{"id":6080,"date":"2017-04-01T01:00:00","date_gmt":"2017-03-31T17:00:00","guid":{"rendered":"http:\/\/swarma.org\/%swarma-paper%\/"},"modified":"2018-12-11T15:36:24","modified_gmt":"2018-12-11T07:36:24","slug":"%e5%bc%a0%e6%b1%9f%ef%bc%9a%e4%bb%8e%e3%80%8c%e7%bc%98%e8%b5%b7%e6%80%a7%e7%a9%ba%e3%80%8d%e5%88%b0%e3%80%8c%e4%ba%ba%e5%b7%a5%e6%99%ba%e8%83%bd%e3%80%8d","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=6080","title":{"rendered":"\u5f20\u6c5f\uff1a\u4ece\u300c\u7f18\u8d77\u6027\u7a7a\u300d\u5230\u300c\u4eba\u5de5\u667a\u80fd\u300d"},"content":{"rendered":"
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\"\u96c6\u667a\"<\/p>\n

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\u7f18\u8d77\u6027\u7a7a<\/span><\/strong><\/span><\/p>\n


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\u4eba\u5de5\u667a\u80fd<\/span><\/strong><\/span><\/p>\n


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 \u5982\u679c\u6211\u4eec\u627f\u8ba4\u90a3\u5957\u201c\u7f18\u8d77\u6027\u7a7a\u201d\u7684\u8bf4\u6cd5\uff0c\u4e5f\u5c31\u662f\u8bf4\u4e16\u754c\u4e0a\u7684\u4e07\u4e8b\u4e07\u7269\u90fd\u662f\u6211\u4eec\u4f5c\u4e3a\u89c2\u5bdf\u8005\u5728\u5207\u65ad\u4e86\u56e0\u679c\u7ea0\u7f20\u4e4b\u7f51\u4e4b\u540e\u521b\u9020\u51fa\u6765\u7684\uff0c\u90a3\u4e48\uff0c\u6211\u4eec\u4e0d\u662f\u65e9\u5df2\u7ecf\u201c\u521b\u9020\u201d\u51fa\u4e86\u4e00\u5207\u7684\u4e00\u5207\uff0c\u751a\u81f3\u4e8e\u73b0\u5728\u79d1\u5b66\u5bb6\u4eec\u6b63\u5728\u5168\u529b\u653b\u514b\u7684\u4eba\u5de5\u667a\u80fd\u4e86\u5417\uff1f<\/span><\/p>\n

\u8bf4\u6765\u4e5f\u662f\u597d\u7b11\uff0c\u79d1\u5b66\u5bb6\u4eec\u8d39\u5c3d\u5fc3\u601d\u8981\u53bb\u518d\u9020\u4e00\u4e2a\u5177\u5907\u667a\u80fd\u7684\u673a\u5668\uff0c\u7136\u800c\u5374\u5fd8\u8bb0\u4e86\uff0c\u8fd9\u79cd\u673a\u5668\u672c\u5df2\u7ecf\u5b58\u5728\u3002\u4eba\u5de5\u667a\u80fd\u7684\u53d1\u5c55\u5386\u53f2\u4e5f\u7684\u786e\u6697\u793a\u4e86\u4eba\u7c7b\u79d1\u5b66\u5bb6\u6b63\u5728\u515c\u4e00\u4e2a\u8d85\u7ea7\u5927\u7684\u5708\u5b50\u2026\u2026<\/span><\/p>\n

1956\u5e74\uff0c\u4eba\u5de5\u667a\u80fd\u8bde\u751f\u3002Newell\u548cSimon\u7b49\u4eba\u7f16\u5236\u7684\u7a0b\u5e8f\u201c\u903b\u8f91\u7406\u8bba\u5bb6\u201d\u53ef\u4ee5\u81ea\u52a8\u8bc1\u660e\u300a\u6570\u5b66\u539f\u7406\u300b\uff08\u6570\u7406\u903b\u8f91\u7684\u7ecf\u5178\u6559\u79d1\u4e66\uff0c\u5927\u54f2\u5b66\u5bb6\u3001\u6570\u5b66\u5bb6\u7f57\u7d20\u8457\uff09\u7b2c\u4e8c\u7ae0\u4e2d\u768438\u6761\u5b9a\u7406\uff1bSamuel\u7814\u5236\u4e86\u4e00\u4e2a\u8df3\u68cb\u7a0b\u5e8f\uff0c\u8be5\u7a0b\u5e8f\u5177\u6709\u81ea\u5b66\u4e60\u80fd\u529b\uff0c\u5e76\u57283\u5e74\u540e\u6253\u8d25\u4e86Samuel\u672c\u4eba\uff0c5\u5e74\u540e\u51fb\u8d25\u4e86\u5dde\u9645\u51a0\u519b\u3002<\/span><\/p>\n

