{"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":42721,"title":"Fun with a compass","description":"Each night for the past week, you have been having the same nightmare: You find yourself back in your junior high school geometry class, armed with nothing but a compass and a straight edge. Your teacher gives you a number, and asks you if it is possible to construct a regular polygon with that many sides inside the unit circle using nothing but the compass and straight edge.\r\nAfter waking up in a cold sweat again, you decide to write a MATLAB script to see if you can solve your nightmare. The dream is burned into your memory, so you remember all of the numbers that your teacher gave to you. Write a script that will allow you to solve this problem, and sleep peacefully once again.\r\nNote - You don't actually have to construct the n-sided polygon. You just need to determine if it's possible to do so. You can assume that all of the numbers are integers greater than 2.","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: 207px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 103.5px; transform-origin: 407px 103.5px; 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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach night for the past week, you have been having the same nightmare: You find yourself back in your junior high school geometry class, armed with nothing but a compass and a straight edge. Your teacher gives you a number, and asks you if it is possible to construct a regular polygon with that many sides inside the unit circle using nothing but the compass and straight edge.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 374px 8px; transform-origin: 374px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAfter waking up in a cold sweat again, you decide to write a MATLAB script to see if you can solve your nightmare. The dream is burned into your memory, so you remember all of the numbers that your teacher gave to you. Write a script that will allow you to solve this problem, and sleep peacefully once again.\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: 375.5px 8px; transform-origin: 375.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNote - You don't actually have to construct the n-sided polygon. You just need to determine if it's possible to do so. You can assume that all of the numbers are integers greater than 2.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = compass_construction(x)\r\n  y = x;\r\nend","test_suite":"x = 3; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 5; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 6; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 7; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 9; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 13; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 17; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 21; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 51; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 257; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 258; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 640; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 1234; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 2016; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 2056; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 65535; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 65536; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 65537; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 65538; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 1e5; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 196611; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 327685; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":"2022-01-04T06:41:03.000Z","rescore_all_solutions":true,"group_id":37,"created_at":"2016-02-11T19:32:52.000Z","updated_at":"2026-02-27T10:14:32.000Z","published_at":"2016-02-11T19:32:52.000Z","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\u003eEach night for the past week, you have been having the same nightmare: You find yourself back in your junior high school geometry class, armed with nothing but a compass and a straight edge. Your teacher gives you a number, and asks you if it is possible to construct a regular polygon with that many sides inside the unit circle using nothing but the compass and straight edge.\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\u003eAfter waking up in a cold sweat again, you decide to write a MATLAB script to see if you can solve your nightmare. The dream is burned into your memory, so you remember all of the numbers that your teacher gave to you. Write a script that will allow you to solve this problem, and sleep peacefully once again.\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\u003eNote - You don't actually have to construct the n-sided polygon. You just need to determine if it's possible to do so. You can assume that all of the numbers are integers greater than 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":42721,"title":"Fun with a compass","description":"Each night for the past week, you have been having the same nightmare: You find yourself back in your junior high school geometry class, armed with nothing but a compass and a straight edge. Your teacher gives you a number, and asks you if it is possible to construct a regular polygon with that many sides inside the unit circle using nothing but the compass and straight edge.\r\nAfter waking up in a cold sweat again, you decide to write a MATLAB script to see if you can solve your nightmare. The dream is burned into your memory, so you remember all of the numbers that your teacher gave to you. Write a script that will allow you to solve this problem, and sleep peacefully once again.\r\nNote - You don't actually have to construct the n-sided polygon. You just need to determine if it's possible to do so. You can assume that all of the numbers are integers greater than 2.","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: 207px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 103.5px; transform-origin: 407px 103.5px; 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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach night for the past week, you have been having the same nightmare: You find yourself back in your junior high school geometry class, armed with nothing but a compass and a straight edge. Your teacher gives you a number, and asks you if it is possible to construct a regular polygon with that many sides inside the unit circle using nothing but the compass and straight edge.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 374px 8px; transform-origin: 374px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAfter waking up in a cold sweat again, you decide to write a MATLAB script to see if you can solve your nightmare. The dream is burned into your memory, so you remember all of the numbers that your teacher gave to you. Write a script that will allow you to solve this problem, and sleep peacefully once again.\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: 375.5px 8px; transform-origin: 375.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNote - You don't actually have to construct the n-sided polygon. You just need to determine if it's possible to do so. You can assume that all of the numbers are integers greater than 2.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = compass_construction(x)\r\n  y = x;\r\nend","test_suite":"x = 3; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 5; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 6; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 7; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 9; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 13; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 17; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 21; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 51; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 257; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 258; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 640; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 1234; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 2016; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 2056; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 65535; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 65536; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 65537; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 65538; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 1e5; y_correct = 0;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 196611; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n%%\r\nx = 327685; y_correct = 1;\r\nassert(isequal(compass_construction(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":"2022-01-04T06:41:03.000Z","rescore_all_solutions":true,"group_id":37,"created_at":"2016-02-11T19:32:52.000Z","updated_at":"2026-02-27T10:14:32.000Z","published_at":"2016-02-11T19:32:52.000Z","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\u003eEach night for the past week, you have been having the same nightmare: You find yourself back in your junior high school geometry class, armed with nothing but a compass and a straight edge. 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