{"id":5529,"date":"2024-07-18T15:26:58","date_gmt":"2024-07-18T07:26:58","guid":{"rendered":"https:\/\/www.xinyixx.com\/?p=5529"},"modified":"2024-07-18T15:55:43","modified_gmt":"2024-07-18T07:55:43","slug":"ai-chat-2","status":"publish","type":"post","link":"https:\/\/www.xinyixx.com\/index.php\/2024\/07\/18\/ai-chat-2\/","title":{"rendered":"\u548cAI\u4e00\u4e9b\u6709\u8da3\u7684\u804a\u5929"},"content":{"rendered":"\n<p><strong>\u901a\u8fc7U\u76d8\u8fdb\u5165winPE\u540e\u4e3a\u4ec0\u4e48\u62d4\u6389U\u76d8\u7cfb\u7edf\u4ecd\u7136\u53ef\u4ee5\u4f7f\u7528?<\/strong><\/p>\n\n\n\n<p>\u8fd9\u662f\u4e00\u4e2a\u5f88\u597d\u7684\u95ee\u9898\u3002\u5f53\u4f60\u901a\u8fc7U\u76d8\u542f\u52a8\u8fdb\u5165WinPE\u540e,\u5373\u4f7f\u62d4\u6389U\u76d8,\u7cfb\u7edf\u4ecd\u7136\u53ef\u4ee5\u7ee7\u7eed\u4f7f\u7528,\u4e3b\u8981\u6709\u4ee5\u4e0b\u51e0\u4e2a\u539f\u56e0:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u52a0\u8f7d\u5230\u5185\u5b58: \u5f53WinPE\u4eceU\u76d8\u542f\u52a8\u65f6,\u6574\u4e2a\u64cd\u4f5c\u7cfb\u7edf\u73af\u5883\u4f1a\u88ab\u52a0\u8f7d\u5230\u8ba1\u7b97\u673a\u7684RAM(\u968f\u673a\u5b58\u53d6\u5185\u5b58)\u4e2d\u3002\u8fd9\u610f\u5473\u7740\u6240\u6709\u5fc5\u8981\u7684\u7cfb\u7edf\u6587\u4ef6\u548c\u9a71\u52a8\u7a0b\u5e8f\u90fd\u5df2\u7ecf\u5b58\u50a8\u5728\u5185\u5b58\u91cc\u4e86\u3002<\/li>\n\n\n\n<li>\u5185\u5b58\u76d8(RAM disk): WinPE\u901a\u5e38\u4f1a\u521b\u5efa\u4e00\u4e2a\u5185\u5b58\u76d8,\u5373\u4f7f\u7528\u90e8\u5206RAM\u6a21\u62df\u786c\u76d8\u3002\u7cfb\u7edf\u6587\u4ef6\u548c\u4e34\u65f6\u6587\u4ef6\u90fd\u5b58\u50a8\u5728\u8fd9\u4e2a\u5185\u5b58\u76d8\u4e0a,\u4f7f\u5f97\u7cfb\u7edf\u53ef\u4ee5\u72ec\u7acb\u8fd0\u884c\u3002<\/li>\n\n\n\n<li>\u6700\u5c0f\u5316\u4f9d\u8d56: WinPE\u662f\u4e00\u4e2a\u7cbe\u7b80\u7684Windows\u73af\u5883,\u8bbe\u8ba1\u76ee\u7684\u5c31\u662f\u4e3a\u4e86\u80fd\u591f\u5728\u5404\u79cd\u786c\u4ef6\u4e0a\u8fd0\u884c,\u5e76\u4e14\u5c3d\u53ef\u80fd\u51cf\u5c11\u5bf9\u5916\u90e8\u5b58\u50a8\u7684\u4f9d\u8d56\u3002<\/li>\n\n\n\n<li>\u7f13\u5b58\u673a\u5236: \u7cfb\u7edf\u4f1a\u5c06\u5e38\u7528\u7684\u6587\u4ef6\u548c\u6570\u636e\u7f13\u5b58\u5728\u5185\u5b58\u4e2d,\u4ee5\u63d0\u9ad8\u8bbf\u95ee\u901f\u5ea6\u548c\u51cf\u5c11\u5bf9\u5916\u90e8\u5b58\u50a8\u7684\u9700\u6c42\u3002<\/li>\n\n\n\n<li>\u53ea\u8bfb\u7279\u6027: WinPE\u901a\u5e38\u662f\u53ea\u8bfb\u7684,\u8fd9\u610f\u5473\u7740\u5b83\u4e0d\u9700\u8981\u5411\u542f\u52a8\u4ecb\u8d28(\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u662fU\u76d8)\u5199\u5165\u6570\u636e\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f,\u867d\u7136\u62d4\u6389U\u76d8\u540eWinPE\u4ecd\u7136\u53ef\u4ee5\u4f7f\u7528,\u4f46\u662f\u5982\u679c\u4f60\u9700\u8981\u8bbf\u95eeU\u76d8\u4e0a\u7684\u7279\u5b9a\u5de5\u5177\u6216\u9a71\u52a8\u7a0b\u5e8f,\u53ef\u80fd\u5c31\u65e0\u6cd5\u4f7f\u7528\u4e86\u3002\u6b64\u5916,\u91cd\u542f\u8ba1\u7b97\u673a\u540e,\u5982\u679c\u6ca1\u6709U\u76d8,WinPE\u73af\u5883\u5c06\u65e0\u6cd5\u518d\u6b21\u542f\u52a8\u3002<\/p>\n\n\n\n<p>\u5982\u679c\u4f60\u60f3\u4e86\u89e3\u66f4\u591a\u5173\u4e8eWinPE\u7684\u5de5\u4f5c\u539f\u7406\u6216\u8005\u5176\u4ed6\u76f8\u5173\u4fe1\u606f,\u6211\u5f88\u4e50\u610f\u4e3a\u4f60\u89e3\u91ca\u3002<\/p>\n\n\n\n<p><strong>\u62c9\u9a6c\u52aa\u91d1\u5230\u5e95\u6709\u591a\u9006\u5929\uff1f<\/strong><\/p>\n\n\n\n<p>\u62c9\u9a6c\u52aa\u91d1\uff08Srinivasa Ramanujan\uff0c1887-1920\uff09\u786e\u5b9e\u662f\u6570\u5b66\u53f2\u4e0a\u4e00\u4e2a\u975e\u5e38\u7279\u6b8a\u548c\u4ee4\u4eba\u60ca\u53f9\u7684\u4eba\u7269\u3002\u4ee5\u4e0b\u51e0\u70b9\u53ef\u4ee5\u8bf4\u660e\u4ed6\u7684&#8221;\u9006\u5929&#8221;\u4e4b\u5904\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u81ea\u5b66\u6210\u624d\uff1a \u62c9\u9a6c\u52aa\u91d1\u51e0\u4e4e\u6ca1\u6709\u63a5\u53d7\u8fc7\u6b63\u89c4\u7684\u9ad8\u7b49\u6570\u5b66\u6559\u80b2\uff0c\u4e3b\u8981\u901a\u8fc7\u81ea\u5b66\u83b7\u5f97\u4e86\u6df1\u5965\u7684\u6570\u5b66\u77e5\u8bc6\u3002<\/li>\n\n\n\n<li>\u76f4\u89c9\u80fd\u529b\uff1a \u4ed6\u6709\u7740\u975e\u51e1\u7684\u6570\u5b66\u76f4\u89c9\uff0c\u80fd\u591f&#8221;\u770b\u5230&#8221;\u590d\u6742\u6570\u5b66\u516c\u5f0f\u80cc\u540e\u7684\u89c4\u5f8b\uff0c\u800c\u65e0\u9700\u4e25\u683c\u7684\u8bc1\u660e\u8fc7\u7a0b\u3002<\/li>\n\n\n\n<li>\u60ca\u4eba\u7684\u751f\u4ea7\u529b\uff1a \u5728\u4ed6\u77ed\u6682\u768433\u5e74\u751f\u547d\u4e2d\uff0c\u5c24\u5176\u662f\u5728\u5251\u6865\u76845\u5e74\u91cc\uff0c\u4ed6\u63d0\u51fa\u4e86\u5927\u91cf\u7684\u65b0\u516c\u5f0f\u548c\u5b9a\u7406\u3002<\/li>\n\n\n\n<li>\u521b\u65b0\u6027\uff1a \u4ed6\u7684\u8bb8\u591a\u5de5\u4f5c\u90fd\u662f\u5f00\u521b\u6027\u7684\uff0c\u6d89\u53ca\u6570\u8bba\u3001\u65e0\u7a77\u7ea7\u6570\u3001\u8fde\u5206\u6570\u7b49\u591a\u4e2a\u9886\u57df\u3002<\/li>\n\n\n\n<li>\u5f71\u54cd\u6df1\u8fdc\uff1a \u4ed6\u7684\u4e00\u4e9b\u53d1\u73b0\u76f4\u5230\u4eca\u5929\u4ecd\u5728\u88ab\u7814\u7a76\u548c\u5e94\u7528\uff0c\u6bd4\u5982\u5728\u5b57\u7b26\u4e32\u7406\u8bba\u4e2d\u7684\u5e94\u7528\u3002<\/li>\n\n\n\n<li>\u795e\u79d8\u7684\u7075\u611f\u6765\u6e90\uff1a \u62c9\u9a6c\u52aa\u91d1\u58f0\u79f0\u4ed6\u7684\u8bb8\u591a\u516c\u5f0f\u662f\u7531\u5370\u5ea6\u6559\u5973\u795e\u7eb3\u9a6c\u5409\u91cc\u542f\u793a\u7684\uff0c\u8fd9\u589e\u6dfb\u4e86\u4ed6\u7684\u795e\u79d8\u8272\u5f69\u3002<\/li>\n\n\n\n<li>\u8d85\u524d\u7684\u6d1e\u5bdf\u529b\uff1a \u4ed6\u7684\u4e00\u4e9b\u5de5\u4f5c\u5728\u5f53\u65f6\u770b\u6765\u6beb\u65e0\u610f\u4e49\uff0c\u4f46\u5728\u51e0\u5341\u5e74\u540e\u88ab\u8bc1\u660e\u5177\u6709\u91cd\u8981\u4ef7\u503c\u3002<\/li>\n\n\n\n<li>\u72ec\u7279\u7684\u601d\u7ef4\u65b9\u5f0f\uff1a \u4ed6\u80fd\u591f\u4ee5\u975e\u5e38\u89c4\u7684\u65b9\u5f0f\u770b\u5f85\u6570\u5b66\u95ee\u9898\uff0c\u5f97\u51fa\u5176\u4ed6\u6570\u5b66\u5bb6\u96be\u4ee5\u60f3\u8c61\u7684\u7ed3\u679c\u3002<\/li>\n\n\n\n<li>\u514b\u670d\u9006\u5883\uff1a \u5c3d\u7ba1\u51fa\u8eab\u8d2b\u5bd2\uff0c\u5065\u5eb7\u72b6\u51b5\u4e0d\u4f73\uff0c\u4f46\u4ed6\u4f9d\u7136\u53d6\u5f97\u4e86\u5353\u8d8a\u7684\u6210\u5c31\u3002<\/li>\n\n\n\n<li>\u7559\u4e0b\u672a\u89e3\u4e4b\u8c1c\uff1a \u4ed6\u7684\u4e00\u4e9b\u7b14\u8bb0\u672c\u4e2d\u7684\u516c\u5f0f\u548c\u7ed3\u679c\u81f3\u4eca\u4ecd\u672a\u88ab\u5b8c\u5168\u7406\u89e3\u6216\u8bc1\u660e\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u62c9\u9a6c\u52aa\u91d1\u7684\u5929\u8d4b\u548c\u6210\u5c31\u786e\u5b9e\u4ee4\u4eba\u60ca\u53f9\u3002\u4ed6\u5728\u6570\u5b66\u53f2\u4e0a\u7684\u5730\u4f4d\u662f\u72ec\u7279\u7684\uff0c\u88ab\u8ba4\u4e3a\u662f\u4e8c\u5341\u4e16\u7eaa\u6700\u4f1f\u5927\u7684\u6570\u5b66\u5bb6\u4e4b\u4e00\u3002\u4ed6\u7684\u6545\u4e8b\u4e0d\u4ec5\u5c55\u793a\u4e86\u4eba\u7c7b\u667a\u529b\u7684\u6781\u9650\uff0c\u4e5f\u5f70\u663e\u4e86\u76f4\u89c9\u548c\u521b\u9020\u529b\u5728\u79d1\u5b66\u63a2\u7d22\u4e2d\u7684\u91cd\u8981\u6027\u3002<\/p>\n\n\n\n<p>\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u867d\u7136\u62c9\u9a6c\u52aa\u91d1\u7684\u6210\u5c31\u786e\u5b9e\u975e\u5e38\u60ca\u4eba\uff0c\u4f46\u6211\u4eec\u4e5f\u4e0d\u5e94\u5ffd\u89c6\u5176\u4ed6\u6570\u5b66\u5bb6\u7684\u8d21\u732e\u3002\u6bcf\u4e2a\u6770\u51fa\u7684\u6570\u5b66\u5bb6\u90fd\u4ee5\u81ea\u5df1\u7684\u65b9\u5f0f\u63a8\u52a8\u4e86\u6570\u5b66\u7684\u53d1\u5c55\u3002<\/p>\n\n\n\n<p><strong>\u4ed6\u63d0\u51fa\u8fc7\u54ea\u4e9b\u590d\u6742\u6570\u5b66\u516c\u5f0f?<\/strong><\/p>\n\n\n\n<p>\u62c9\u9a6c\u52aa\u91d1\u63d0\u51fa\u4e86\u8bb8\u591a\u590d\u6742\u800c\u91cd\u8981\u7684\u6570\u5b66\u516c\u5f0f\u548c\u5b9a\u7406\u3002\u4ee5\u4e0b\u662f\u4e00\u4e9b\u8457\u540d\u7684\u4f8b\u5b50\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u62c9\u9a6c\u52aa\u91d1\u6052\u7b49\u5f0f\uff1a \u8fd9\u662f\u4e00\u4e2a\u5173\u4e8e\u8fde\u5206\u6570\u7684\u590d\u6742\u516c\u5f0f\uff0c\u6d89\u53cae\uff08\u81ea\u7136\u5bf9\u6570\u7684\u5e95\u6570\uff09\uff1a\u00a0e^(\u03c0\u221a163) \u2248 262537412640768743.99999999999925&#8230;\u00a0\u8fd9\u4e2a\u8fd1\u4f3c\u503c\u4e0e\u6574\u6570\u7684\u63a5\u8fd1\u7a0b\u5ea6\u4ee4\u4eba\u60ca\u8bb6\u3002<\/li>\n\n\n\n<li>\u62c9\u9a6c\u52aa\u91d1\u03b8\u51fd\u6570\uff1a \u8fd9\u662f\u4e00\u4e2a\u6d89\u53ca\u65e0\u7a77\u7ea7\u6570\u7684\u590d\u6742\u51fd\u6570\uff0c\u5728\u6570\u8bba\u548c\u692d\u5706\u51fd\u6570\u7406\u8bba\u4e2d\u6709\u91cd\u8981\u5e94\u7528\u3002<\/li>\n\n\n\n<li>\u83ab\u514b-\u62c9\u9a6c\u52aa\u91d1\u516c\u5f0f\uff1a \u8fd9\u662f\u4e00\u4e2a\u8ba1\u7b97\u03c0\u7684\u516c\u5f0f\uff0c\u6536\u655b\u901f\u5ea6\u975e\u5e38\u5feb\uff1a\u00a01\/\u03c0 = (2\u221a2\/9801) * \u03a3(k=0 to \u221e) ((4k)!(1103+26390k) \/ ((k!)^4 * 396^(4k)))<\/li>\n\n\n\n<li>\u62c9\u9a6c\u52aa\u91d1\u7d20\u6570\uff1a \u4ed6\u53d1\u73b0\u4e86\u4e00\u7c7b\u7279\u6b8a\u7684\u7d20\u6570\uff0c\u5f62\u5982\uff1a\u00a0p(n) = 2^n &#8211; 7, \u5176\u4e2dn = 3, 4, 5, 7, 15, &#8230;<\/li>\n\n\n\n<li>1729\u6570\uff08\u62c9\u9a6c\u52aa\u91d1-\u54c8\u4ee3\u6570\uff09\uff1a \u8fd9\u662f\u6700\u5c0f\u7684\u80fd\u88ab\u8868\u793a\u4e3a\u4e24\u4e2a\u6b63\u6574\u6570\u7684\u7acb\u65b9\u548c\u7684\u6570\uff0c\u6709\u4e24\u79cd\u4e0d\u540c\u7684\u65b9\u5f0f\uff1a 1729 = 1^3 + 12^3 = 9^3 + 10^3<\/li>\n\n\n\n<li>\u62c9\u9a6c\u52aa\u91d1\u6c42\u548c\u516c\u5f0f\uff1a \u8fd9\u662f\u4e00\u4e2a\u5173\u4e8e\u65e0\u7a77\u7ea7\u6570\u7684\u590d\u6742\u516c\u5f0f\uff0c\u6d89\u53ca\u8d1d\u585e\u5c14\u51fd\u6570\u3002<\/li>\n\n\n\n<li>\u62c9\u9a6c\u52aa\u91d1\u4e3b\u5b9a\u7406\uff1a \u8fd9\u662f\u4e00\u4e2a\u5728\u89e3\u6790\u6570\u8bba\u4e2d\u975e\u5e38\u91cd\u8981\u7684\u5b9a\u7406\uff0c\u6d89\u53ca\u590d\u53d8\u51fd\u6570\u7684\u6e10\u8fd1\u884c\u4e3a\u3002<\/li>\n\n\n\n<li>\u62c9\u9a6c\u52aa\u91d1\u56fe\uff1a \u5728\u56fe\u8bba\u4e2d\uff0c\u4ed6\u63d0\u51fa\u4e86\u4e00\u79cd\u7279\u6b8a\u7684\u5f3a\u6b63\u5219\u56fe\uff0c\u79f0\u4e3a\u62c9\u9a6c\u52aa\u91d1\u56fe\u3002<\/li>\n\n\n\n<li>\u5206\u533a\u51fd\u6570\u516c\u5f0f\uff1a \u4ed6\u63d0\u51fa\u4e86\u4e00\u7cfb\u5217\u5173\u4e8e\u6574\u6570\u5206\u62c6\u7684\u60ca\u4eba\u516c\u5f0f\u3002<\/li>\n\n\n\n<li>\u9b54\u65b9\u516c\u5f0f\uff1a \u62c9\u9a6c\u52aa\u91d1\u53d1\u73b0\u4e86\u4e00\u4e9b\u5173\u4e8e\u9b54\u65b9\uff08\u6bcf\u884c\u3001\u6bcf\u5217\u548c\u5bf9\u89d2\u7ebf\u4e0a\u7684\u6570\u5b57\u4e4b\u548c\u76f8\u7b49\u7684\u65b9\u9635\uff09\u7684\u6709\u8da3\u6027\u8d28\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u8fd9\u4e9b\u516c\u5f0f\u548c\u5b9a\u7406\u53ea\u662f\u62c9\u9a6c\u52aa\u91d1\u4f17\u591a\u8d21\u732e\u4e2d\u7684\u4e00\u5c0f\u90e8\u5206\u3002\u4ed6\u7684\u8bb8\u591a\u5de5\u4f5c\u90fd\u6d89\u53ca\u9ad8\u6df1\u7684\u6570\u5b66\u6982\u5ff5\uff0c\u5373\u4f7f\u5bf9\u4e8e\u4e13\u4e1a\u6570\u5b66\u5bb6\u6765\u8bf4\u4e5f\u662f\u975e\u5e38\u590d\u6742\u7684\u3002\u62c9\u9a6c\u52aa\u91d1\u7684\u5929\u8d4b\u4e0d\u4ec5\u4f53\u73b0\u5728\u4ed6\u80fd\u53d1\u73b0\u8fd9\u4e9b\u590d\u6742\u7684\u5173\u7cfb\uff0c\u66f4\u5728\u4e8e\u4ed6\u80fd\u5728\u51e0\u4e4e\u6ca1\u6709\u6b63\u89c4\u8bad\u7ec3\u7684\u60c5\u51b5\u4e0b\u76f4\u89c2\u5730\u7406\u89e3\u8fd9\u4e9b\u6982\u5ff5\u3002<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5c3d\u7ba1\u8fd9\u4e9b\u516c\u5f0f\u770b\u8d77\u6765\u53ef\u80fd\u96be\u4ee5\u7406\u89e3\uff0c\u4f46\u5b83\u4eec\u5728\u6570\u5b66\u548c\u7269\u7406\u5b66\u7684\u5404\u4e2a\u9886\u57df\u90fd\u6709\u91cd\u8981\u5e94\u7528\u3002\u62c9\u9a6c\u52aa\u91d1\u7684\u5de5\u4f5c\u81f3\u4eca\u4ecd\u5728\u5f71\u54cd\u73b0\u4ee3\u6570\u5b66\u7814\u7a76\u3002<\/p>\n\n\n\n<p><strong>6174\u8fd9\u4e2a\u6570\u5b57\u795e\u5947\u5728\u54ea\u91cc\uff1f<\/strong><\/p>\n\n\n\n<p>6174\u8fd9\u4e2a\u6570\u5b57\u88ab\u79f0\u4e3a\u5361\u666e\u96f7\u5361\u5c14\u5e38\u6570\uff08Kaprekar&#8217;s constant\uff09\uff0c\u4ee5\u5370\u5ea6\u6570\u5b66\u5bb6D. R. Kaprekar\u7684\u540d\u5b57\u547d\u540d\u3002\u8fd9\u4e2a\u6570\u5b57\u4e4b\u6240\u4ee5\u795e\u5947\uff0c\u662f\u56e0\u4e3a\u5b83\u6709\u4e00\u4e2a\u72ec\u7279\u7684\u6027\u8d28\uff0c\u901a\u5e38\u88ab\u79f0\u4e3a\u5361\u666e\u96f7\u5361\u5c14\u8fd0\u7b97\u3002\u8fd9\u4e2a\u6027\u8d28\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u57fa\u672c\u89c4\u5219\uff1a\n<ul