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\n

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<\/span><\/p>\n

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<\/span>\"\u96c6\u667a\"
<\/p>\n

\u4eba\u5de5\u667a\u80fd\u5927\u81f4\u7684\u53d1\u5c55\u66f2\u7ebf<\/span><\/strong><\/p>\n

<\/span><\/p>\n

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Brooks\u662f<\/span>MIT\u7684\u6559\u6388\uff0c\u4ed6\u6709\u4e00\u53e5\u540d\u8a00\uff0c\u53eb\u505a<\/span>\u201c\u5927\u8c61\u4e0d\u73a9\u8c61\u68cb<\/span>\u201d\uff0c\u610f\u601d\u662f\u8bf4\u4f20\u7edf\u7684\u4eba\u5de5\u667a\u80fd\u5e9f\u4e86\u534a\u5929\u52b2\u6559\u4f1a\u673a\u5668\u53bb\u4e0b\u8c61\u68cb\uff0c\u505a\u63a8\u7406\uff0c\u7136\u800c\u8fd9\u5374\u4e0e\u751f\u7269\u7684\u5929\u6027\u80cc\u9053\u800c\u9a70\uff0c\u5927\u8c61\u4e0d\u4f1a\u4e0b\u68cb\u4f46\u5374\u6709\u57fa\u672c\u7684\u667a\u80fd\uff0c\u751a\u81f3\u8fde\u8682\u8681\u548c\u87d1\u8782\u90fd\u77e5\u9053\u8d8b\u5229\u907f\u5bb3\u3002\u4e8e\u662f<\/span>Brooks\u5728\u4ed6\u7684<\/span>MIT\u5b9e\u9a8c\u5ba4\u4e2d\u642d\u5efa\u4e86\u4e00\u5957\u673a\u5668\u6606\u866b\u52a8\u7269\u56ed\uff0c\u8fd9\u4e9b\u6606\u866b\u90fd\u6ca1\u6709\u590d\u6742\u7684\u667a\u80fd\uff0c\u4f46\u5374\u53ef\u4ee5\u7075\u6d3b\u5730\u4e0e\u73af\u5883\u4ea4\u4e92\u3002<\/span><\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u6df1\u5ea6\u5b66\u4e60\u7f51\u7edc\u901a\u8fc71000\u4e07\u5f20YouTube\u89c6\u9891\u56fe\u7247\u5b66\u4e60\u51fa\u6765\u7684\u732b\u8138<\/span><\/strong><\/p>\n

