map of all indices that have mutual value exclusion (row,col,3x3), idxmap[81,27]. Another key step is to have an Evolve function that implements all single option values determined by the idxmap. A critical performance enhancement is a Sudoku Consistency Checker that checks for illegal replications of values. Illegal placements by Evolve occur when an incorrect value is asserted into the matrix during recursion trials. The recursive solver finds an idx with minimum options based on idxmap. The values for the idx location are asserted, Evolved, Consistency Checked, and then recursion call if Consistent. When all is Consistent and no unknowns remain the Sudoku is solved. Solution times are in the milli-seconds even for Evil, minimum 17 value, Sudokus.","description_html":"\u003cp\u003eSolve a Standard 9x9 \u003ca href = \"http://en.wikipedia.org/wiki/Sudoku\"\u003eSudoku\u003c/a\u003e. Values 1 thru 9 occur in each row, column, and the nine non-overlapping 3x3 matrices starting at the top left corner. \u003ca href = \"http://www.free-sudoku.com/sudoku.php?dchoix=evil\"\u003eSudoku practice site\u003c/a\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e m, a 9x9 matrix of values 0 thru 9. Unknowns are 0s.\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e mout, a 9x9 matrix of values 1 thru 9 that satisfy Sudoku rules.\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring:\u003c/b\u003e Time (msec) to solve the Hard Sudoku\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003em         mout\r\n390701506 398721546\r\n042890701 542896731\r\n106540890 176543892\r\n820600150 829674153\r\n400138009 457138269\r\n031002087 631952487\r\n065087304 965287314\r\n703065920 713465928\r\n204309075 284319675\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eSudoku Variations:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eFuture challenges will involve the Sudoku variations Diagonal, Arrow(Sums), Inequality, Irregular, and others as they present themselves.\u003c/p\u003e\u003cp\u003e\u003cb\u003eAlgorithm Spoiler:\u003c/b\u003e\r\nSudoku's can be readily solved using minimal choice recursion with consistency check. A key step is an index map of all indices that have mutual value exclusion (row,col,3x3), idxmap[81,27]. Another key step is to have an Evolve function that implements all single option values determined by the idxmap. A critical performance enhancement is a Sudoku Consistency Checker that checks for illegal replications of values. Illegal placements by Evolve occur when an incorrect value is asserted into the matrix during recursion trials. The recursive solver finds an idx with minimum options based on idxmap. The values for the idx location are asserted, Evolved, Consistency Checked, and then recursion call if Consistent. When all is Consistent and no unknowns remain the Sudoku is solved. Solution times are in the milli-seconds even for Evil, minimum 17 value, Sudokus.\u003c/p\u003e","function_template":"function mout=sudoku_solver(m)\r\n% m is a 9x9 Sudoku array with 0 for unknown values\r\n% create mout a consistent sudoku array\r\n  mout=m;\r\nend","test_suite":"assignin('caller','score',500);\r\n%%\r\n% Test 1\r\nmstr=['012300007'; '040600010'; '078900020'; '000000040'; '100000002'; '060000000'; '080001230'; '090004060'; '300007890']; \r\n% convert string to array\r\nm=zeros(9);\r\nfor i=1:9\r\n m(i,:)=mstr(i,:)-'0'  ; \r\nend\r\n\r\ntic\r\nmout=sudoku_solver(m)\r\ntoc\r\n\r\nvalid=all(arrayfun(@(i) all(sum([mout mout']==i)),1:length(mout)));\r\nassert(valid==1)\r\n\r\nptr=find(m\u003e0);\r\nvalid2=isequal(m(ptr),mout(ptr));\r\nassert(valid2==1)\r\n\r\n%%\r\n% Test 2\r\nmstr=['000004500'; '000003600'; '432008700'; '867000000'; '000000000'; '000000417'; '001900854'; '006400000'; '003700000']; \r\n% convert string to array\r\nm=zeros(9);\r\nfor i=1:9\r\n m(i,:)=mstr(i,:)-'0'  ; \r\nend\r\n\r\ntic\r\nmout=sudoku_solver(m)\r\ntoc\r\n\r\nvalid=all(arrayfun(@(i) all(sum([mout mout']==i)),1:length(mout)));\r\nassert(valid==1)\r\n\r\nptr=find(m\u003e0);\r\nvalid2=isequal(m(ptr),mout(ptr));\r\nassert(valid2==1)\r\n\r\n%%\r\n% Test 3\r\nmstr=['120034000'; '000000056'; '000200000'; '007800002'; '600000001'; '500006300'; '000008000'; '340000000'; '000560078']; \r\n% convert string to array\r\nm=zeros(9);\r\nfor i=1:9\r\n m(i,:)=mstr(i,:)-'0'  ; \r\nend\r\n\r\ntic\r\nmout=sudoku_solver(m)\r\ntoc\r\n\r\nvalid=all(arrayfun(@(i) all(sum([mout