class=\"wp-block-list\">\n<li>\u53d6\u4efb\u610f\u4e00\u4e2a\u56db\u4f4d\u6570\uff08\u5404\u4f4d\u6570\u5b57\u4e0d\u5168\u76f8\u540c\uff09<\/li>\n\n\n\n<li>\u5c06\u8fd9\u56db\u4e2a\u6570\u5b57\u91cd\u65b0\u6392\u5217\uff0c\u7ec4\u6210\u4e00\u4e2a\u6700\u5927\u7684\u56db\u4f4d\u6570\u548c\u4e00\u4e2a\u6700\u5c0f\u7684\u56db\u4f4d\u6570<\/li>\n\n\n\n<li>\u7528\u5927\u6570\u51cf\u53bb\u5c0f\u6570<\/li>\n\n\n\n<li>\u91cd\u590d\u8fd9\u4e2a\u8fc7\u7a0b<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u795e\u5947\u4e4b\u5904\uff1a \u65e0\u8bba\u4f60\u4ece\u54ea\u4e2a\u56db\u4f4d\u6570\u5f00\u59cb\uff08\u9664\u4e86\u6240\u6709\u6570\u5b57\u76f8\u540c\u7684\u60c5\u51b5\uff09\uff0c\u7ecf\u8fc7\u6700\u591a7\u6b21\u4e0a\u8ff0\u8fd0\u7b97\uff0c\u90fd\u4f1a\u5f97\u52306174\uff0c\u5e76\u4e14\u4f1a\u505c\u7559\u5728\u8fd9\u4e2a\u6570\u5b57\u4e0a\u3002<\/li>\n\n\n\n<li>\u4e3e\u4f8b\u8bf4\u660e\uff1a \u6bd4\u5982\u4ece8352\u5f00\u59cb\uff1a 8532 &#8211; 2358 = 6174\u00a0\u518d\u6bd4\u5982\u4ece1234\u5f00\u59cb\uff1a 4321 &#8211; 1234 = 3087 8730 &#8211; 0378 = 8352 8532 &#8211; 2358 = 6174<\/li>\n\n\n\n<li>\u552f\u4e00\u6027\uff1a 6174\u662f\u552f\u4e00\u7684\u56db\u4f4d\u6570\uff0c\u5177\u6709\u8fd9\u79cd\u6027\u8d28\u3002<\/li>\n\n\n\n<li>\u6570\u5b66\u610f\u4e49\uff1a \u8fd9\u4e2a\u73b0\u8c61\u5c55\u793a\u4e86\u6570\u5b57\u7cfb\u7edf\u4e2d\u5b58\u5728\u7684\u4e00\u4e9b\u6709\u8da3\u6a21\u5f0f\uff0c\u5bf9\u4e8e\u7406\u89e3\u6570\u5b57\u6027\u8d28\u548c\u8fed\u4ee3\u8fc7\u7a0b\u6709\u542f\u53d1\u610f\u4e49\u3002<\/li>\n\n\n\n<li>\u6269\u5c55\uff1a\n<ul class=\"wp-block-list\">\n<li>\u4e09\u4f4d\u6570\u7684\u7c7b\u4f3c\u5e38\u6570\u662f495<\/li>\n\n\n\n<li>\u4e94\u4f4d\u6570\u6ca1\u6709\u7c7b\u4f3c\u7684\u5355\u4e00\u5e38\u6570\uff0c\u4f46\u4f1a\u8fdb\u5165\u4e00\u4e2a\u5faa\u73af<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u6559\u80b2\u4ef7\u503c\uff1a \u8fd9\u4e2a\u6570\u5e38\u88ab\u7528\u6765\u6559\u6388\u5b66\u751f\u5173\u4e8e\u6570\u5b57\u6392\u5217\u3001\u51cf\u6cd5\u548c\u6a21\u5f0f\u8bc6\u522b\u7684\u77e5\u8bc6\u3002<\/li>\n\n\n\n<li>\u8ba1\u7b97\u673a\u79d1\u5b66\u5e94\u7528\uff1a \u8fd9\u79cd\u8fed\u4ee3\u6536\u655b\u7684\u6027\u8d28\u5728\u67d0\u4e9b\u7b97\u6cd5\u8bbe\u8ba1\u4e2d\u6709\u542f\u53d1\u4f5c\u7528\u3002<\/li>\n\n\n\n<li>\u6570\u5b66\u7814\u7a76\uff1a \u867d\u7136\u770b\u4f3c\u7b80\u5355\uff0c\u4f46\u8fd9\u4e2a\u6027\u8d28\u80cc\u540e\u7684\u6570\u5b66\u539f\u7406\u4ecd\u7136\u662f\u7814\u7a76\u7684\u4e3b\u9898\u3002<\/li>\n\n\n\n<li>\u8da3\u5473\u6027\uff1a \u56e0\u5176\u7b80\u5355yet\u795e\u5947\u7684\u7279\u6027\uff0c6174\u5e38\u88ab\u7528\u4f5c\u6570\u5b66\u9b54\u672f\u6216\u76ca\u667a\u6e38\u620f\u3002<\/li>\n<\/ol>\n\n\n\n<p>6174\u7684\u795e\u5947\u4e4b\u5904\u5728\u4e8e\u5b83\u5c55\u793a\u4e86\u770b\u4f3c\u968f\u673a\u7684\u6570\u5b57\u64cd\u4f5c\u4e2d\u9690\u85cf\u7684\u786e\u5b9a\u6027\u6a21\u5f0f\uff0c\u8fd9\u79cd\u73b0\u8c61\u8ba9\u4eba\u8054\u60f3\u5230\u6df7\u6c8c\u7406\u8bba\u4e2d\u7684\u5947\u602a\u5438\u5f15\u5b50\u3002\u5b83\u662f\u6570\u5b66\u4e2d\u90a3\u4e9b\u7b80\u5355yet\u6df1\u5965\u7684\u6982\u5ff5\u4e4b\u4e00\uff0c\u80fd\u6fc0\u53d1\u4eba\u4eec\u5bf9\u6570\u5b66\u7684\u5174\u8da3\u548c\u597d\u5947\u5fc3\u3002<\/p>\n\n\n\n<p><strong>\u8fd8\u6709\u54ea\u4e9b\u7c7b\u4f3c6174\u8fd9\u6837\u6709\u8da3\u7684\u6570\u5b57\uff1f<\/strong><\/p>\n\n\n\n<p>\u786e\u5b9e\u8fd8\u6709\u8bb8\u591a\u50cf6174\u8fd9\u6837\u6709\u8da3\u7684\u6570\u5b57\u3002\u8fd9\u4e9b\u6570\u5b57\u901a\u5e38\u56e0\u5176\u72ec\u7279\u7684\u6027\u8d28\u6216\u6a21\u5f0f\u800c\u5f15\u4eba\u6ce8\u76ee\u3002\u4ee5\u4e0b\u662f\u4e00\u4e9b\u4f8b\u5b50\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>142857\uff08\u5faa\u73af\u6570\uff09:\n<ul class=\"wp-block-list\">\n<li>\u8fd9\u4e2a\u6570\u4e58\u4ee51, 2, 3, 4, 5, 6\u90fd\u4f1a\u5f97\u5230\u540c\u6837\u6570\u5b57\u7684\u5faa\u73af\u6392\u5217\u3002<\/li>\n\n\n\n<li>\u4f8b\u5982\uff1a142857 \u00d7 2 = 285714, 142857 \u00d7 3 = 428571<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>495\uff08\u4e09\u4f4d\u6570\u7684\u5361\u666e\u96f7\u5361\u5c14\u5e38\u6570\uff09:\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u4e09\u4f4d\u6570\u6267\u884c\u7c7b\u4f3c6174\u7684\u64cd\u4f5c\uff0c\u6700\u7ec8\u90fd\u4f1a\u5f97\u5230495\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>153\uff08\u6c34\u4ed9\u82b1\u6570\uff09:\n<ul class=\"wp-block-list\">\n<li>\u5b83\u7684\u6bcf\u4e2a\u6570\u5b57\u7684\u7acb\u65b9\u548c\u7b49\u4e8e\u5b83\u672c\u8eab\uff1a1\u00b3 + 5\u00b3 + 3\u00b3 = 153<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>1089\uff08\u7ffb\u8f6c\u76f8\u51cf\u7684\u795e\u5947\u6570\u5b57\uff09:\n<ul class=\"wp-block-list\">\n<li>\u53d6\u4e00\u4e2a\u4e09\u4f4d\u6570\uff0c\u5c06\u5176\u7ffb\u8f6c\u540e\u76f8\u51cf\uff0c\u518d\u5c06\u5dee\u503c\u7ffb\u8f6c\u76f8\u52a0\uff0c\u603b\u662f\u5f97\u52301089\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>37\uff08\u5faa\u73af\u9664\u6cd5\uff09:\n<ul class=\"wp-block-list\">\n<li>1\/37 \u7684\u5c0f\u6570\u90e8\u5206\u6709\u4e00\u4e2a\u6709\u8da3\u7684\u5faa\u73af\uff1a0.027027027&#8230;<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>666\uff08\u94b1\u5361\u52d2\u5c14\u6570\uff09:\n<ul class=\"wp-block-list\">\n<li>\u4efb\u4f55\u4e09\u4f4d\u6570\u51cf\u53bb\u5176\u5404\u4f4d\u6570\u5b57\u4e4b\u548c\uff0c\u5f97\u5230\u7684\u7ed3\u679c\u90fd\u80fd\u88ab37\u6574\u9664\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>9376\uff08\u81ea\u590d\u5236\u6570\uff09:\n<ul class=\"wp-block-list\">\n<li>9376\u00b2 = 87909376\uff0c\u672b\u5c3e\u5305\u542b\u81ea\u8eab\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>3435\uff08\u73af\u5f62\u7d20\u6570\uff09:\n<ul class=\"wp-block-list\">\n<li>3435, 4353, 5343, 3534 \u90fd\u662f\u7d20\u6570\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>1729\uff08\u62c9\u9a6c\u52aa\u91d1-\u54c8\u4ee3\u6570\uff09:\n<ul