{"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":1387,"title":"Points on a circle.","description":"This problem is related to \u003curl=http://www.mathworks.com/matlabcentral/cody/problems/1283-points-on-a-sphere\u003eProblem 1283, Points on a Sphere.\u003e  In this case, instead of a sphere, you have a circle.  Given a radius R, calculate the number of points on the circumference of the circle that have two integer coordinates.  For a circle of radius 5, you would have 12 points:\r\n\r\n* (0, 5) and (0, -5)\r\n* (5, 0) and (-5, 0)\r\n* (4, 3) and (4, -3)\r\n* (-4, 3) and (-4, -3)\r\n* (3, 4) and (3, -4)\r\n* (-3, 4) and (-3, -4)\r\n\r\nSome radii are quite large, so watch out.  Good luck!","description_html":"\u003cp\u003eThis problem is related to \u003ca href = \"url=http://www.mathworks.com/matlabcentral/cody/problems/1283-points-on-a-sphere\u0026gt;Problem\"\u003e1283, Points on a Sphere.\u003c/a\u003e  In this case, instead of a sphere, you have a circle.  Given a radius R, calculate the number of points on the circumference of the circle that have two integer coordinates.  For a circle of radius 5, you would have 12 points:\u003c/p\u003e\u003cul\u003e\u003cli\u003e(0, 5) and (0, -5)\u003c/li\u003e\u003cli\u003e(5, 0) and (-5, 0)\u003c/li\u003e\u003cli\u003e(4, 3) and (4, -3)\u003c/li\u003e\u003cli\u003e(-4, 3) and (-4, -3)\u003c/li\u003e\u003cli\u003e(3, 4) and (3, -4)\u003c/li\u003e\u003cli\u003e(-3, 4) and (-3, -4)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eSome radii are quite large, so watch out.  Good luck!\u003c/p\u003e","function_template":"function y = circle_points(r)\r\n  y = r;\r\nend","test_suite":"%%\r\nassert(isequal(circle_points(1),4))\r\n%%\r\nassert(isequal(circle_points(3),4))\r\n%%\r\nassert(isequal(circle_points(5),12))\r\n%%\r\nassert(isequal(circle_points(65),36))\r\n%%\r\nassert(isequal(circle_points(64090),324))\r\n%%\r\nassert(isequal(circle_points(326441),12))\r\n%%\r\nassert(isequal(circle_points(359125),420))\r\n%%\r\nassert(isequal(circle_points(1000001),36))\r\n%%\r\nassert(isequal(circle_points(2417899275),20))\r\n%%\r\nassert(isequal(circle_points(31432690549),8748))\r\n%%\r\nassert(isequal(circle_points(11472932050385),78732))\r\n%%\r\nassert(isequal(circle_points(1021090952484265),236196))\r\n%%\r\nassert(isequal(circle_points(6095127531752228),78732))\r\n%%\r\nassert(isequal(circle_points(5*circle_points(630209)),12))\r\n%%\r\ny=arrayfun(@(x) circle_points(x),1000:2000);\r\n[m1,m2]=max(y);\r\nassert(isequal(m1-m2,2));\r\n[h1,h2]=hist(y,unique(y));\r\nassert(isequal(prod(h1-h2),1399066124544000))","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":"2018-02-22T17:55:59.000Z","rescore_all_solutions":true,"group_id":20,"created_at":"2013-03-25T18:05:05.000Z","updated_at":"2026-02-16T11:09:55.000Z","published_at":"2013-03-25T18:44:35.000Z","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\u003eThis problem is related to\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=\\\"url=http://www.mathworks.com/matlabcentral/cody/problems/1283-points-on-a-sphere\u003eProblem\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1283, Points on a Sphere.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e In this case, instead of a sphere, you have a circle. Given a radius R, calculate the number of points on the circumference of the circle that have two integer coordinates. For a circle of radius 5, you would have 12 points:\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=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(0, 5) and (0, -5)\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=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(5, 0) and (-5, 0)\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=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(4, 3) and (4, -3)\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=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(-4, 3) and (-4, -3)\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=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(3, 4) and (3, -4)\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=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(-3, 4) and (-3, -4)\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\u003eSome radii are quite large, so watch out. Good luck!