{"id":2873,"date":"2023-07-02T13:49:11","date_gmt":"2023-07-02T05:49:11","guid":{"rendered":"https:\/\/wordpress.cine.idv.tw\/?p=2873"},"modified":"2023-07-07T11:25:55","modified_gmt":"2023-07-07T03:25:55","slug":"magic-square-constant-combinations","status":"publish","type":"post","link":"https:\/\/wordpress.cine.idv.tw\/index.php\/2023\/07\/02\/magic-square-constant-combinations\/","title":{"rendered":"\u9b54\u65b9\u9663\u5e38\u6578\u7684\u7d44\u5408\u6709\u5e7e\u500b\uff1f"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Lu \u5bf6\u8c9d\u5728\u8b80\u300c\u6578\u5b78\u5929\u65b9\u591c\u8b5a\uff1a\u85a9\u7c73\u723e\u7684\u5947\u5e7b\u4e4b\u65c5\u300d\u6642\uff0c\u66f8\u4e2d\u6709\u63d0\u5230\u56db\u968e\u9b54\u65b9\u9663\u7684\u9b54\u65b9\u9663\u5e38\u6578\u662f 34 \uff0c\u4e14\u7e3d\u5171\u6709 86 \u7a2e\u53ef\u4ee5\u5f97\u5230\u7e3d\u548c\u70ba\u9b54\u65b9\u9663\u5e38\u6578\u7684\u7d44\u5408\u3002\u56e0\u70ba\u9019\u500b\u984c\u76ee\u8ddf\u525b\u525b\u624d\u505a\u5b8c\u7684\u5c0f\u516d\u7368\u7acb\u7814\u7a76\u984c\u76ee\u6709\u95dc\u806f\uff0c\u6240\u4ee5 Lu \u5bf6\u8c9d\u5f88\u8208\u596e\u7684\u8dd1\u4f86\uff0c\u628a\u9019\u500b\u88ab\u4f5c\u8005\u7a31\u70ba\u60e1\u9b54\u7d1a\u65b9\u9663\u7684\u56db\u968e\u9b54\u65b9\u9663\u62ff\u7d66\u6211\u770b\u3002\u96d6\u7136\u6211\u4e0d\u77e5\u9053\u70ba\u4ec0\u9ebc\uff0c\u4f5c\u8005\u8a8d\u70ba\u56db\u968e\u9b54\u65b9\u9663\u5c31\u662f\u300c\u60e1\u9b54\u7d1a\u300d\u7684\u9b54\u65b9\u9663\uff1f\uff08\u90a3\u5176\u4ed6\u66f4\u9ad8\u7b49\u7d1a\u7684\u9ad8\u968e\u9b54\u65b9\u9663\u6703\u662f\u300c\u60e1\u9b54\u7d1a\u300d\u7684\u60e1\u9b54\u7238\u5abd\uff1f\uff09\uff0c\u4e0d\u904e\u6211\u9084\u662f\u5f88\u8a8d\u771f\u7684\u60f3\u60f3\u770b\uff0c\u9019\u7a2e\u9b54\u65b9\u9663\u5e38\u6578\u7684\u7d44\u5408\u500b\u6578\u8a72\u600e\u9ebc\u6c42\u53d6\uff1f<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u9b54\u65b9\u9663\u5e38\u6578<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u500b n \u968e\u9b54\u65b9\u9663\u4e2d\u7684\u6578\u5b57\u7e3d\u548c\u70ba (1 + n<sup>2<\/sup>) * n<sup>2<\/sup> \/ 2 \uff0c\u5176\u4e2d\u5171\u6709 n \u5217 (\u6216 n \u884c) \u7d44\u6210\u9019\u500b\u7e3d\u548c\uff0c\u56e0\u6b64\u6211\u5011\u628a\u9019\u500b\u7e3d\u548c\u7684\u503c\u9664\u4ee5 n \uff0c\u5c31\u6703\u662f\u6bcf\u884c(\u6216\u6bcf\u5217)\u7684\u548c\uff0c\u4e5f\u5c31\u6703\u662f\u9b54\u65b9\u9663\u5e38\u6578\u7684\u516c\u5f0f\uff1a (1 + n<sup>2<\/sup>) * n \/ 2 \u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u56db\u968e\u9b54\u65b9\u9663<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u628a n = 4 \u5e36\u5165\u4e0a\u8ff0\u9b54\u65b9\u9663\u5e38\u6578\u7684\u516c\u5f0f  (1 + 4<sup>2<\/sup>) * 4 \/ 2 = 17 * 2 = 34 \uff0c\u9019\u5c31\u662f\u8a72\u66f8\u4e2d\u63d0\u5230\u7684\u56db\u968e\u9b54\u65b9\u9663\u7684\u9b54\u65b9\u9663\u5e38\u6578 34 \u3002\u90a3\u9ebc\u53ef\u4ee5\u5f97\u5230\u9019\u500b\u548c\u7684\u56db\u500b\u6578\u5b57\u7d44\u5408\u6709 86 \u7a2e\u8a72\u600e\u9ebc\u6c42\u5f97\u5462\uff1f \u4e00\u6642\u4e4b\u9593\u6c92\u4ec0\u9ebc\u60f3\u6cd5\uff0c\u6240\u4ee5\u5c31\u76f4\u89ba\u5730\u5beb\u500b\u7a0b\u5f0f\u4f86\u7b97\u7b97\u770b\u5427\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>combinations = 0\ncombinations_list = &#91;]\nfor i in range(1, 17):\n    for j in range(i + 1, 17):\n        for k in range(j + 1, 17):\n            for l in range(k + 1, 17):\n                if (i + j + k + l) == 34:\n                    combinations = combinations + 1\n                    combinations_list.append((i, j, k, l))\nprint(combinations)\nfor cl in combinations_list:\n    print(cl)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u9019\u6bb5\u7a0b\u5f0f\u78bc\u6703\u8f38\u51fa\u7e3d\u5171\u6709 86 \u7d44 1 ~ 16 \u7684\u6578\u5b57\u4e2d\uff0c\u4efb\u9078\u56db\u500b\u6578\u5b57\u5176\u548c\u70ba 34 \u7684\u7d44\u5408\u3002\u6240\u4ee5\u53ef\u4ee5\u9019\u6a23\u4f86\u9a57\u8b49\u66f8\u88e1\u9762\u63d0\u4f9b\u7684\u5171\u6709 86 \u7a2e\u6578\u5b57\u548c\u70ba 34 \u7684\u7d44\u5408\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">n \u968e\u9b54\u65b9\u9663<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u63a5\u8457\uff0c\u5982\u679c\u6211\u5011\u60f3\u8981\u77e5\u9053\u66f4\u9ad8\u968e\u7684\u9b54\u65b9\u9663\u7684\u6578\u5b57\u4e2d\uff0c\u53ef\u4ee5\u7d44\u5408\u51fa\u8a72\u968e\u6578\u4e4b\u9b54\u65b9\u9663\u5e38\u6578\u7684\u6578\u5b57\u7d44\u5408\u6709\u591a\u5c11\u500b\u8a72\u600e\u9ebc\u8fa6\u5462\uff1f\u6211\u5011\u53ef\u4ee5\u628a\u4e0a\u9762\u7b97\u56db\u968e\u7d44\u5408\u7684\u7a0b\u5f0f\u7a0d\u5fae\u4fee\u6539\u4e00\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>import itertools\n\nn = 4\nc = 0\ncl = &#91;]\nfor comb in itertools.combinations(range(1, n**2 + 1), n):\n    if sum(comb) == n * (n ** 2 + 1) \/ 2:\n        c = c + 1\n        cl.append(comb)\n\nprint(c)\nfor t in cl:\n    print(t)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u9019\u6a23\u6211\u5011\u53ea\u8981\u628a n \u66ff\u63db\u6210 5, 6, 7, 8,&#8230; \u9019\u4e9b\u66f4\u9ad8\u7684\u968e\u6578\uff0c\u5c31\u53ef\u4ee5\u77e5\u9053\u7b26\u5408\u7684\u6578\u5b57\u7d44\u5408\u6709\u5e7e\u7d44\u5566\u3002\uff08n = 5, c = <strong>1394<\/strong>; n = 6, c = <strong>32134<\/strong>; n = 7, c = <strong>957332<\/strong>; n = 8, c = <strong>35154340<\/strong>; &#8230;)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f9e\u7d44\u5408\u6578\u5b57\u6210\u9577\u7684\u901f\u7387\u4f86\u770b\uff0c\u8d85\u904e 8 \u968e\u7684\u9b54\u65b9\u9663\u5e38\u6578\u7684\u53ef\u80fd\u7d44\u5408\uff0c\u61c9\u8a72\u5c31\u8d85\u51fa\u4e00\u822c\u500b\u4eba\u96fb\u8166\u7684\u8a08\u7b97\u80fd\u529b\uff0c\u4ee5\u81ea\u5df1\u7684 Apple MacBook M2 Pro \u96fb\u8166\u4f86\u8aaa\uff0c 8 \u968e\u5171\u67093500\u842c\u7a2e\u4ee5\u4e0a\u7684\u7d44\u5408\uff0c\u9700\u8981\u82b1\u8cbb 20 \u5206\u9418\u4ee5\u4e0a\u624d\u53ef\u4ee5\u5f97\u5230\u7d50\u679c\u56c9\uff0c\u66f4\u4e0d\u8981\u8aaa 20 \u968e\u9019\u7a2e\u9b54\u65b9\u9663\u4e86\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5229\u7528\u5beb\u7a0b\u5f0f\u4f86\u627e\u7d44\u5408\u6578\u4e0d\u96e3\uff0c\u96e3\u7684\u662f\u627e\u51fa\u9b54\u65b9\u9663\u80cc\u5f8c\u6240\u4ee3\u8868\u7684\u6578\u5b78\u898f\u5f8b\uff0c\u4e4b\u5f8c\u518d\u770b\u770b\u662f\u5426\u6709\u5176\u4ed6\u7684\u898b\u89e3\u53ef\u4ee5\u8ddf Lu \u5bf6\u8c9d\u5206\u4eab\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u53c3\u8003\u8cc7\u6599<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.books.com.tw\/products\/0010427474\">\u6578\u5b78\u5929\u65b9\u591c\u8b5a\uff1a\u85a9\u7c73\u723e\u7684\u5947\u5e7b\u4e4b\u65c5<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Magic_square\">\u9b54\u65b9\u9663 @ Wikipedia<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Lu \u5bf6\u8c9d\u5728\u8b80\u300c\u6578\u5b78\u5929\u65b9\u591c\u8b5a\uff1a\u85a9\u7c73\u723e\u7684\u5947\u5e7b\u4e4b\u65c5\u300d\u6642\uff0c\u66f8\u4e2d\u6709\u63d0\u5230\u56db\u968e\u9b54\u65b9\u9663\u7684\u9b54\u65b9\u9663\u5e38\u6578\u662f 34 \uff0c\u4e14\u7e3d\u5171\u6709 86 \u7a2e\u53ef\u4ee5\u5f97\u5230\u7e3d\u548c\u70ba\u9b54\u65b9\u9663\u5e38\u6578\u7684\u7d44\u5408\u3002\u56e0\u70ba\u9019\u500b\u984c\u76ee\u8ddf\u525b\u525b\u624d\u505a\u5b8c\u7684\u5c0f\u516d\u7368\u7acb\u7814\u7a76\u984c\u76ee\u6709\u95dc\u806f\uff0c\u6240\u4ee5 Lu \u5bf6\u8c9d\u5f88\u8208\u596e\u7684 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2876,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[141,13],"tags":[232,121,231],"class_list":["post-2873","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-141","category-it","tag-magic-square","tag-python","tag-231"],"featured_image_src":"https:\/\/i0.wp.com\/wordpress.cine.idv.tw\/wp-content\/uploads\/2023\/07\/4by4.png?fit=424%2C426&ssl=1","author_info":{"display_name":"shortie","author_link":"https:\/\/wordpress.cine.idv.tw\/index.php\/author\/shortie\/"},"yoast_head":"<!-- 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