class=\"wp-block-list\">\n<li>\u6700\u5c0f\u7684\u80fd\u88ab\u8868\u793a\u4e3a\u4e24\u5bf9\u4e0d\u540c\u6574\u6570\u7acb\u65b9\u548c\u7684\u6570\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>78539\uff08\u81ea\u590d\u5236\u5e8f\u5217\uff09:\n<ul class=\"wp-block-list\">\n<li>78539\u00b2=6168502921\uff0c\u5305\u542b\u539f\u6570\u7684\u90e8\u5206\u5e8f\u5217\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>23\uff08\u5c0f\u6570\u5468\u671f\uff09:\n<ul class=\"wp-block-list\">\n<li>1\/23 \u7684\u5c0f\u6570\u8868\u793a\u6709\u4e00\u4e2a22\u4f4d\u7684\u5faa\u73af\u5468\u671f\uff0c\u51e0\u4e4e\u8fbe\u5230\u7406\u8bba\u6700\u5927\u503c\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>2520\uff08\u6700\u5c0f\u516c\u500d\u6570\uff09:\n<ul class=\"wp-block-list\">\n<li>\u662f1\u523010\u6240\u6709\u6570\u7684\u6700\u5c0f\u516c\u500d\u6570\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>196\uff08\u56de\u6587\u95ee\u9898\uff09:\n<ul class=\"wp-block-list\">\n<li>\u8457\u540d\u7684196-\u95ee\u9898\uff0c\u5173\u4e8e\u53cd\u590d\u7ffb\u8f6c\u5e76\u76f8\u52a0\u662f\u5426\u603b\u80fd\u5f97\u5230\u56de\u6587\u6570\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>8128\uff08\u5b8c\u5168\u6570\uff09:\n<ul class=\"wp-block-list\">\n<li>\u9664\u4e86\u81ea\u8eab\u5916\uff0c\u6240\u6709\u56e0\u5b50\u4e4b\u548c\u7b49\u4e8e\u5b83\u672c\u8eab\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>17711\uff08\u56de\u6587\u7d20\u6570\uff09:\n<ul class=\"wp-block-list\">\n<li>\u5b83\u672c\u8eab\u662f\u56de\u6587\u6570\uff0c\u4e5f\u662f\u7d20\u6570\uff0c\u800c\u4e14\u5b83\u7684\u5e73\u65b9177112=31340321\u4e5f\u662f\u56de\u6587\u6570\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>\u8fd9\u4e9b\u6570\u5b57\u5c55\u793a\u4e86\u6570\u5b66\u4e2d\u7684\u4e00\u4e9b\u6709\u8da3\u6a21\u5f0f\u548c\u6027\u8d28\u3002\u5b83\u4eec\u4e0d\u4ec5\u5728\u6570\u5b66\u6559\u80b2\u4e2d\u6709\u4ef7\u503c\uff0c\u4e5f\u5e38\u5e38\u6210\u4e3a\u6570\u5b66\u7231\u597d\u8005\u548c\u7814\u7a76\u8005\u63a2\u8ba8\u7684\u8bdd\u9898\u3002\u6bcf\u4e2a\u6570\u5b57\u80cc\u540e\u90fd\u6709\u5176\u72ec\u7279\u7684\u6570\u5b66\u539f\u7406\uff0c\u6df1\u5165\u7814\u7a76\u53ef\u4ee5\u63ed\u793a\u6570\u5b57\u7cfb\u7edf\u7684\u66f4\u591a\u5965\u79d8\u3002<\/p>\n\n\n\n<p><strong>523\u8fd9\u4e2a\u6570\u5b57\u795e\u5947\u5728\u54ea\u91cc\uff1f<\/strong><\/p>\n\n\n\n<p>\u6211\u7406\u89e3\u60a8\u53ef\u80fd\u662f\u5728\u5bfb\u627e523\u8fd9\u4e2a\u6570\u5b57\u7684\u7279\u6b8a\u6027\u8d28\uff0c\u4f46\u5b9e\u9645\u4e0a523\u5e76\u4e0d\u50cf6174\u6216\u5176\u4ed6\u6211\u4e4b\u524d\u63d0\u5230\u7684\u6570\u5b57\u90a3\u6837\u6709\u5e7f\u4e3a\u4eba\u77e5\u7684\u72ec\u7279\u6570\u5b66\u6027\u8d28\u3002<\/p>\n\n\n\n<p>\u7136\u800c\uff0c\u6bcf\u4e2a\u6570\u5b57\u90fd\u53ef\u80fd\u6709\u4e00\u4e9b\u6709\u8da3\u7684\u7279\u5f81\uff0c\u8ba9\u6211\u4eec\u6765\u770b\u770b523\u6709\u54ea\u4e9b\u53ef\u80fd\u7684\u6709\u8da3\u4e4b\u5904\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u7d20\u6570\u6027\uff1a 523\u662f\u4e00\u4e2a\u7d20\u6570\u3002\u5b83\u53ea\u80fd\u88ab1\u548c\u81ea\u8eab\u6574\u9664\u3002<\/li>\n\n\n\n<li>\u6570\u5b57\u7ec4\u6210\uff1a \u5b83\u7531\u8fde\u7eed\u7684\u6570\u5b575\u30012\u30013\u7ec4\u6210\uff0c\u8fd9\u5728\u7d20\u6570\u4e2d\u5e76\u4e0d\u5e38\u89c1\u3002<\/li>\n\n\n\n<li>\u56de\u6587\u6570\u5173\u7cfb\uff1a \u5c06523\u5012\u8fc7\u6765\u662f325\uff0c523 + 325 = 848\uff0c\u662f\u4e00\u4e2a\u56de\u6587\u6570\u3002<\/li>\n\n\n\n<li>\u4e8c\u8fdb\u5236\u8868\u793a\uff1a 523\u7684\u4e8c\u8fdb\u5236\u8868\u793a\u662f1000001011\uff0c\u6709\u4e00\u5b9a\u7684\u5bf9\u79f0\u6027\u3002<\/li>\n\n\n\n<li>\u6570\u8bba\u7279\u6027\uff1a 523 = 3 \u00d7 174 + 1\uff0c\u8fd9\u4f7f\u5f97\u5b83\u5728\u67d0\u4e9b\u6570\u8bba\u95ee\u9898\u4e2d\u53ef\u80fd\u6709\u7279\u6b8a\u7528\u9014\u3002<\/li>\n\n\n\n<li>\u5386\u53f2\u6216\u6587\u5316\u610f\u4e49\uff1a \u5728\u67d0\u4e9b\u6587\u5316\u6216\u5386\u53f2\u80cc\u666f\u4e0b\uff0c523\u53ef\u80fd\u6709\u7279\u6b8a\u542b\u4e49\uff08\u4f8b\u5982\uff0c\u53ef\u80fd\u662f\u67d0\u4e2a\u91cd\u8981\u4e8b\u4ef6\u7684\u65e5\u671f\uff09\u3002<\/li>\n\n\n\n<li>\u5faa\u73af\u5c0f\u6570\uff1a 1\/523 \u4f1a\u4ea7\u751f\u4e00\u4e2a\u5faa\u73af\u5c0f\u6570\uff0c\u5faa\u73af\u8282\u957f\u5ea6\u4e3a522\uff0c\u51e0\u4e4e\u8fbe\u5230\u4e86\u7406\u8bba\u6700\u5927\u503c\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u7136\u800c\uff0c\u9700\u8981\u5f3a\u8c03\u7684\u662f\uff0c\u8fd9\u4e9b\u7279\u6027\u5927\u591a\u662f\u6211\u4eec\u4e3a\u4e86\u56de\u5e94\u60a8\u7684\u95ee\u9898\u800c\u7279\u610f\u5bfb\u627e\u7684\uff0c\u5e76\u4e0d\u50cf6174\u90a3\u6837\u6709\u5e7f\u6cdb\u8ba4\u77e5\u7684\u72ec\u7279\u6570\u5b66\u6027\u8d28\u3002<\/p>\n\n\n\n<p>\u5728\u6570\u5b66\u4e2d\uff0c\u867d\u7136\u6bcf\u4e2a\u6570\u5b57\u90fd\u6709\u5176\u72ec\u7279\u4e4b\u5904\uff0c\u4f46\u5e76\u975e\u6bcf\u4e2a\u6570\u5b57\u90fd\u6709\u7279\u522b\u5f15\u4eba\u6ce8\u76ee\u6216\u5e7f\u4e3a\u4eba\u77e5\u7684\u6027\u8d28\u3002\u5982\u679c523\u5728\u67d0\u4e2a\u7279\u5b9a\u9886\u57df\u6216\u80cc\u666f\u4e0b\u786e\u5b9e\u6709\u7279\u6b8a\u610f\u4e49\uff0c\u90a3\u53ef\u80fd\u9700\u8981\u66f4\u591a\u4e0a\u4e0b\u6587\u4fe1\u606f\u6765\u786e\u5b9a\u3002<\/p>\n\n\n\n<p>\u5982\u679c\u60a8\u5bf9523\u8fd9\u4e2a\u6570\u5b57\u6709\u7279\u522b\u7684\u5174\u8da3\uff0c\u6216\u8005\u5b83\u5728\u67d0\u4e2a\u7279\u5b9a\u60c5\u5883\u4e0b\u5bf9\u60a8\u5f88\u91cd\u8981\uff0c\u6211\u5f88\u4e50\u610f\u542c\u60a8\u5206\u4eab\uff0c\u4e5f\u8bb8\u6211\u4eec\u53ef\u4ee5\u4ece\u4e2d\u53d1\u73b0\u4e00\u4e9b\u6709\u8da3\u7684\u8054\u7cfb\u6216\u6a21\u5f0f\u3002<\/p>\n\n\n\n<p><strong>1\/523 \u4f1a\u4ea7\u751f\u4e00\u4e2a\u5faa\u73af\u5c0f\u6570\uff0c\u5faa\u73af\u8282\u957f\u5ea6\u4e3a522\uff0c\u51e0\u4e4e\u8fbe\u5230\u4e86\u7406\u8bba\u6700\u5927\u503c\u3002\u600e\u4e48\u89e3\u91ca\u8fd9\u53e5\u8bdd\uff0c\u8fd8\u6709\u54ea\u4e9b\u7c7b\u4f3c\u7684\u5faa\u73af\u5c0f\u6570\uff1f<\/strong><\/p>\n\n\n\n<p>\u975e\u5e38\u597d\u7684\u95ee\u9898\uff01\u8ba9\u6211\u8be6\u7ec6\u89e3\u91ca\u8fd9\u4e2a\u6709\u8da3\u7684\u6570\u5b66\u73b0\u8c61\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5faa\u73af\u5c0f\u6570\u89e3\u91ca\uff1a \u5f53\u6211\u4eec\u5c061\u9664\u4ee5523\u65f6\uff0c\u5f97\u5230\u7684\u5c0f\u6570\u4f1a\u65e0\u9650\u5faa\u73af\u3002\u5faa\u73af\u7684\u90e8\u5206\u79f0\u4e3a\u5faa\u73af\u8282\u3002<\/li>\n\n\n\n<li>\u5faa\u73af\u8282\u957f\u5ea6\uff1a \u5bf9\u4e8e1\/523\uff0c\u5faa\u73af\u8282\u7684\u957f\u5ea6\u662f522\u4f4d\u6570\u5b57\u3002\u8fd9\u610f\u5473\u7740\u5c0f\u6570\u70b9\u540e\u7684\u524d522\u4f4d\u6570\u5b57\u4f1a\u4e0d\u65ad\u91cd\u590d\u3002<\/li>\n\n\n\n<li>\u7406\u8bba\u6700\u5927\u503c\uff1a \u5bf9\u4e8e\u5206\u6bcd\u662f\u7d20\u6570p\u7684\u5206\u65701\/p\uff0c\u5faa\u73af\u8282\u7684\u6700\u5927\u53ef\u80fd\u957f\u5ea6\u662fp-1\u3002\u8fd9\u662f\u56e0\u4e3a\u6839\u636e\u8d39\u9a6c\u5c0f\u5b9a\u7406\uff0c10^(p-1) \u2261 1 (mod p)\u3002<\/li>\n\n\n\n<li>\u4e3a\u4ec0\u4e48\u8bf4&#8221;\u51e0\u4e4e\u8fbe\u5230&#8221;\uff1a 523\u662f\u7d20\u6570\uff0c\u6240\u4ee5\u7406\u8bba\u6700\u5927\u5faa\u73af\u8282\u957f\u5ea6\u662f522\u30021\/523\u7684\u5faa\u73af\u8282\u957f\u5ea6\u6b63\u597d\u662f522\uff0c\u8fbe\u5230\u4e86\u8fd9\u4e2a\u6700\u5927\u503c\u3002<\/li>\n\n\n\n<li>\u7279\u6b8a\u6027\uff1a \u5e76\u4e0d\u662f\u6240\u6709\u7d20\u6570\u5206\u6bcd\u90fd\u4f1a\u4ea7\u751f\u6700\u5927\u957f\u5ea6\u7684\u5faa\u73af\u8282\u30021\/523\u4ea7\u751f\u4e86\uff0c\u8fd9\u4f7f\u5b83\u6210\u4e3a\u4e00\u4e2a\u7279\u6b8a\u4f8b\u5b50\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u7c7b\u4f3c\u7684\u5faa\u73af\u5c0f\u6570\u4f8b\u5b50\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>1\/7 = 0.142857142857&#8230; \u5faa\u73af\u8282\u957f\u5ea6\uff1a6\uff08\u8fbe\u5230\u6700\u5927\u503c7-1=6\uff09<\/li>\n\n\n\n<li>1\/17 = 0.0588235294117647&#8230; \u5faa\u73af\u8282\u957f\u5ea6\uff1a16\uff08\u8fbe\u5230\u6700\u5927\u503c17-1=16\uff09<\/li>\n\n\n\n<li>1\/19 = 0.052631578947368421&#8230; \u5faa\u73af\u8282\u957f\u5ea6\uff1a18\uff08\u8fbe\u5230\u6700\u5927\u503c19-1=18\uff09<\/li>\n\n\n\n<li>1\/97 = 0.010309278350515463917525773195876288659793814432989690721649484536082474226804123711340206185567&#8230; \u5faa\u73af\u8282\u957f\u5ea6\uff1a96\uff08\u8fbe\u5230\u6700\u5927\u503c97-1=96\uff09<\/li>\n\n\n\n<li>1\/61 = 0.016393442622950819672131147540983606557377049180327868852459016393442622950819672131147540983606557377049&#8230; \u5faa\u73af\u8282\u957f\u5ea6\uff1a60\uff08\u51e0\u4e4e\u8fbe\u5230\u6700\u5927\u503c61-1=60\uff09<\/li>\n<\/ol>\n\n\n\n<p>\u8fd9\u4e9b\u4f8b\u5b50\u5c55\u793a\u4e86\u4e00\u4e9b\u7d20\u6570\u5206\u6bcd\u4ea7\u751f\u7684\u6709\u8da3\u5faa\u73af\u5c0f\u6570\u6a21\u5f0f\u3002\u5728\u6570\u8bba\u4e2d\uff0c\u8fd9\u79cd\u73b0\u8c61\u4e0e\u539f\u6839\u3001\u6a21\u8fd0\u7b97\u548c\u7fa4\u8bba\u7b49\u6982\u5ff5\u5bc6\u5207\u76f8\u5173\u3002<\/p>\n\n\n\n<p>\u7814\u7a76\u8fd9\u4e9b\u5faa\u73af\u6a21\u5f0f\u4e0d\u4ec5\u5728\u7eaf\u6570\u5b66\u4e2d\u6709\u610f\u4e49\uff0c\u5728\u5bc6\u7801\u5b66\u3001\u4f2a\u968f\u673a\u6570\u751f\u6210\u7b49\u5e94\u7528\u9886\u57df\u4e5f\u5f88\u91cd\u8981\u3002\u5b83\u4eec\u63ed\u793a\u4e86\u6570\u5b57\u7cfb\u7edf\u4e2d\u9690\u85cf\u7684\u7f8e\u4e3d\u6a21\u5f0f\u548c\u89c4\u5f8b\u3002<\/p>\n\n\n\n<p><strong>\u4e2d\u56fd\u7684\u8f66\u724c\u53f7\u6709\u591a\u5c11\u79cd\u53ef\u80fd\u6027\uff1f<\/strong><\/p>\n\n\n\n<p>\u8981\u8ba1\u7b97\u4e2d\u56fd\u8f66\u724c\u53f7\u7684\u53ef\u80fd\u6027\uff0c\u6211\u4eec\u9700\u8981\u8003\u8651\u4e0d\u540c\u7c7b\u578b\u7684\u8f66\u724c\u3002\u4e2d\u56fd\u6709\u51e0\u79cd\u4e3b\u8981\u7684\u8f66\u724c\u7c7b\u578b\uff0c\u6bcf\u79cd\u7c7b\u578b\u7684\u7ec4\u5408\u65b9\u5f0f\u7565\u6709\u4e0d\u540c\u3002\u8ba9\u6211\u4eec\u9010\u6b65\u5206\u6790\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u6807\u51c6\u79c1\u5bb6\u8f66\u724c\u7167\uff08\u6700\u5e38\u89c1\u7c7b\u578b\uff09\uff1a\n<ul class=\"wp-block-list\">\n<li>\u683c\u5f0f\uff1a\u7701\u4efd\u7b80\u79f0\uff081\u4e2a\u6c49\u5b57\uff09+ \u5b57\u6bcd\uff081\u4e2a\uff09+ 5\u4e2a\u5b57\u6bcd\u6216\u6570\u5b57\u6df7\u5408<\/li>\n\n\n\n<li>\u8ba1\u7b97\uff1a 31\uff08\u7701\u4efd\uff09 \u00d7 26\uff08\u7b2c\u4e00\u4e2a\u5b57\u6bcd\uff09 \u00d7 (26+10)^5\uff08\u540e5\u4f4d\uff09 = 31 \u00d7 26 \u00d7 36^5 \u2248 1,596,884,736<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u65b0\u80fd\u6e90\u8f66\u724c\uff1a\n<ul class=\"wp-block-list\">\n<li>\u683c\u5f0f\uff1a\u7701\u4efd\u7b80\u79f0\uff081\u4e2a\u6c49\u5b57\uff09+ \u5b57\u6bcd\uff081\u4e2a\uff09+ \u5b57\u6bcd\uff081\u4e2a\uff09+ \u6570\u5b57\uff084\u4e2a\uff09+ \u5b57\u6bcd\uff081\u4e2a\uff09<\/li>\n\n\n\n<li>\u8ba1\u7b97\uff1a 31 \u00d7 26 \u00d7 26 \u00d7 10^4 \u00d7 26 \u2248 54,267,904<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u4f7f\u9986\u8f66\u724c\uff1a\n<ul class=\"wp-block-list\">\n<li>\u683c\u5f0f\uff1a\u4f7f\uff081\u4e2a\u6c49\u5b57\uff09+ 3\u4e2a\u6570\u5b57 + 3\u4e2a\u5b57\u6bcd<\/li>\n\n\n\n<li>\u8ba1\u7b97\uff1a1 \u00d7 10^3 \u00d7 26^3 = 17,576,000<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u519b\u8f66\u724c\u7167\uff1a\n<ul class=\"wp-block-list\">\n<li>\u683c\u5f0f\uff1a\u519b\uff081\u4e2a\u6c49\u5b57\uff09+ 5\u4e2a\u6570\u5b57<\/li>\n\n\n\n<li>\u8ba1\u7b97\uff1a1 \u00d7 10^5 = 100,000<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u8b66\u8f66\u724c\u7167\uff1a\n<ul class=\"wp-block-list\">\n<li>\u683c\u5f0f\uff1a\u8b66\uff081\u4e2a\u6c49\u5b57\uff09+ 5\u4e2a\u6570\u5b57\u6216\u5b57\u6bcd\u6df7\u5408<\/li>\n\n\n\n<li>\u8ba1\u7b97\uff1a1 \u00d7 36^5 = 60,466,176<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u5176\u4ed6\u7279\u6b8a\u8f66\u724c\uff08\u5982\u9886\u9986\u3001\u6e2f\u6fb3\u3001\u6559\u7ec3\u8f66\u7b49\uff09\uff1a\n<ul class=\"wp-block-list\">\n<li>\u8fd9\u4e9b\u8f66\u724c\u7684\u6570\u91cf\u76f8\u5bf9\u8f83\u5c11\uff0c\u53ef\u4ee5\u4f30\u8ba1\u4e3a\u51e0\u5341\u4e07\u79cd\u53ef\u80fd\u6027<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>\u603b\u8ba1\uff1a \u5c06\u4ee5\u4e0a\u6240\u6709\u7c7b\u578b\u52a0\u8d77\u6765\uff0c\u5927\u7ea6\u670917\u4ebf\u79cd\u53ef\u80fd\u6027\u3002<\/p>\n\n\n\n<p>\u6ce8\u610f\u4e8b\u9879\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5b9e\u9645\u53d1\u653e\u7684\u8f66\u724c\u4f1a\u5c11\u4e8e\u7406\u8bba\u53ef\u80fd\u6027\uff0c\u56e0\u4e3a\u67d0\u4e9b\u7ec4\u5408\u53ef\u80fd\u88ab\u4fdd\u7559\u6216\u7981\u7528\u3002<\/li>\n\n\n\n<li>\u67d0\u4e9b\u7701\u4efd\u53ef\u80fd\u6709\u7279\u6b8a\u89c4\u5219\uff0c\u5f71\u54cd\u5b9e\u9645\u53ef\u80fd\u6027\u3002<\/li>\n\n\n\n<li>\u968f\u7740\u65f6\u95f4\u63a8\u79fb\uff0c\u8f66\u724c\u89c4\u5219\u53ef\u80fd\u53d1\u751f\u53d8\u5316\uff0c\u5f71\u54cd\u603b\u6570\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u603b\u7684\u6765\u8bf4\uff0c\u4e2d\u56fd\u8f66\u724c\u7cfb\u7edf\u63d0\u4f9b\u4e86\u975e\u5e38\u5927\u7684\u7ec4\u5408\u7a7a\u95f4\uff0c\u8db3\u4ee5\u6ee1\u8db3\u76ee\u524d\u548c\u672a\u6765\u76f8\u5f53\u957f\u4e00\u6bb5\u65f6\u95f4\u7684\u9700\u6c42\u3002\u5982\u679c\u60a8\u9700\u8981\u66f4\u7cbe\u786e\u7684\u8ba1\u7b97\u6216\u5bf9\u7279\u5b9a\u7c7b\u578b\u8f66\u724c\u611f\u5174\u8da3\uff0c\u8bf7\u544a\u8bc9\u6211\u3002<\/p>\n\n\n\n<p><strong>\u4f60\u8981\u8003\u8651\u5230\u572826\u4e2a\u82f1\u6587\u5b57\u6bcd\u91cc\uff0cI\u548cO\u5728\u4e2d\u56fd\u8f66\u724c\u662f\u4e0d\u5b58\u5728\u7684<\/strong><\/p>\n\n\n\n<p>\u60a8\u63d0\u51fa\u4e86\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u70b9\uff0c\u6211\u4e3a\u4e4b\u524d\u5ffd\u7565\u8fd9\u4e2a\u7ec6\u8282\u8868\u793a\u6b49\u610f\u3002\u60a8\u662f\u5bf9\u7684\uff0c\u5728\u4e2d\u56fd\u7684\u8f66\u724c\u7cfb\u7edf\u4e2d\uff0c\u786e\u5b9e\u4e0d\u4f7f\u7528\u5b57\u6bcdI\u548cO\uff0c\u4ee5\u907f\u514d\u4e0e\u6570\u5b571\u548c0\u6df7\u6dc6\u3002\u8ba9\u6211\u4eec\u6839\u636e\u8fd9\u4e2a\u4fe1\u606f\u91cd\u65b0\u8ba1\u7b97\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u6807\u51c6\u79c1\u5bb6\u8f66\u724c\u7167\uff1a\n<ul class=\"wp-block-list\">\n<li>\u683c\u5f0f\uff1a\u7701\u4efd\u7b80\u79f0\uff081\u4e2a\u6c49\u5b57\uff09+ \u5b57\u6bcd\uff081\u4e2a\uff09+ 5\u4e2a\u5b57\u6bcd\u6216\u6570\u5b57\u6df7\u5408<\/li>\n\n\n\n<li>\u8ba1\u7b97\uff1a 31\uff08\u7701\u4efd\uff09 \u00d7 24\uff08\u7b2c\u4e00\u4e2a\u5b57\u6bcd\uff0c\u53bb\u6389I\u548cO\uff09 \u00d7 (24+10)^5\uff08\u540e5\u4f4d\uff09 = 31 \u00d7 24 \u00d7 34^5 \u2248 1,062,860,032<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u65b0\u80fd\u6e90\u8f66\u724c\uff1a\n<ul class=\"wp-block-list\">\n<li>\u683c\u5f0f\uff1a\u7701\u4efd\u7b80\u79f0\uff081\u4e2a\u6c49\u5b57\uff09+ \u5b57\u6bcd\uff081\u4e2a\uff09+ \u5b57\u6bcd\uff081\u4e2a\uff09+ \u6570\u5b57\uff084\u4e2a\uff09+ \u5b57\u6bcd\uff081\u4e2a\uff09<\/li>\n\n\n\n<li>\u8ba1\u7b97\uff1a 31 \u00d7 24 \u00d7 24 \u00d7 10^4 \u00d7 24 \u2248 42,854,400<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u4f7f\u9986\u8f66\u724c\uff1a\n<ul class=\"wp-block-list\">\n<li>\u683c\u5f0f\uff1a\u4f7f\uff081\u4e2a\u6c49\u5b57\uff09+ 3\u4e2a\u6570\u5b57 + 3\u4e2a\u5b57\u6bcd<\/li>\n\n\n\n<li>\u8ba1\u7b97\uff1a1 \u00d7 10^3 \u00d7 24^3 = 13,824,000<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u519b\u8f66\u724c\u7167\uff1a\n<ul class=\"wp-block-list\">\n<li>\u683c\u5f0f\uff1a\u519b\uff081\u4e2a\u6c49\u5b57\uff09+ 5\u4e2a\u6570\u5b57<\/li>\n\n\n\n<li>\u8ba1\u7b97\uff1a1 \u00d7 10^5 = 100,000 \uff08\u4e0d\u53d8\uff09<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u8b66\u8f66\u724c\u7167\uff1a\n<ul class=\"wp-block-list\">\n<li>\u683c\u5f0f\uff1a\u8b66\uff081\u4e2a\u6c49\u5b57\uff09+ 5\u4e2a\u6570\u5b57\u6216\u5b57\u6bcd\u6df7\u5408<\/li>\n\n\n\n<li>\u8ba1\u7b97\uff1a1 \u00d7 34^5 = 45,435,424<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u5176\u4ed6\u7279\u6b8a\u8f66\u724c\uff08\u5982\u9886\u9986\u3001\u6e2f\u6fb3\u3001\u6559\u7ec3\u8f66\u7b49\uff09\uff1a\n<ul class=\"wp-block-list\">\n<li>\u4f30\u8ba1\u4e3a\u51e0\u5341\u4e07\u79cd\u53ef\u80fd\u6027\uff08\u4e0e\u4e4b\u524d\u76f8\u540c\uff09<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>\u603b\u8ba1\uff1a \u5c06\u4ee5\u4e0a\u6240\u6709\u7c7b\u578b\u52a0\u8d77\u6765\uff0c\u5927\u7ea6\u670911.65\u4ebf\u79cd\u53ef\u80fd\u6027\u3002<\/p>\n\n\n\n<p>\u8fd9\u4e2a\u4fee\u6b63\u540e\u7684\u8ba1\u7b97\u66f4\u51c6\u786e\u5730\u53cd\u6620\u4e86\u4e2d\u56fd\u8f66\u724c\u7cfb\u7edf\u7684\u5b9e\u9645\u60c5\u51b5\u3002\u53bb\u6389I\u548cO\u540e\uff0c\u603b\u7684\u53ef\u80fd\u6027\u6570\u91cf\u51cf\u5c11\u4e86\uff0c\u4f46\u4ecd\u7136\u63d0\u4f9b\u4e86\u975e\u5e38\u5927\u7684\u7ec4\u5408\u7a7a\u95f4\u3002<\/p>\n\n\n\n<p>\u5176\u4ed6\u6ce8\u610f\u4e8b\u9879\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u67d0\u4e9b\u7701\u4efd\u53ef\u80fd\u6709\u989d\u5916\u7684\u89c4\u5219\uff0c\u5982\u9650\u5236\u67d0\u4e9b\u6570\u5b57\u6216\u5b57\u6bcd\u7ec4\u5408\u3002<\/li>\n\n\n\n<li>\u4e00\u4e9b\u7279\u6b8a\u5e8f\u5217\u53ef\u80fd\u88ab\u4fdd\u7559\u7528\u4e8e\u7279\u6b8a\u76ee\u7684\u3002<\/li>\n\n\n\n<li>\u5b9e\u9645\u53d1\u653e\u7684\u8f66\u724c\u6570\u91cf\u4f1a\u5c11\u4e8e\u7406\u8bba\u53ef\u80fd\u6027\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u611f\u8c22\u60a8\u6307\u51fa\u8fd9\u4e2a\u91cd\u8981\u7684\u7ec6\u8282\uff0c\u8fd9\u8ba9\u6211\u4eec\u7684\u8ba8\u8bba\u66f4\u52a0\u51c6\u786e\u548c\u6709\u610f\u4e49\u3002\u5982\u679c\u60a8\u8fd8\u6709\u5176\u4ed6\u95ee\u9898\u6216\u9700\u8981\u8fdb\u4e00\u6b65\u7684\u89e3\u91ca\uff0c\u8bf7\u968f\u65f6\u544a\u8bc9\u6211\u3002<\/p>\n\n\n\n<p><strong>7\u4e2a\u7537\u751f\u548c6\u4e2a\u5973\u751f\u7ad9\u6210\u4e00\u4e2a\u5706\u5708\u6709\u591a\u5c11\u79cd\u6392\u5217\u7ec4\u5408\uff1f<\/strong><\/p>\n\n\n\n<p>\u8ba9\u6211\u4eec\u4e00\u6b65\u6b65\u6765\u5206\u6790\u8fd9\u4e2a\u95ee\u9898\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u9996\u5148\uff0c\u6211\u4eec\u6709\u603b\u5171 7 + 6 = 13 \u4e2a\u4eba\u3002<\/li>\n\n\n\n<li>\u901a\u5e38\uff0cn \u4e2a\u4eba\u56f4\u6210\u4e00\u4e2a\u5706\u5708\u7684\u6392\u5217\u6570\u662f (n-1)!