mout']==i)),1:length(mout)));\r\nassert(valid==1)\r\n\r\nptr=find(m\u003e0);\r\nvalid2=isequal(m(ptr),mout(ptr));\r\nassert(valid2==1)\r\n\r\n\r\n%%\r\n% Timed Test on a Hard Sudoku\r\n% Non-Valid answer creates a Max score but not a fail\r\n% Hard Sudoku\r\nmstr=['005700009'; '030090010'; '100005300'; '600004700'; '040010050'; '002500001'; '004600002'; '080020040'; '200008600']; \r\n% convert string to array\r\nm=zeros(9);\r\nfor i=1:9\r\n m(i,:)=mstr(i,:)-'0'  ; \r\nend\r\n\r\ntime0=cputime;\r\n mout=sudoku_solver(m)\r\netime=(cputime-time0)*1000 % msec\r\nvalid=all(arrayfun(@(i) all(sum([mout mout']==i)),1:length(mout)));\r\nptr=find(m\u003e0);\r\nvalid2=isequal(m(ptr),mout(ptr));\r\n% Not Asserting for Valid answer\r\nif ~valid,etime=500;end\r\nif ~valid2,etime=500;end\r\nassignin('caller','score',min(500,floor(etime)));","published":true,"deleted":false,"likes_count":8,"comments_count":2,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":52,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-01-02T00:31:17.000Z","updated_at":"2026-04-08T09:57:58.000Z","published_at":"2014-01-02T01:30:54.000Z","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\u003eSolve a Standard 9x9\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/Sudoku\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSudoku\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Values 1 thru 9 occur in each row, column, and the nine non-overlapping 3x3 matrices starting at the top left corner.\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.free-sudoku.com/sudoku.php?dchoix=evil\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSudoku practice site\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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: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 m, a 9x9 matrix of values 0 thru 9. Unknowns are 0s.\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: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 mout, a 9x9 matrix of values 1 thru 9 that satisfy Sudoku rules.\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: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 Time (msec) to solve the Hard Sudoku\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\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=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[m         mout\\n390701506 398721546\\n042890701 542896731\\n106540890 176543892\\n820600150 829674153\\n400138009 457138269\\n031002087 631952487\\n065087304 965287314\\n703065920 713465928\\n204309075 284319675]]\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSudoku Variations:\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\u003eFuture challenges will involve the Sudoku variations Diagonal, Arrow(Sums), Inequality, Irregular, and others as they present themselves.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAlgorithm Spoiler:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Sudoku's can be readily solved using minimal choice recursion with consistency check. A key step is an index map of all indices that have mutual value exclusion (row,col,3x3), idxmap[81,27]. Another key step is to have an Evolve function that implements all single option values determined by the idxmap. A critical performance enhancement is a Sudoku Consistency Checker that checks for illegal replications of values. Illegal placements by Evolve occur when an incorrect value is asserted into the matrix during recursion trials. The recursive solver finds an idx with minimum options based on idxmap. The values for the idx location are asserted, Evolved, Consistency Checked, and then recursion call if Consistent. When all is Consistent and no unknowns remain the Sudoku is solved. Solution times are in the milli-seconds even for Evil, minimum 17 value, Sudokus.\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":2085,"title":"Sudoku Solver - Standard 9x9","description":"Solve a Standard 9x9 \u003chttp://en.wikipedia.org/wiki/Sudoku Sudoku\u003e. Values 1 thru 9 occur in each row, column, and the nine non-overlapping 3x3 matrices starting at the top left corner. \u003chttp://www.free-sudoku.com/sudoku.php?dchoix=evil Sudoku practice site\u003e.\r\n\r\n*Input:* m, a 9x9 matrix of values 0 thru 9. Unknowns are 0s.\r\n\r\n*Output:* mout, a 9x9 matrix of values 1 thru 9 that satisfy Sudoku rules.