<\/span><\/p>\n

2011\u5e74\uff0c\u8c37\u6b4cX\u5b9e\u9a8c\u5ba4\u7684\u7814\u7a76\u4eba\u5458\u4eceYouTube\u89c6\u9891\u4e2d\u62bd\u53d6\u51fa1000\u4e07\u5f20\u9759\u6001\u56fe\u7247\uff0c\u628a\u5b83\u5582\u7ed9\u201c\u8c37\u6b4c\u5927\u8111\u201d\u2014\u2014\u4e00\u4e2a\u91c7\u7528\u4e86\u6240\u8c13\u6df1\u5ea6\u5b66\u4e60\u6280\u672f\u7684\u5927\u578b\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\uff0c\u8bd5\u56fe\u5728\u8fd9\u4e9b\u56fe\u7247\u4e2d\u5bfb\u627e\u91cd\u590d\u51fa\u73b0\u7684\u6a21\u5f0f\u3002\u4e09\u5929\u540e\uff0c\u8fd9\u53f0\u8d85\u7ea7\u201c\u5927\u8111\u201d\u5728\u6ca1\u6709\u4eba\u7c7b\u7684\u5e2e\u52a9\u4e0b\uff0c\u5c45\u7136\u81ea\u5df1\u53d1\u73b0\u4e86\u201c\u732b\u201d\u30022012\u5e7411\u6708\uff0c\u5fae\u8f6f\u5728\u4e2d\u56fd\u7684\u4e00\u6b21\u6d3b\u52a8\u4e2d\uff0c\u5c55\u793a\u4e86\u4ed6\u4eec\u65b0\u7814\u5236\u7684\u4e00\u4e2a\u5168\u81ea\u52a8\u7684\u540c\u58f0\u7ffb\u8bd1\u7cfb\u7edf\u2014\u2014\u91c7\u7528\u4e86\u6df1\u5ea6\u5b66\u4e60\u6280\u672f\u7684\u8ba1\u7b97\u7cfb\u7edf\u3002\u6f14\u8bb2\u8005\u7528\u82f1\u6587\u6f14\u8bb2\uff0c\u8fd9\u53f0\u673a\u5668\u80fd\u5b9e\u65f6\u5730\u5b8c\u6210\u8bed\u97f3\u8bc6\u522b\u3001\u673a\u5668\u7ffb\u8bd1\u548c\u4e2d\u6587\u7684\u8bed\u97f3\u5408\u6210\uff0c\u4e5f\u5c31\u662f\u673a\u5668\u5b8c\u6210\u4e86\u540c\u58f0\u4f20\u8bd1\u30022016\u5e74\uff0cGoogle\u65d7\u4e0b\u7684DeepMind\u56e2\u961f\u5f00\u53d1\u51fa\u7684\u8d85\u7ea7\u673a\u5668AlphaGo\u6700\u7ec8\u4ee54\u6bd41\u7684\u5927\u6bd4\u5206\u6218\u80dc\u4e86\u4eba\u7c7b\u56f4\u68cb\u4e16\u754c\u51a0\u519b\u674e\u4e16\u77f3\u3002\u4eba\u8138\u8bc6\u522b\u3001\u673a\u5668\u7ffb\u8bd1\u3001\u5507\u8bed\u8bc6\u522b\u3001\u673a\u5668\u4f5c\u66f2\u3001\u7ed8\u753b\u2026\u2026\uff0c\u4e00\u4e2a\u4e2a\u9886\u57df\u90fd\u88ab\u7a81\u7834\uff0c\u5728\u8fd9\u4e24\u5e74\u4e2d\uff0c\u6211\u4eec\u4e00\u8d77\u89c1\u8bc1\u4e86\u673a\u5668\u7684\u771f\u6b63\u89c9\u9192\u3002<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u4eba\u673a\u5927\u6218\u4e2d\uff0cAlphaGo\u6b63\u5728\u5bf9\u4e0a\u767e\u4e07\u4e2a\u68cb\u5c40\u5c55\u5f00\u5927\u8303\u56f4\u641c\u7d22<\/span><\/strong><\/p>\n

<\/span><\/p>\n

\u8fd9\u5c31\u662f\u6df1\u5ea6\u5b66\u4e60\u9769\u547d\u2014\u2014\u4eba\u5de5\u667a\u80fd\u7684\u5168\u65b0\u7bc7\u7ae0\u3002\u6548\u6cd5\u4eba\u7c7b\u7684\u5927\u8111\u7ed3\u6784\uff0c\u4eba\u4eec\u8bbe\u8ba1\u4e86\u8d8a\u6765\u8d8a\u6df1\u7684\u795e\u7ecf\u7f51\u7edc\u3002\u4e8e\u6b64\u540c\u65f6\uff0c\u4eba\u4eec\u8fd8\u7ed9\u8fd9\u4e9b\u7f51\u7edc\u5582\u98df\u4e86\u5927\u91cf\u7684\u6570\u636e\uff0c\u4e8e\u662f\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u5c31\u6447\u8eab\u4e00\u53d8\u6210\u4e3a\u4e86\u53ef\u4ee5\u5728\u5f62\u8c61\u601d\u7ef4\u548c\u76f4\u89c9\u601d\u7ef4\u4e0a\u90fd\u582a\u4e0e\u4eba\u7c7b\u5ab2\u7f8e\u7684\u4eba\u5de5\u667a\u80fd\u673a\u5668\u4e86\u3002\u7d27\u63a5\u7740\uff0c\u4eba\u5de5\u667a\u80fd\u5c06\u8ba9\u4e00\u534a\u4ee5\u4e0a\u7684\u4eba\u7c7b\u5931\u4e1a\uff0c\u4eba\u5de5\u667a\u80fd\u5c06\u572830\u5e74\u5185\u8d85\u8d8a\u4eba\u7c7b\u667a\u6167\uff0c\u5947\u70b9\u5df2\u7ecf\u4e34\u8fd1\uff0c\u5404\u79cd\u201c\u5927\u9884\u8a00\u201d\u53c8\u4e00\u6b21\u63a5\u8e35\u800c\u6765\u2026\u2026<\/span><\/p>\n