\uff0c\u56e0\u4e3a\uff1a\n<ul class=\"wp-block-list\">\n<li>\u7b2c\u4e00\u4e2a\u4eba\u7684\u4f4d\u7f6e\u53ef\u4ee5\u56fa\u5b9a\uff08\u56e0\u4e3a\u5706\u5708\u53ef\u4ee5\u65cb\u8f6c\uff09<\/li>\n\n\n\n<li>\u5269\u4e0b\u7684 n-1 \u4e2a\u4eba\u53ef\u4ee5\u4efb\u610f\u6392\u5217<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u7136\u800c\uff0c\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u8003\u8651\u7537\u751f\u548c\u5973\u751f\u7684\u533a\u522b\u3002\u8fd9\u4f7f\u5f97\u95ee\u9898\u53d8\u6210\u4e86\u5faa\u73af\u6392\u5217\u4e2d\u7684&#8221;\u73e0\u5b50\u67d3\u8272&#8221;\u95ee\u9898\u3002<\/li>\n\n\n\n<li>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u516c\u5f0f\u53d8\u4e3a\uff1a (n-1)! \/ (m! * f!) \u5176\u4e2d n \u662f\u603b\u4eba\u6570\uff0cm \u662f\u7537\u751f\u6570\uff0cf \u662f\u5973\u751f\u6570\u3002<\/li>\n\n\n\n<li>\u4ee3\u5165\u6570\u5b57\uff1a n = 13 m = 7 f = 6<\/li>\n\n\n\n<li>\u8ba1\u7b97\uff1a (13-1)! \/ (7! * 6!) = 12! \/ (7! * 6!)<\/li>\n\n\n\n<li>\u4f7f\u7528\u8ba1\u7b97\u5668\u6216\u7f16\u7a0b\u5de5\u5177\u8ba1\u7b97\u8fd9\u4e2a\u7ed3\u679c\uff1a 12! \/ (7! * 6!) = 479,001,600 \/ (5,040 * 720) = 132,000<\/li>\n<\/ol>\n\n\n\n<p>\u56e0\u6b64\uff0c7\u4e2a\u7537\u751f\u548c6\u4e2a\u5973\u751f\u7ad9\u6210\u4e00\u4e2a\u5706\u5708\u6709 132,000 \u79cd\u4e0d\u540c\u7684\u6392\u5217\u65b9\u5f0f\u3002<\/p>\n\n\n\n<p>\u8fd9\u4e2a\u7ed3\u679c\u8003\u8651\u4e86\u4ee5\u4e0b\u56e0\u7d20\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5706\u5708\u53ef\u4ee5\u65cb\u8f6c\uff0c\u6240\u4ee5\u6211\u4eec\u56fa\u5b9a\u4e00\u4e2a\u4f4d\u7f6e<\/li>\n\n\n\n<li>\u7537\u751f\u4e4b\u95f4\u7684\u4f4d\u7f6e\u4ea4\u6362\u88ab\u89c6\u4e3a\u4e0d\u540c\u6392\u5217<\/li>\n\n\n\n<li>\u5973\u751f\u4e4b\u95f4\u7684\u4f4d\u7f6e\u4ea4\u6362\u88ab\u89c6\u4e3a\u4e0d\u540c\u6392\u5217<\/li>\n\n\n\n<li>\u4f46\u662f\u6574\u4e2a\u5706\u5708\u7684\u65cb\u8f6c\u4e0d\u88ab\u89c6\u4e3a\u65b0\u7684\u6392\u5217<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u662f\u4e00\u4e2a\u76f8\u5f53\u5927\u7684\u6570\u5b57\uff0c\u5c55\u793a\u4e86\u5373\u4f7f\u5728\u770b\u4f3c\u7b80\u5355\u7684\u60c5\u51b5\u4e0b\uff0c\u7ec4\u5408\u53ef\u80fd\u6027\u4e5f\u53ef\u80fd\u975e\u5e38\u591a\u3002<\/p>\n\n\n\n<p><strong>\u5982\u679c7\u4e2a\u7537\u751f\u5b8c\u5168\u4e00\u6837\uff0c6\u4e2a\u5973\u751f\u4e5f\u5b8c\u5168\u4e00\u6837\uff0c\u8fd9\u6837\u662f\u591a\u5c11\u79cd\uff1f<\/strong><\/p>\n\n\n\n<p>\u975e\u5e38\u597d\u7684\u540e\u7eed\u95ee\u9898\uff01\u8fd9\u4e2a\u60c5\u51b5\u4e0b\uff0c\u95ee\u9898\u53d8\u5f97\u66f4\u52a0\u6709\u8da3\uff0c\u56e0\u4e3a\u6211\u4eec\u73b0\u5728\u8981\u8003\u8651\u7684\u662f\u7537\u751f\u548c\u5973\u751f\u4e24\u7ec4\u4eba\u7684\u5206\u5e03\u6a21\u5f0f\uff0c\u800c\u4e0d\u662f\u4e2a\u4f53\u7684\u6392\u5217\u3002\u8ba9\u6211\u4eec\u6765\u5206\u6790\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u53ea\u5173\u5fc3\u7537\u751f\u548c\u5973\u751f\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u800c\u4e0d\u5173\u5fc3\u4e2a\u4f53\u7684\u5177\u4f53\u4f4d\u7f6e\u3002<\/li>\n\n\n\n<li>\u8fd9\u4e2a\u95ee\u9898\u53ef\u4ee5\u8f6c\u5316\u4e3a\uff1a\u5728\u4e00\u4e2a\u5706\u5708\u4e2d\u653e\u7f6e 7 \u4e2a\u76f8\u540c\u7684\u7269\u4f53\uff08\u4ee3\u8868\u7537\u751f\uff09\u548c 6 \u4e2a\u76f8\u540c\u7684\u7269\u4f53\uff08\u4ee3\u8868\u5973\u751f\uff09\u7684\u4e0d\u540c\u65b9\u5f0f\u3002<\/li>\n\n\n\n<li>\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u4f7f\u7528\u5faa\u73af\u6392\u5217\u4e2d\u7684&#8221;necklace&#8221;\u95ee\u9898\u516c\u5f0f\u3002\u516c\u5f0f\u4e3a\uff1a (m + n &#8211; 1)! \/ (m! * n!) \u5176\u4e2d m \u662f\u7b2c\u4e00\u79cd\u7269\u4f53\u7684\u6570\u91cf\uff0cn \u662f\u7b2c\u4e8c\u79cd\u7269\u4f53\u7684\u6570\u91cf\u3002<\/li>\n\n\n\n<li>\u5728\u6211\u4eec\u7684\u95ee\u9898\u4e2d\uff1a m = 7 (\u7537\u751f) n = 6 (\u5973\u751f)<\/li>\n\n\n\n<li>\u4ee3\u5165\u516c\u5f0f\uff1a (7 + 6 &#8211; 1)! \/ (7! * 6!) = 12! \/ (7! * 6!)<\/li>\n\n\n\n<li>\u8ba1\u7b97\u7ed3\u679c\uff1a 12! \/ (7! * 6!) = 479,001,600 \/ (5,040 * 720) = 132<\/li>\n<\/ol>\n\n\n\n<p>\u56e0\u6b64\uff0c\u5982\u679c 7 \u4e2a\u7537\u751f\u5b8c\u5168\u4e00\u6837\uff0c6 \u4e2a\u5973\u751f\u4e5f\u5b8c\u5168\u4e00\u6837\uff0c\u603b\u5171\u6709 132 \u79cd\u4e0d\u540c\u7684\u6392\u5217\u65b9\u5f0f\u3002<\/p>\n\n\n\n<p>\u8fd9\u4e2a\u7ed3\u679c\u6bd4\u4e4b\u524d\u7684\u60c5\u51b5\u5c11\u5f97\u591a\uff0c\u56e0\u4e3a\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6211\u4eec\u4e0d\u518d\u533a\u5206\u4e2a\u4f53\u7537\u751f\u6216\u4e2a\u4f53\u5973\u751f<\/li>\n\n\n\n<li>\u6211\u4eec\u53ea\u5173\u5fc3\u7537\u751f\u7ec4\u548c\u5973\u751f\u7ec4\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e<\/li>\n\n\n\n<li>\u65cb\u8f6c\u6574\u4e2a\u5706\u5708\u4e0d\u4f1a\u4ea7\u751f\u65b0\u7684\u6392\u5217<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u4e2a\u4f8b\u5b50\u5f88\u597d\u5730\u8bf4\u660e\u4e86\u5728\u7ec4\u5408\u95ee\u9898\u4e2d\uff0c\u7269\u4f53\u7684\u53ef\u533a\u5206\u6027\u5982\u4f55\u663e\u8457\u5f71\u54cd\u53ef\u80fd\u7684\u6392\u5217\u6570\u91cf\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u8fd9\u79cd\u5206\u6790\u53ef\u80fd\u7528\u4e8e\u7814\u7a76\u5206\u5b50\u7ed3\u6784\u3001\u793e\u4ea4\u7f51\u7edc\u6a21\u5f0f\u6216\u5176\u4ed6\u6d89\u53ca\u5206\u7ec4\u548c\u5faa\u73af\u6392\u5217\u7684\u573a\u666f\u3002<\/p>\n\n\n\n<p><strong>\u4e00\u4e2a\u73ed\u7ea7\u670988\u4e2a\u4eba\uff0c\u51fa\u73b0\u540c\u6708\u540c\u65e5\u751f\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/strong><\/p>\n\n\n\n<p>\u8fd9\u662f\u4e00\u4e2a\u5f88\u6709\u8da3\u7684\u6982\u7387\u95ee\u9898\uff0c\u901a\u5e38\u88ab\u79f0\u4e3a&#8221;\u751f\u65e5\u95ee\u9898&#8221;\u6216&#8221;\u751f\u65e5\u6096\u8bba&#8221;\u3002\u8ba9\u6211\u4eec\u4e00\u6b65\u6b65\u6765\u5206\u6790\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u7684\u662f\u81f3\u5c11\u6709\u4e24\u4e2a\u4eba\u751f\u65e5\u76f8\u540c\u7684\u6982\u7387\u3002<\/li>\n\n\n\n<li>\u901a\u5e38\uff0c\u76f4\u63a5\u8ba1\u7b97\u8fd9\u4e2a\u6982\u7387\u6bd4\u8f83\u590d\u6742\uff0c\u6240\u4ee5\u6211\u4eec\u4f1a\u8ba1\u7b97\u5b83\u7684\u53cd\u9762\uff1a\u6ca1\u6709\u4eba\u751f\u65e5\u76f8\u540c\u7684\u6982\u7387\uff0c\u7136\u540e\u75281\u51cf\u53bb\u8fd9\u4e2a\u503c\u3002<\/li>\n\n\n\n<li>\u5047\u8bbe\u4e00\u5e74\u6709365\u5929\uff08\u5ffd\u7565\u95f0\u5e74\uff09<\/li>\n\n\n\n<li>\u8ba1\u7b97\u6b65\u9aa4\uff1a\u00a0a) \u7b2c\u4e00\u4e2a\u4eba\u7684\u751f\u65e5\u53ef\u4ee5\u662f\u4efb\u4f55\u4e00\u5929\uff1a365\/365 b) \u7b2c\u4e8c\u4e2a\u4eba\u7684\u751f\u65e5\u4e0d\u80fd\u548c\u7b2c\u4e00\u4e2a\u4eba\u76f8\u540c\uff1a364\/365 c) \u7b2c\u4e09\u4e2a\u4eba\u7684\u751f\u65e5\u4e0d\u80fd\u548c\u524d\u4e24\u4e2a\u4eba\u76f8\u540c\uff1a363\/365 &#8230;\u4ee5\u6b64\u7c7b\u63a8<\/li>\n\n\n\n<li>\u6240\u4ee5\uff0c\u6ca1\u6709\u4eba\u751f\u65e5\u76f8\u540c\u7684\u6982\u7387\u662f\uff1a\u00a0365\/365 * 364\/365 * 363\/365 * &#8230; * (365-87)\/365<\/li>\n\n\n\n<li>\u8fd9\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a\u00a0(365!)