{"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":2028,"title":"Magic Concentric Circles","description":"Consider 4 magic circle circles around a single number in the sequence 1:n where the sum along the diameters is always equal, and the sum for each circle is also equal.\r\n\r\nIf n=33 then return a truth function corresponding to whether the supplied matrix is magic or not. Diameter numbers are written in columns, and the centre number thus appears in each diameter sequence. Rows contain numbers along semi circles.\r\n\r\nExample\r\n\r\n c = [ 20 33 12 4  ;\r\n       16 1  31 21 ;\r\n       23 13 19 4 ;\r\n       10 22 7  30 ;\r\n       9  9  9  9  ;\r\n       2  18 25 34 ;\r\n       29 26 11 3  ;\r\n       32 17 5  15 ;\r\n       6  8  28 27 ]; \r\n\r\nis not magic over 1:n\r\n \r\n c = [ 20 33 12 4  ;\r\n       16 1  31 21 ;\r\n       23 13 19 14 ;\r\n       10 22 7  30 ;\r\n       9  9  9  9  ;\r\n       2  18 25 24 ;\r\n       29 26 11 3  ;\r\n       32 17 5  15 ;\r\n       6  8  28 27 ]; \r\n\r\nis magic\r\n\r\nSee \u003chttp://en.wikipedia.org/wiki/Magic_circle_(mathematics)\u003e\r\n","description_html":"\u003cp\u003eConsider 4 magic circle circles around a single number in the sequence 1:n where the sum along the diameters is always equal, and the sum for each circle is also equal.\u003c/p\u003e\u003cp\u003eIf n=33 then return a truth function corresponding to whether the supplied matrix is magic or not. Diameter numbers are written in columns, and the centre number thus appears in each diameter sequence. Rows contain numbers along semi circles.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cpre\u003e c = [ 20 33 12 4  ;\r\n       16 1  31 21 ;\r\n       23 13 19 4 ;\r\n       10 22 7  30 ;\r\n       9  9  9  9  ;\r\n       2  18 25 34 ;\r\n       29 26 11 3  ;\r\n       32 17 5  15 ;\r\n       6  8  28 27 ]; \u003c/pre\u003e\u003cp\u003eis not magic over 1:n\u003c/p\u003e\u003cpre\u003e c = [ 20 33 12 4  ;\r\n       16 1  31 21 ;\r\n       23 13 19 14 ;\r\n       10 22 7  30 ;\r\n       9  9  9  9  ;\r\n       2  18 25 24 ;\r\n       29 26 11 3  ;\r\n       32 17 5  15 ;\r\n       6  8  28 27 ]; \u003c/pre\u003e\u003cp\u003eis magic\u003c/p\u003e\u003cp\u003eSee \u003ca href = \"http://en.wikipedia.org/wiki/Magic_circle_(mathematics)\"\u003ehttp://en.wikipedia.org/wiki/Magic_circle_(mathematics)\u003c/a\u003e\u003c/p\u003e","function_template":"function tf = ismagic0(c)\r\n  tf=?;\r\nend","test_suite":"%%\r\nc=[ 20 33 12 4  ;\r\n    16 1  31 21 ;\r\n    23 13 19 4 ;\r\n    10 22 7  30 ;\r\n    9  9  9  9  ;\r\n    2  18 25 34 ;\r\n    29 26 11 3  ;\r\n    32 17 5  15 ;\r\n    6  8  28 27 ];\r\ny_correct = 0;\r\nassert(isequal(ismagic0(c),y_correct))\r\n%%\r\nc=[ 20 33 12 4  ;\r\n    16 1  31 21 ;\r\n    23 13 19 14 ;\r\n    10 22 7  30 ;\r\n    9  9  9  9  ;\r\n    2  18 25 24 ;\r\n    29 26 11 3  ;\r\n    32 17 5  15 ;\r\n    6  8  28 27 ];\r\ny_correct = 1;\r\nassert(isequal(ismagic0(c),y_correct))\r\n%%\r\nc=[24 10 23 16;\r\n    25 22 13 1;\r\n    18 7  19 31;\r\n    2  30 14 21;\r\n    9  9  9  9;\r\n    4  6  32 29;\r\n    12 8  17 26;\r\n    33 28 5  11;\r\n    20 27 15 3];\r\ny_correct = 1;\r\nassert(isequal(ismagic0(c),y_correct))\r\n%%\r\nc=[ 30 29  2 32;\r\n    7  18 26 17;\r\n    22 25 11 5;\r\n    10 24 3  15;\r\n    9  9  9  9;\r\n    27 20 16 23;\r\n    28 33 1  13;\r\n    8  12 31 19;\r\n    6  4  21 14];\r\ny_correct = 0;\r\nassert(isequal(ismagic0(c),y_correct))\r\n%%\r\nc=[30 2  29 32;\r\n    7  18 26 17;\r\n    22 25 11 5;\r\n    10 24 16  15;\r\n    9  9  9  9;\r\n    27 20 3 23;\r\n    28 33 1  13;\r\n    8  12 31 19;\r\n    6  4  21 14];\r\ny_correct = 1;\r\nassert(isequal(ismagic0(c),y_correct))\r\n%%\r\nc=[30 2  29 32;\r\n    7  18 26 17;\r\n    22 25 11 5;\r\n    10 24 3  15;\r\n    9  9  9  9;\r\n    27 20 16 23;\r\n    28 33 1  13;\r\n    8  