<\/span>
<\/p>\n


<\/span><\/p>\n


<\/span><\/p>\n

\u7a7a\u7684\u667a\u6167<\/span><\/strong><\/span><\/p>\n


<\/span><\/strong><\/span><\/p>\n

<\/span><\/p>\n

\u4ed4\u7ec6\u54c1\u5473\u4eba\u5de5\u667a\u80fd\u5b66\u79d1\u7684\u53d1\u5c55\u5c31\u4f1a\u53d1\u73b0\uff0c\u4eba\u4eec\u8d4b\u4e88\u673a\u5668\u667a\u6167\u7684\u8fc7\u7a0b\u6070\u6070\u662f\u9010\u6e10\u653e\u7a7a\u4eba\u7c7b\u667a\u6167\u7684\u8fc7\u7a0b\u3002\u5f00\u59cb\uff0c\u4eba\u4eec\u8bd5\u56fe\u7ed9\u673a\u5668\u5f3a\u884c\u704c\u8f93\u77e5\u8bc6\uff0c\u4e8e\u662f\u673a\u5668\u88ab\u6491\u5f97\u53d7\u4e0d\u4e86\u4e86\uff0c\u7ec8\u4e8e\u8131\u4e0d\u4e86\u201c\u4eba\u5de5\u611a\u8822\u201d\u7684\u9a82\u540d\u3002<\/span><\/p>\n

\u540e\u6765\uff0c\u4eba\u4eec\u5c06\u8fd9\u4e9b\u77e5\u8bc6\u653e\u7a7a\uff0c\u8f6c\u800c\u8bbe\u8ba1\u601d\u7ef4\u673a\u5668\u7684\u67b6\u6784\uff0c\u800c\u4e0d\u518d\u5173\u5fc3\u5b83\u601d\u8003\u7684\u5185\u5bb9\u3002\u8fd9\u5c31\u4eff\u4f5b\u662f\u73b0\u4ee3\u6559\u80b2\u4e2d\u7684<\/span>\u201c\u542f\u53d1\u5f0f\u6559\u5b66<\/span>\u201d\uff0c\u6211\u4eec\u4e0d\u518d\u704c\u8f93\u77e5\u8bc6\u7ed9\u5c0f\u5b69\uff0c\u800c\u662f\u7ed9\u4ed6\u63d0\u4f9b\u4e00\u4e2a\u821e\u53f0\uff0c\u4efb\u5176\u81ea\u7531\u5730\u751f\u957f\u3002\u4e8e\u662f\uff0c\u8fd9\u4e9b\u7f51\u7edc\u5c31\u4f1a\u81ea\u7136\u957f\u51fa\u6765\u80fd\u591f\u9002\u5e94\u73af\u5883\u7684\u77e5\u8bc6\u3002<\/span><\/span><\/p>\n

\u6df1\u5ea6\u5b66\u4e60\u4e4b\u6240\u4ee5\u6210\u529f\u6709\u4e24\u4e2a\u5173\u952e\u56e0\u7d20\uff0c\u4e00\u662f\u6709\u6b63\u786e\u7684\u7f51\u7edc\u7ed3\u6784\uff1b\u4e8c\u662f\u6709\u5927\u6570\u636e\u7684\u5582\u98df\u3002\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u533a\u522b\u4e8e\u65e9\u671f\u795e\u7ecf\u7f51\u7edc\u7684\u6700\u5927\u7279\u5f81\u5c31\u662f\u5c06\u6709\u5173\u7a7a\u95f4\u5e73\u79fb\u3001\u65cb\u8f6c\u7b49\u5bf9\u79f0\u548c\u65f6\u95f4\u4e0a\u7684\u957f\u7a0b\u8054\u7cfb\u8fd9\u6837\u7684\u5148\u9a8c\u77e5\u8bc6\u505a\u5230\u4e86\u7f51\u7edc\u7684\u5927\u6846\u67b6\u4e2d\u3002\u7136\u540e\uff0c\u4eba\u4eec\u518d\u5c06\u4e0e\u4eba\u7c7b\u6d3b\u52a8\u76f8\u5173\u7684\u5927\u6570\u636e\u5582\u7ed9\u8fd9\u4e9b<\/span>\u201c\u5982\u9965\u4f3c\u6e34<\/span>\u201d\u7684\u7f51\u7edc\uff0c\u8ba9\u4ed6\u4eec\u5145\u5206\u5730\u6f14\u5316\uff0c\u6700\u7ec8\u5f62\u6210\u4e86\u582a\u4e0e\u4eba\u7c7b\u76f8\u6bd4\u62df\u7684\u667a\u6167\u3002<\/span><\/span><\/p>\n