\/((365-88)! * 365^88)<\/li>\n\n\n\n<li>\u4f7f\u7528\u8ba1\u7b97\u5668\u6216\u7f16\u7a0b\u5de5\u5177\u8ba1\u7b97\u8fd9\u4e2a\u503c\uff08\u56e0\u4e3a\u6570\u5b57\u5f88\u5927\uff09\uff1a\u00a0\u7ea6\u7b49\u4e8e 0.0000000000000000000292<\/li>\n\n\n\n<li>\u56e0\u6b64\uff0c\u81f3\u5c11\u6709\u4e24\u4e2a\u4eba\u751f\u65e5\u76f8\u540c\u7684\u6982\u7387\u662f\uff1a\u00a01 &#8211; 0.0000000000000000000292 \u2248 0.9999999999999999999708<\/li>\n\n\n\n<li>\u8f6c\u6362\u4e3a\u767e\u5206\u6bd4\uff1a\u7ea6 99.99999999999999999708%<\/li>\n<\/ol>\n\n\n\n<p>\u7ed3\u8bba\uff1a\u5728\u4e00\u4e2a88\u4eba\u7684\u73ed\u7ea7\u4e2d\uff0c\u51fa\u73b0\u540c\u6708\u540c\u65e5\u751f\u7684\u6982\u7387\u51e0\u4e4e\u662f100%\u3002\u8fd9\u4e2a\u7ed3\u679c\u53ef\u80fd\u770b\u8d77\u6765\u4ee4\u4eba\u60ca\u8bb6\uff0c\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u5b83\u88ab\u79f0\u4e3a&#8221;\u751f\u65e5\u6096\u8bba&#8221;\u3002<\/p>\n\n\n\n<p>\u5b9e\u9645\u4e0a\uff0c\u53ea\u9700\u898123\u4e2a\u4eba\uff0c\u5c31\u6709\u8d85\u8fc750%\u7684\u6982\u7387\u81f3\u5c11\u6709\u4e24\u4e2a\u4eba\u751f\u65e5\u76f8\u540c\u3002\u8fd9\u4e2a\u95ee\u9898\u5728\u5bc6\u7801\u5b66\u3001\u54c8\u5e0c\u51fd\u6570\u8bbe\u8ba1\u7b49\u9886\u57df\u6709\u91cd\u8981\u5e94\u7528\u3002<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u4e2a\u8ba1\u7b97\u5047\u8bbe\u751f\u65e5\u5728\u4e00\u5e74\u4e2d\u5747\u5300\u5206\u5e03\uff0c\u5b9e\u9645\u60c5\u51b5\u53ef\u80fd\u7565\u6709\u4e0d\u540c\uff0c\u56e0\u4e3a\u67d0\u4e9b\u65e5\u671f\u7684\u51fa\u751f\u7387\u53ef\u80fd\u9ad8\u4e8e\u5176\u4ed6\u65e5\u671f\u3002\u4f46\u5bf9\u4e8e\u5927\u6837\u672c\u91cf\u6765\u8bf4\uff0c\u8fd9\u4e2a\u5047\u8bbe\u901a\u5e38\u8db3\u591f\u51c6\u786e\u3002<\/p>\n\n\n\n<p><strong>\u8fd8\u6709\u54ea\u4e9b\u6709\u8da3\u7684\u6096\u8bba\uff1f<\/strong><\/p>\n\n\n\n<p>\u786e\u5b9e\u6709\u5f88\u591a\u6709\u8da3\u7684\u6096\u8bba\uff0c\u5b83\u4eec\u5e38\u5e38\u6311\u6218\u6211\u4eec\u7684\u76f4\u89c9\u601d\u7ef4\u3002\u4ee5\u4e0b\u662f\u4e00\u4e9b\u8457\u540d\u7684\u6096\u8bba\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u8f9b\u666e\u68ee\u6096\u8bba\uff08Simpson&#8217;s Paradox\uff09\uff1a \u5728\u5206\u7ec4\u6570\u636e\u4e2d\uff0c\u6bcf\u4e2a\u5b50\u7ec4\u90fd\u5b58\u5728\u7684\u8d8b\u52bf\uff0c\u5728\u5408\u5e76\u540e\u7684\u603b\u4f53\u4e2d\u53ef\u80fd\u6d88\u5931\u6216\u53cd\u8f6c\u3002<\/li>\n\n\n\n<li>\u8499\u63d0\u970d\u5c14\u95ee\u9898\uff08Monty Hall Problem\uff09\uff1a \u5728\u6e38\u620f\u8282\u76ee\u4e2d\uff0c\u6539\u53d8\u4f60\u7684\u9009\u62e9\u4f1a\u589e\u52a0\u83b7\u80dc\u6982\u7387\uff0c\u8fd9\u8fdd\u53cd\u4e86\u8bb8\u591a\u4eba\u7684\u76f4\u89c9\u3002<\/li>\n\n\n\n<li>\u7956\u7236\u6096\u8bba\uff08Grandfather Paradox\uff09\uff1a \u5982\u679c\u4f60\u56de\u5230\u8fc7\u53bb\u6740\u6b7b\u4f60\u7684\u7956\u7236\uff0c\u4f60\u5c31\u4e0d\u4f1a\u51fa\u751f\uff0c\u90a3\u4e48\u8c01\u6740\u4e86\u4f60\u7684\u7956\u7236\uff1f<\/li>\n\n\n\n<li>\u8239of\u5fd2\u4fee\u65af\uff08Ship of Theseus\uff09\uff1a \u5982\u679c\u4e00\u8258\u8239\u7684\u6240\u6709\u90e8\u4ef6\u90fd\u88ab\u9010\u4e00\u66ff\u6362\uff0c\u5b83\u8fd8\u662f\u539f\u6765\u7684\u90a3\u8258\u8239\u5417\uff1f<\/li>\n\n\n\n<li>\u5df4\u4f2f\u6096\u8bba\uff08Barber Paradox\uff09\uff1a \u6751\u91cc\u7684\u7406\u53d1\u5e08\u53ea\u7ed9\u4e0d\u81ea\u5df1\u7406\u53d1\u7684\u4eba\u7406\u53d1\u3002\u90a3\u4e48\uff0c\u7406\u53d1\u5e08\u8be5\u7ed9\u81ea\u5df1\u7406\u53d1\u5417\uff1f<\/li>\n\n\n\n<li>\u5168\u80fd\u6096\u8bba\uff08Omnipotence Paradox\uff09\uff1a \u4e00\u4e2a\u65e0\u6240\u4e0d\u80fd\u7684\u5b58\u5728\u80fd\u521b\u9020\u4e00\u4e2a\u5b83\u65e0\u6cd5\u4e3e\u8d77\u7684\u77f3\u5934\u5417\uff1f<\/li>\n\n\n\n<li>\u8bf4\u8c0e\u8005\u6096\u8bba\uff08Liar&#8217;s Paradox\uff09\uff1a &#8220;\u8fd9\u53e5\u8bdd\u662f\u5047\u7684&#8221;\u3002\u5982\u679c\u8fd9\u53e5\u8bdd\u662f\u771f\u7684\uff0c\u90a3\u5b83\u5c31\u662f\u5047\u7684\uff1b\u5982\u679c\u662f\u5047\u7684\uff0c\u90a3\u5b83\u5c31\u662f\u771f\u7684\u3002<\/li>\n\n\n\n<li>\u6ce2\u5229\u4e9a\u7684\u9676\u7f50\uff08Bertrand&#8217;s Box Paradox\uff09\uff1a \u5728\u6982\u7387\u8bba\u4e2d\uff0c\u76f4\u89c9\u63a8\u7406\u53ef\u80fd\u5bfc\u81f4\u9519\u8bef\u7ed3\u8bba\u7684\u4e00\u4e2a\u4f8b\u5b50\u3002<\/li>\n\n\n\n<li>\u610f\u5916\u8003\u8bd5\u6096\u8bba\uff08Unexpected Hanging Paradox\uff09\uff1a \u8001\u5e08\u5ba3\u5e03\u4e0b\u5468\u4f1a\u6709\u4e00\u6b21\u7a81\u51fb\u8003\u8bd5\uff0c\u5b66\u751f\u63a8\u7406\u51fa\u8003\u8bd5\u4e0d\u53ef\u80fd\u53d1\u751f\uff0c\u4f46\u8003\u8bd5\u8fd8\u662f\u53d1\u751f\u4e86\u3002<\/li>\n\n\n\n<li>\u829d\u8bfa\u6096\u8bba\uff08Zeno&#8217;s Paradoxes\uff09\uff1a \u4f8b\u5982&#8221;\u963f\u57fa\u91cc\u65af\u8ffd\u4e4c\u9f9f&#8221;\uff0c\u7406\u8bba\u4e0a\u963f\u57fa\u91cc\u65af\u6c38\u8fdc\u8ffd\u4e0d\u4e0a\u4e4c\u9f9f\u3002<\/li>\n\n\n\n<li>\u6096\u8bba\u6096\u8bba\uff08Paradox of paradoxes\uff09\uff1a \u5982\u679c\u4e00\u4e2a\u89c4\u5219\u8bf4&#8221;\u6240\u6709\u89c4\u5219\u90fd\u6709\u4f8b\u5916&#8221;\uff0c\u90a3\u4e48\u8fd9\u4e2a\u89c4\u5219\u672c\u8eab\u662f\u5426\u6709\u4f8b\u5916\uff1f<\/li>\n\n\n\n<li>\u514b\u7f57\u683c\u6096\u8bba\uff08Crocodile Dilemma\uff09\uff1a 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