\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":1387,"title":"Points on a circle.","description":"This problem is related to \u003curl=http://www.mathworks.com/matlabcentral/cody/problems/1283-points-on-a-sphere\u003eProblem 1283, Points on a Sphere.\u003e  In this case, instead of a sphere, you have a circle.  Given a radius R, calculate the number of points on the circumference of the circle that have two integer coordinates.  For a circle of radius 5, you would have 12 points:\r\n\r\n* (0, 5) and (0, -5)\r\n* (5, 0) and (-5, 0)\r\n* (4, 3) and (4, -3)\r\n* (-4, 3) and (-4, -3)\r\n* (3, 4) and (3, -4)\r\n* (-3, 4) and (-3, -4)\r\n\r\nSome radii are quite large, so watch out.  Good luck!","description_html":"\u003cp\u003eThis problem is related to \u003ca href = \"url=http://www.mathworks.com/matlabcentral/cody/problems/1283-points-on-a-sphere\u0026gt;Problem\"\u003e1283, Points on a Sphere.\u003c/a\u003e  In this case, instead of a sphere, you have a circle.  Given a radius R, calculate the number of points on the circumference of the circle that have two integer coordinates.  For a circle of radius 5, you would have 12 points:\u003c/p\u003e\u003cul\u003e\u003cli\u003e(0, 5) and (0, -5)\u003c/li\u003e\u003cli\u003e(5, 0) and (-5, 0)\u003c/li\u003e\u003cli\u003e(4, 3) and (4, -3)\u003c/li\u003e\u003cli\u003e(-4, 3) and (-4, -3)\u003c/li\u003e\u003cli\u003e(3, 4) and (3, -4)\u003c/li\u003e\u003cli\u003e(-3, 4) and (-3, -4)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eSome radii are quite large, so watch out.  Good luck!\u003c/p\u003e","function_template":"function y = circle_points(r)\r\n  y = r;\r\nend","test_suite":"%%\r\nassert(isequal(circle_points(1),4))\r\n%%\r\nassert(isequal(circle_points(3),4))\r\n%%\r\nassert(isequal(circle_points(5),12))\r\n%%\r\nassert(isequal(circle_points(65),36))\r\n%%\r\nassert(isequal(circle_points(64090),324))\r\n%%\r\nassert(isequal(circle_points(326441),12))\r\n%%\r\nassert(isequal(circle_points(359125),420))\r\n%%\r\nassert(isequal(circle_points(1000001),36))\r\n%%\r\nassert(isequal(circle_points(2417899275),20))\r\n%%\r\nassert(isequal(circle_points(31432690549),8748))\r\n%%\r\nassert(isequal(circle_points(11472932050385),78732))\r\n%%\r\nassert(isequal(circle_points(1021090952484265),236196))\r\n%%\r\nassert(isequal(circle_points(6095127531752228),78732))\r\n%%\r\nassert(isequal(circle_points(5*circle_points(630209)),12))\r\n%%\r\ny=arrayfun(@(x) circle_points(x),1000:2000);\r\n[m1,m2]=max(y);\r\nassert(isequal(m1-m2,2));\r\n[h1,h2]=hist(y,unique(y));\r\nassert(isequal(prod(h1-h2),1399066124544000))","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":"2018-02-22T17:55:59.000Z","rescore_all_solutions":true,"group_id":20,"created_at":"2013-03-25T18:05:05.000Z","updated_at":"2026-02-16T11:09:55.000Z","published_at":"2013-03-25T18:44:35.000Z","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\u003eThis problem is related to\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=\\\"url=http://www.mathworks.com/matlabcentral/cody/problems/1283-points-on-a-sphere\u003eProblem\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1283, Points on a Sphere.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e In this case, instead of a sphere, you have a circle. Given a radius R, calculate the number of points on the circumference of the circle that have two integer coordinates. For a circle of radius 5, you would have 12 points:\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=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(0, 5) and (0, -5)\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=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(5, 0) and (-5, 0)\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=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(4, 3) and (4, -3)\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=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(-4, 3) and (-4, -3)\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=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(3, 4) and (3, -4)\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=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(-3, 4) and (-3, -4)\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\u003eSome radii are quite large, so watch out. 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