\u51e0\u4e4e\u53ef\u4ee5\u8fd9\u6837\u8bf4\uff0c\u6bcf\u5f53\u6211\u4eec\u653e\u677e\u4e00\u6b21\u4eba\u7c7b\u81ea\u5df1\u7684\u6210\u89c1\uff0c\u6211\u4eec\u7684\u673a\u5668\u5c31\u4f1a\u66f4\u52a0\u667a\u6167\u4e00\u4e9b\u3002\u6240\u4ee5\uff0c\u73b0\u5728\u7684\u4eba\u5de5\u667a\u80fd\u662f\u5b83\u81ea\u5df1\u751f\u957f\u51fa\u6765\u7684\u667a\u6167\uff0c\u6211\u4eec\u867d\u7136\u8bbe\u8ba1\u4e86\u5b83\uff0c\u4f46\u5374\u6ca1\u6709\u591a\u5c11\u53d1\u8a00\u6743\u3002\u4f60\u95ee<\/span>AlphaGo\u7684\u8bbe\u8ba1\u5e08\uff0c\u4ed6\u4e5f\u4e0d\u89c1\u5f97\u80fd\u544a\u8bc9\u4f60<\/span>AlphaGo\u7a76\u7adf\u662f\u600e\u6837\u60f3\u51fa\u90a3\u4e9b\u5999\u62db\u7684\u3002<\/span><\/span><\/p>\n

\u6240\u8c13\u771f\u7a7a\u80fd\u591f\u751f\u5999\u6709\uff0c\u73b0\u4ee3\u7684\u4eba\u5de5\u667a\u80fd\u53d1\u5c55\u5386\u7a0b\u4eff\u4f5b\u6b63\u5728\u89c1\u8bc1\u4f5b\u6559\u4e2d\u7a7a\u7684\u667a\u6167\u3002<\/span><\/p>\n

<\/span>\"\u96c6\u667a\"
<\/p>\n

\u57c3\u820d\u5c14\u7684\u83ab\u6bd4\u4e4c\u65af\u5e26\uff0c\u524d\u666f\u548c\u80cc\u666f\u6b63\u5728\u878d\u5408\u4e0e\u4e92\u6362\uff0c\u54ea\u4e00\u4e2a\u66f4\u771f\u5b9e\uff1f<\/span><\/strong><\/p>\n

<\/span><\/p>\n

\u7136\u800c\uff0c\u83b7\u5f97\u7a7a\u7684\u667a\u6167\u6ca1\u6709\u90a3\u4e48\u7b80\u5355\u3002\u7279\u522b\u662f\uff0c\u6211\u4eec\u5e94\u8be5\u600e\u6837\u5b9e\u65bd\u7a7a\u5462\uff1f\u5f7b\u5e95\u7684\u7a7a\u4e0d\u5c31\u662f\u4ec0\u4e48\u90fd\u4e0d\u505a\u5417\uff1f\u65e2\u7136\u6211\u4eec\u4e0d\u80fd\u6839\u636e\u81ea\u5df1\u7684\u4e3b\u89c2\u81c6\u60f3\u6765\u6784\u5efa\u4eba\u5de5\u667a\u80fd\uff0c\u90a3\u4e48\uff0c\u6211\u4eec\u8fd8\u5236\u9020\u673a\u5668\u5e72\u4ec0\u4e48\uff1f\u8ba9\u6211\u4eec\u56de\u5230\u4eba\u7c7b\u7684\u86ee\u8352\u65f6\u4ee3\uff0c\u6210\u5929\u8863\u4e0d\u853d\u4f53\u3001\u8339\u6bdb\u996e\u8840\u4e0d\u5c31\u5b8c\u4e86\uff1f<\/span><\/p>\n