\r\n\r\n*Scoring:* Time (msec) to solve the Hard Sudoku\r\n\r\n*Example:*\r\n\r\n  m         mout\r\n  390701506 398721546\r\n  042890701 542896731\r\n  106540890 176543892\r\n  820600150 829674153\r\n  400138009 457138269\r\n  031002087 631952487\r\n  065087304 965287314\r\n  703065920 713465928\r\n  204309075 284319675\r\n\r\n*Sudoku Variations:*\r\n\r\nFuture challenges will involve the Sudoku variations Diagonal, Arrow(Sums), Inequality, Irregular, and others as they present themselves.\r\n\r\n*Algorithm Spoiler:*\r\nSudoku's can be readily solved using minimal choice recursion with consistency check. A key step is an index map of all indices that have mutual value exclusion (row,col,3x3), idxmap[81,27]. Another key step is to have an Evolve function that implements all single option values determined by the idxmap. A critical performance enhancement is a Sudoku Consistency Checker that checks for illegal replications of values. Illegal placements by Evolve occur when an incorrect value is asserted into the matrix during recursion trials. The recursive solver finds an idx with minimum options based on idxmap. The values for the idx location are asserted, Evolved, Consistency Checked, and then recursion call if Consistent. When all is Consistent and no unknowns remain the Sudoku is solved. Solution times are in the milli-seconds even for Evil, minimum 17 value, Sudokus.","description_html":"\u003cp\u003eSolve a Standard 9x9 \u003ca href = \"http://en.wikipedia.org/wiki/Sudoku\"\u003eSudoku\u003c/a\u003e. Values 1 thru 9 occur in each row, column, and the nine non-overlapping 3x3 matrices starting at the top left corner. \u003ca href = \"http://www.free-sudoku.com/sudoku.php?dchoix=evil\"\u003eSudoku practice site\u003c/a\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e m, a 9x9 matrix of values 0 thru 9. Unknowns are 0s.\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e mout, a 9x9 matrix of values 1 thru 9 that satisfy Sudoku rules.\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring:\u003c/b\u003e Time (msec) to solve the Hard Sudoku\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003em         mout\r\n390701506 398721546\r\n042890701 542896731\r\n106540890 176543892\r\n820600150 829674153\r\n400138009 457138269\r\n031002087 631952487\r\n065087304 965287314\r\n703065920 713465928\r\n204309075 284319675\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eSudoku Variations:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eFuture challenges will involve the Sudoku variations Diagonal, Arrow(Sums), Inequality, Irregular, and others as they present themselves.\u003c/p\u003e\u003cp\u003e\u003cb\u003eAlgorithm Spoiler:\u003c/b\u003e\r\nSudoku's can be readily solved using minimal choice recursion with consistency check. A key step is an index map of all indices that have mutual value exclusion (row,col,3x3), idxmap[81,27]. Another key step is to have an Evolve function that implements all single option values determined by the idxmap. A critical performance enhancement is a Sudoku Consistency Checker that checks for illegal replications of values. Illegal placements by Evolve occur when an incorrect value is asserted into the matrix during recursion trials. The recursive solver finds an idx with minimum options based on idxmap. The values for the idx location are asserted, Evolved, Consistency Checked, and then recursion call if Consistent. When all is Consistent and no unknowns remain the Sudoku is solved. Solution times are in the milli-seconds even for Evil, minimum 17 value, Sudokus.\u003c/p\u003e","function_template":"function mout=sudoku_solver(m)\r\n% m is a 9x9 Sudoku array with 0 for unknown values\r\n% create mout a consistent sudoku array\r\n  mout=m;\r\nend","test_suite":"assignin('caller','score',500);\r\n%%\r\n% Test 1\r\nmstr=['012300007'; '040600010'; '078900020'; '000000040'; '100000002'; '060000000'; '080001230'; '090004060'; '300007890']; \r\n% convert string to array\r\nm=zeros(9);\r\nfor i=1:9\r\n m(i,:)=mstr(i,:)-'0'  ; \r\nend\r\n\r\ntic\r\nmout=sudoku_solver(m)\r\ntoc\r\n\r\nvalid=all(arrayfun(@(i) all(sum([mout mout']==i)),1:length(mout)));\r\nassert(valid==1)\r\n\r\nptr=find(m\u003e0);\r\nvalid2=isequal(m(ptr),mout(ptr));\r\nassert(valid2==1)\r\n\r\n%%\r\n% Test 2\r\nmstr=['000004500'; '000003600'; '432008700'; '867000000'; '000000000'; '000000417'; '001900854'; '006400000'; '003700000']; \r\n% convert string to