12 31 19;\r\n    6  4  21 14];\r\ny_correct = 1;\r\nassert(isequal(ismagic0(c),y_correct))\r\n%%\r\nc=[ 30 2  29 32;\r\n    22 25 11 4;\r\n    7  18 26 17;\r\n    9  23 2  15;\r\n    8  9  9  10;\r\n    28 21 17 23;\r\n    8  12 31 19;\r\n    29 33 1  13;\r\n    6  4  21 14];\r\ny_correct = 0;\r\nassert(isequal(ismagic0(c),y_correct))\r\n%%\r\nc=[ 20 34 11  4  ;\r\n    16 0  31 21 ;\r\n    23 13 19 14 ;\r\n    10 22 7  30 ;\r\n    9  9  9  9  ;\r\n    2  18 25 24 ;\r\n    29 26 11 3  ;\r\n    32 17 6  15 ;\r\n    6  8  28 27 ];\r\ny_correct = 0;\r\nassert(isequal(ismagic0(c),y_correct))\r\n%%\r\nc=randi(32,9,4);\r\ny_correct = 0;\r\nassert(isequal(ismagic0(c),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":17471,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-12-01T08:02:45.000Z","updated_at":"2013-12-02T15:15:37.000Z","published_at":"2013-12-01T08:44:55.000Z","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\u003eConsider 4 magic circle circles around a single number in the sequence 1:n where the sum along the diameters is always equal, and the sum for each circle is also equal.\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\u003eIf n=33 then return a truth function corresponding to whether the supplied matrix is magic or not. Diameter numbers are written in columns, and the centre number thus appears in each diameter sequence. Rows contain numbers along semi circles.\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\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[ c = [ 20 33 12 4  ;\\n       16 1  31 21 ;\\n       23 13 19 4 ;\\n       10 22 7  30 ;\\n       9  9  9  9  ;\\n       2  18 25 34 ;\\n       29 26 11 3  ;\\n       32 17 5  15 ;\\n       6  8  28 27 ];]]\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\u003eis not magic over 1:n\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[ c = [ 20 33 12 4  ;\\n       16 1  31 21 ;\\n       23 13 19 14 ;\\n       10 22 7  30 ;\\n       9  9  9  9  ;\\n       2  18 25 24 ;\\n       29 26 11 3  ;\\n       32 17 5  15 ;\\n       6  8  28 27 ];]]\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\u003eis magic\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\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/Magic_circle_(mathematics\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://en.wikipedia.org/wiki/Magic_circle_(mathematics\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\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":2028,"title":"Magic Concentric Circles","description":"Consider 4 magic circle circles around a single number in the sequence 1:n where the sum along the diameters is always equal, and the sum for each circle is also equal.\r\n\r\nIf n=33 then return a truth function corresponding to whether the supplied matrix is magic or not. Diameter numbers are written in columns, and the centre number thus appears in each diameter sequence. Rows contain numbers along semi circles.\r\n\r\nExample\r\n\r\n c = [ 20 33 12 4  ;\r\n       16 1  31 21 ;\r\n       23 13 19 4 ;\r\n       10 22 7  30 ;\r\n       9  9  9  9  ;\r\n       2  18 25 34 ;\r\n       29 26 11 3  ;\r\n       32 17 5  15 ;\r\n       6  8  28 27 ]; \r\n\r\nis not magic over 1:n\r\n \r\n c = [ 20 33 12 4  ;\r\n       16 1  31 21 ;\r\n       23 13 19 14 ;\r\n       10 22 7  30 ;\r\n       9  9  9  9  ;\r\n       2  18 25 24 ;\r\n       29 26 11 3  ;\r\n       32 17 5  15 ;\r\n       6  8  28 27 ]; \r\n\r\nis magic\r\n\r\nSee \u003chttp://en.wikipedia.org/wiki/Magic_circle_(mathematics)\u003e\r\n","description_html":"\u003cp\u003eConsider 4 magic circle circles around a single number in the sequence 1:n where the sum along the diameters is always equal, and the sum for each circle is also equal.