 <\/span><\/p>\n

\u5728\u4f5b\u6559\u4e2d\uff0c\u8fd9\u6837\u7684\u89c2\u70b9\u88ab\u79f0\u4e3a<\/span>\u201c\u65ad\u706d\u7a7a<\/span>\u201d\uff0c\u5373\u8ba4\u4e3a\u4e16\u754c\u4e2d\u4e00\u5207\u4e8b\u7269\u90fd\u4e0d\u5b58\u5728\uff0c\u6211\u4eec\u4e5f\u4e0d\u9700\u8981\u505a\u4efb\u4f55\u52aa\u529b\u3002\u7136\u800c\u8fd9\u5e76\u4e0d\u662f\u771f\u6b63\u7684\u7a7a\u3002<\/span><\/span><\/p>\n

 <\/span><\/p>\n

\u771f\u6b63\u7684\u7a7a\u5e76\u4e0d\u662f\u4ec0\u4e48\u90fd\u6ca1\u6709\uff0c\u800c\u662f\u5728\u4e07\u4e8b\u4e07\u7269\u4e4b\u4e0a\u53c8\u6709\u4e00\u4e2a\u66f4\u9ad8\u5c42\u6b21\u7684\u7a7a\u3002\u8fd9\u5c31\u597d\u50cf\u8ba1\u7b97\u673a\u7a0b\u5e8f\u4e0e\u6570\u636e\u7684\u5173\u7cfb\u3002\u6570\u636e\u5c31\u662f\u5177\u4f53\u7684\u6709\uff0c\u800c\u90a3\u4e2a\u80fd\u591f\u9a7e\u9a6d\u6570\u636e\u7684\u89c4\u5219\u6216\u7a0b\u5e8f\u624d\u662f\u771f\u6b63\u7684\u7a7a\u3002\u8fd9\u79cd\u7a7a\u5e76\u4e0d\u662f\u4ec0\u4e48\u90fd\u6ca1\u6709\uff0c\u800c\u662f\u4e00\u4e2a\u66f4\u9ad8\u5c42\u6b21\u7684\u5b58\u5728\uff0c\u9ad8\u5c42\u6b21\u4e00\u51fa\u73b0\uff0c\u6211\u4eec\u4e5f\u5c31\u4e0d\u9700\u8981\u5177\u4f53\u7684\u6709\u4e86\uff0c\u4e8e\u662f\u7a0b\u5e8f\u53ef\u4ee5\u751f\u6210\u65e0\u7a77\u591a\u4e2a\u6570\u636e\u3002\u4e3a\u4e86\u4f53\u4f1a\u8fd9\u79cd\u771f\u7a7a\u751f\u5999\u6709\u7684\u8fc7\u7a0b\uff0c\u8ba9\u6211\u4eec\u6765\u770b\u51e0\u4e2a\u4f8b\u5b50\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u6bd4\u5982\u6211\u4eec\u6709\u4e00\u5806\u6570\u5bf9\uff1a<\/span><\/p>\n

(1,3), (2,5), (5,7), (7,9),\u2026\u2026<\/span><\/p>\n

 <\/span><\/p>\n

\u90a3\u4e48\uff0c<\/span> \u8bf7\u95ee<\/span>11\u548c<\/span>111000\u5206\u522b\u5bf9\u5e94\u7684\u662f\u51e0\uff1f\u5f53\u7136\uff0c\u6211\u4eec\u5f88\u5bb9\u6613\u770b\u51fa\u6765\uff0c\u8fd9\u4e9b\u6570\u5bf9\u53ef\u4ee5\u7528\u8fd9\u6837\u4e00\u4e2a\u65b9\u7a0b\uff1a<\/span>x+2\uff0c\u6765\u6982\u62ec\u3002\u90a3\u4e48\uff0c\u8fd9\u4e9b\u6570\u5bf9\u5c31\u662f\u5177\u4f53\u7684\u6709\uff0c\u800c\u8fd9\u4e2a<\/span>x+2\u624d\u662f\u771f\u6b63\u7684\u7a7a\uff0c\u624d\u662f\u65e0\u3002\u6709\u4e86<\/span>x+2\u8fd9\u4e2a\u65e0\uff0c\u6211\u4eec\u4fbf\u5f88\u5bb9\u6613\u5f97\u5230<\/span>11\u5bf9\u5e94<\/span>13\uff0c<\/span>111000\u5bf9\u5e94<\/span>111002\u3002\u4e8e\u662f\u6211\u4eec\u7528\u7a7a\u5f97\u5230\u4e86\u65e0\u7a77\u4e2a\u6570\u5bf9\u3002<\/span><\/span><\/p>\n