array\r\nm=zeros(9);\r\nfor i=1:9\r\n m(i,:)=mstr(i,:)-'0'  ; \r\nend\r\n\r\ntic\r\nmout=sudoku_solver(m)\r\ntoc\r\n\r\nvalid=all(arrayfun(@(i) all(sum([mout mout']==i)),1:length(mout)));\r\nassert(valid==1)\r\n\r\nptr=find(m\u003e0);\r\nvalid2=isequal(m(ptr),mout(ptr));\r\nassert(valid2==1)\r\n\r\n%%\r\n% Test 3\r\nmstr=['120034000'; '000000056'; '000200000'; '007800002'; '600000001'; '500006300'; '000008000'; '340000000'; '000560078']; \r\n% convert string to array\r\nm=zeros(9);\r\nfor i=1:9\r\n m(i,:)=mstr(i,:)-'0'  ; \r\nend\r\n\r\ntic\r\nmout=sudoku_solver(m)\r\ntoc\r\n\r\nvalid=all(arrayfun(@(i) all(sum([mout mout']==i)),1:length(mout)));\r\nassert(valid==1)\r\n\r\nptr=find(m\u003e0);\r\nvalid2=isequal(m(ptr),mout(ptr));\r\nassert(valid2==1)\r\n\r\n\r\n%%\r\n% Timed Test on a Hard Sudoku\r\n% Non-Valid answer creates a Max score but not a fail\r\n% Hard Sudoku\r\nmstr=['005700009'; '030090010'; '100005300'; '600004700'; '040010050'; '002500001'; '004600002'; '080020040'; '200008600']; \r\n% convert string to array\r\nm=zeros(9);\r\nfor i=1:9\r\n m(i,:)=mstr(i,:)-'0'  ; \r\nend\r\n\r\ntime0=cputime;\r\n mout=sudoku_solver(m)\r\netime=(cputime-time0)*1000 % msec\r\nvalid=all(arrayfun(@(i) all(sum([mout mout']==i)),1:length(mout)));\r\nptr=find(m\u003e0);\r\nvalid2=isequal(m(ptr),mout(ptr));\r\n% Not Asserting for Valid answer\r\nif ~valid,etime=500;end\r\nif ~valid2,etime=500;end\r\nassignin('caller','score',min(500,floor(etime)));","published":true,"deleted":false,"likes_count":8,"comments_count":2,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":52,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-01-02T00:31:17.000Z","updated_at":"2026-04-08T09:57:58.000Z","published_at":"2014-01-02T01:30:54.000Z","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\u003eSolve a Standard 9x9\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/Sudoku\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSudoku\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Values 1 thru 9 occur in each row, column, and the nine non-overlapping 3x3 matrices starting at the top left corner.\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.free-sudoku.com/sudoku.php?dchoix=evil\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSudoku practice site\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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: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 m, a 9x9 matrix of values 0 thru 9. Unknowns are 0s.\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: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 mout, a 9x9 matrix of values 1 thru 9 that satisfy Sudoku rules.\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: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 Time (msec) to solve the Hard Sudoku\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\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=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[m         mout\\n390701506 398721546\\n042890701 542896731\\n106540890 176543892\\n820600150 829674153\\n400138009 457138269\\n031002087 631952487\\n065087304 965287314\\n703065920 713465928\\n204309075 284319675]]\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSudoku Variations:\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\u003eFuture challenges will involve the Sudoku variations Diagonal, Arrow(Sums), Inequality, Irregular, and others as they present themselves.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAlgorithm Spoiler:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Sudoku's can be readily solved using minimal choice recursion with consistency check. A key step is an index map of all indices that have mutual value exclusion (row,col,3x3), idxmap[81,27]. Another key step is to have an Evolve function that implements all single option values determined by the idxmap. A critical performance enhancement is a Sudoku Consistency Checker that checks for illegal replications of values. Illegal placements by Evolve occur when an incorrect value is asserted into the matrix during recursion trials. The recursive solver finds an idx with minimum options based on idxmap. The values for the idx location are asserted, Evolved, Consistency Checked, and then recursion call if Consistent. When all is Consistent and no unknowns remain the Sudoku is solved. 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