\u003c/p\u003e\u003cp\u003eIf n=33 then return a truth function corresponding to whether the supplied matrix is magic or not. Diameter numbers are written in columns, and the centre number thus appears in each diameter sequence. Rows contain numbers along semi circles.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cpre\u003e c = [ 20 33 12 4  ;\r\n       16 1  31 21 ;\r\n       23 13 19 4 ;\r\n       10 22 7  30 ;\r\n       9  9  9  9  ;\r\n       2  18 25 34 ;\r\n       29 26 11 3  ;\r\n       32 17 5  15 ;\r\n       6  8  28 27 ]; \u003c/pre\u003e\u003cp\u003eis not magic over 1:n\u003c/p\u003e\u003cpre\u003e c = [ 20 33 12 4  ;\r\n       16 1  31 21 ;\r\n       23 13 19 14 ;\r\n       10 22 7  30 ;\r\n       9  9  9  9  ;\r\n       2  18 25 24 ;\r\n       29 26 11 3  ;\r\n       32 17 5  15 ;\r\n       6  8  28 27 ]; \u003c/pre\u003e\u003cp\u003eis magic\u003c/p\u003e\u003cp\u003eSee \u003ca href = \"http://en.wikipedia.org/wiki/Magic_circle_(mathematics)\"\u003ehttp://en.wikipedia.org/wiki/Magic_circle_(mathematics)\u003c/a\u003e\u003c/p\u003e","function_template":"function tf = ismagic0(c)\r\n  tf=?;\r\nend","test_suite":"%%\r\nc=[ 20 33 12 4  ;\r\n    16 1  31 21 ;\r\n    23 13 19 4 ;\r\n    10 22 7  30 ;\r\n    9  9  9  9  ;\r\n    2  18 25 34 ;\r\n    29 26 11 3  ;\r\n    32 17 5  15 ;\r\n    6  8  28 27 ];\r\ny_correct = 0;\r\nassert(isequal(ismagic0(c),y_correct))\r\n%%\r\nc=[ 20 33 12 4  ;\r\n    16 1  31 21 ;\r\n    23 13 19 14 ;\r\n    10 22 7  30 ;\r\n    9  9  9  9  ;\r\n    2  18 25 24 ;\r\n    29 26 11 3  ;\r\n    32 17 5  15 ;\r\n    6  8  28 27 ];\r\ny_correct = 1;\r\nassert(isequal(ismagic0(c),y_correct))\r\n%%\r\nc=[24 10 23 16;\r\n    25 22 13 1;\r\n    18 7  19 31;\r\n    2  30 14 21;\r\n    9  9  9  9;\r\n    4  6  32 29;\r\n    12 8  17 26;\r\n    33 28 5  11;\r\n    20 27 15 3];\r\ny_correct = 1;\r\nassert(isequal(ismagic0(c),y_correct))\r\n%%\r\nc=[ 30 29  2 32;\r\n    7  18 26 17;\r\n    22 25 11 5;\r\n    10 24 3  15;\r\n    9  9  9  9;\r\n    27 20 16 23;\r\n    28 33 1  13;\r\n    8  12 31 19;\r\n    6  4  21 14];\r\ny_correct = 0;\r\nassert(isequal(ismagic0(c),y_correct))\r\n%%\r\nc=[30 2  29 32;\r\n    7  18 26 17;\r\n    22 25 11 5;\r\n    10 24 16  15;\r\n    9  9  9  9;\r\n    27 20 3 23;\r\n    28 33 1  13;\r\n    8  12 31 19;\r\n    6  4  21 14];\r\ny_correct = 1;\r\nassert(isequal(ismagic0(c),y_correct))\r\n%%\r\nc=[30 2  29 32;\r\n    7  18 26 17;\r\n    22 25 11 5;\r\n    10 24 3  15;\r\n    9  9  9  9;\r\n    27 20 16 23;\r\n    28 33 1  13;\r\n    8  12 31 19;\r\n    6  4  21 14];\r\ny_correct = 1;\r\nassert(isequal(ismagic0(c),y_correct))\r\n%%\r\nc=[ 30 2  29 32;\r\n    22 25 11 4;\r\n    7  18 26 17;\r\n    9  23 2  15;\r\n    8  9  9  10;\r\n    28 21 17 23;\r\n    8  12 31 19;\r\n    29 33 1  13;\r\n    6  4  21 14];\r\ny_correct = 0;\r\nassert(isequal(ismagic0(c),y_correct))\r\n%%\r\nc=[ 20 34 11  4  ;\r\n    16 0  31 21 ;\r\n    23 13 19 14 ;\r\n    10 22 7  30 ;\r\n    9  9  9  9  ;\r\n    2  18 25 24 ;\r\n    29 26 11 3  ;\r\n    32 17 6  15 ;\r\n    6  8  28 27 ];\r\ny_correct = 0;\r\nassert(isequal(ismagic0(c),y_correct))\r\n%%\r\nc=randi(32,9,4);\r\ny_correct = 0;\r\nassert(isequal(ismagic0(c),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":17471,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-12-01T08:02:45.000Z","updated_at":"2013-12-02T15:15:37.000Z","published_at":"2013-12-01T08:44:55.000Z","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\u003eConsider 4 magic circle circles around a single number in the sequence 1:n where the sum along the diameters is always equal, and the sum for each circle is also equal.\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\u003eIf n=33 then return a truth function corresponding to whether the supplied matrix is magic or not. Diameter numbers are written in columns, and the centre number thus appears in each diameter sequence. 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