 <\/span><\/p>\n

\u518d\u6bd4\u5982\uff0c\u5047\u5982\u7ed9\u4f60\u4e09\u7ec4\u6570\u5bf9\uff0c\u6392\u5217\u6210\u4e00\u4e2a\u8868\uff1a<\/span> <\/span><\/p>\n

 <\/span><\/p>\n

(1,2), (3,6), (4,8), (100,200), \u2026\u2026<\/span><\/p>\n

(3,9), (2,6), (8,24), (100,300), \u2026\u2026 <\/span><\/p>\n

(1,4), (2,8), (3,12), (100,400), \u2026\u2026 <\/span><\/p>\n

\u2026\u2026<\/span><\/p>\n

\u90a3\u4e48\u6211\u95ee\u4f60\u5728\u7b2c<\/span>6\u884c\u4e0a\uff0c<\/span>3\u8fd9\u4e2a\u6570\u5b57\u5bf9\u5e94\u7684\u662f\u591a\u5c11\uff1f\u8981\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u9700\u8981\u5bfb\u627e\u89c4\u5f8b\u3002\u6211\u4eec\u5148\u8981\u627e\u51fa\u7b2c\u4e00\u884c\u7684\u89c4\u5f8b\u662f<\/span>2x\u6ca1\u6709\u7591\u95ee\uff0c\u7b2c\u4e8c\u884c\u5462\uff1f\u662f<\/span>3x\uff0c\u7b2c\u4e09\u884c\u662f<\/span>4x\uff0c\u90a3\u4e48\u7b2c<\/span>6\u884c\u5c31\u5e94\u8be5\u662f<\/span>7x\u4e86\uff0c\u56e0\u800c\u5728\u7b2c<\/span>6\u884c\u4e0a<\/span>3\u5e94\u8be5\u5bf9\u5e94\u7684\u662f<\/span>21\u4e86\uff01<\/span><\/span><\/p>\n

 <\/span><\/p>\n

\u8fd9\u91cc\u8ddf\u524d\u9762\u4f8b\u5b50\u4e0d\u592a\u4e00\u6837\u7684\u662f\uff0c\u867d\u7136\u6211\u4eec\u5f97\u5230\u4e86\u6bcf\u4e00\u884c\u7684\u89c4\u5219\u6bd4\u5982\u7b2c\u4e00\u884c\u7684<\/span>2x\uff0c\u4f46\u662f\u968f\u7740\u884c\u6570\u7684\u589e\u52a0\uff0c\u8fd9\u4e2a\u89c4\u5219\u672c\u8eab\u4e5f\u53d8\u5316\u4e86\uff0c\u56e0\u800c\u7b2c<\/span>2\u884c\u662f<\/span>3x\uff0c\u7b2c<\/span>3\u884c\u662f<\/span>4x\u7b49\u7b49\uff0c\u6240\u4ee5\u6211\u4eec\u53c8\u5f97\u5230\u4e86\u4e00\u6761\u89c4\u5219\u7684\u89c4\u5219\uff0c\u5373\u5982\u679c\u884c\u6570\u662f<\/span>n\u7684\u8bdd\uff0c\u90a3\u4e48\u8fd9\u4e00\u884c\u7684\u89c4\u5219\u5c31\u662f<\/span>(n+1)x\u3002\u6211\u4eec\u663e\u7136\u80fd\u591f\u6839\u636e\u8f93\u5165\u7684<\/span>n\u548c<\/span>x\u8ba1\u7b97\u51fa\u76f8\u5e94\u7684\u6570\u503c\u3002<\/span><\/span><\/p>\n

 <\/span><\/p>\n

\u5230\u8fd9\u91cc\uff0c\u6211\u4eec\u53c8\u7a7a\u4e86\u4e00\u5c42\uff0c\u6211\u4eec\u7528\u4e24\u4e2a\u7a7a\uff08\u4e00\u4e2a\u662fn\uff0c\u4e00\u4e2a\u662fx\uff09\u4e0d\u4ec5\u5f97\u5230\u4e86\u65e0\u7a77\u7684\u6570\u5bf9\uff0c\u800c\u4e14\u5f97\u5230\u4e86\u65e0\u7a77\u4e2a\u5e8f\u5217\u3002\u5f53\u7136\uff0c\u4f9d\u7167\u6b64\u6cd5\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u7ee7\u7eed\u7a7a\u4e0b\u53bb\uff0c\u6211\u4eec\u4e0d\u4ec5\u53ef\u4ee5\u5f97\u5230\u89c4\u5219\uff0c\u8fd8\u53ef\u4ee5\u5f97\u5230\u89c4\u5219\u7684\u89c4\u5219\u5373\u5143\u89c4\u5219\uff0c\u751a\u81f3\u5143\u5143\u89c4\u5219\u2026\u2026<\/span><\/p>\n

 <\/span><\/p>\n

\u8bb0\u5f97\u91d1\u5927\u4fa0\u5728\u4ed6\u7684\u6b66\u4fa0\u5c0f\u8bf4\uff1a\u300a\u501a\u5929\u5c60\u9f99\u8bb0\u300b\u4e2d\u66fe\u8bb2\u8ff0\u4e86\u8fd9\u6837\u4e00\u6bb5\u6545\u4e8b\uff1a\u6b66\u6797\u6cf0\u6597\u5f20\u4e09\u4e30\u5728\u60c5\u6025\u4e4b\u4e0b\u8981\u628a\u4ed6\u65b0\u521b\u7684\u6b66\u529f<\/span>\u201c\u592a\u6781\u62f3<\/span>\u201d\u4f20\u6388\u7ed9\u65b0\u8d77\u4e4b\u79c0\u5f20\u65e0\u5fcc\u3002\u5f20\u65e0\u5fcc\u9664\u4e86\u6709\u4e00\u8eab\u7cbe\u6e5b\u7684<\/span>\u201c\u5185\u529f\u4fee\u4e3a<\/span>\u201d\u4ee5\u5916\u8fd8\u5bf9\u6b66\u5b66\u5177\u6709\u6781\u9ad8\u7684\u609f\u6027\u3002\u56e0\u800c\u5f53\u5f20\u4e09\u4e30\u7ed9\u4ed6\u6253\u8fc7\u4e00\u8d9f\u592a\u6781\u62f3\u4ee5\u540e\uff0c\u4ed6\u5c31\u628a\u6240\u6709\u7684\u62db\u5f0f\u5168\u90e8\u8bb0\u4e0b\u6765\u4e86\u5e76\u4e14\u5f53\u573a\u628a\u6240\u5b66\u7684\u592a\u6781\u62f3\u91cd\u65b0\u518d\u6253\u7ed9\u5f20\u4e09\u4e30\u770b\u3002\u5728\u5f20\u65e0\u5fcc\u7ec3\u62f3\u7684\u8fc7\u7a0b\u4e2d\uff0c\u5f20\u4e09\u4e30\u53cd\u590d\u95ee\u4ed6\u4e00\u4e2a\u95ee\u9898\uff1a<\/span>\u201c\u4f60\u5df2\u7ecf\u5fd8\u6389\u51e0\u62db\u4e86\uff1f<\/span>\u201d\u3002\u4ed6\u7684\u56de\u7b54\u4ee4\u5176\u4ed6\u4eba\u5f02\u5e38\u4e0d\u89e3\uff0c\u56e0\u4e3a\u4ed6\u8d8a\u5728\u90a3\u91cc\u63e3\u6469\u592a\u6781\u62f3\u7684\u5965\u79d8\uff0c\u5fd8\u8bb0\u7684\u62db\u6570\u4e5f\u8d8a\u6765\u8d8a\u591a\u3002\u65c1\u8fb9\u7684\u4eba\u4e0d\u660e\u767d\uff0c\u8fd9\u6837\u7684\u5b66\u6cd5\u5fd8\u7684\u8fd9\u4e48\u5feb\uff0c\u600e\u4e48\u53ef\u80fd\u5b66\u4f1a\u6b66\u529f\u5462\uff1f\u7136\u800c\uff0c\u6ca1\u8fc7\u591a\u957f\u65f6\u95f4\uff0c\u5f20\u65e0\u5fcc\u8bf4\u5df2\u7ecf\u5fd8\u6389\u4e86\u6240\u6709\u7684\u62db\u5f0f\u3002\u5f20\u4e09\u4e30\u7b11\u7740\u8bf4\uff1a<\/span>\u201c\u4e0d\u9519\uff0c\u4f60\u7ec8\u4e8e\u5b66\u4f1a\u4e86<\/span>\u2018\u592a\u6781\u62f3<\/span>\u2019\u201d\u3002<\/span><\/span>\"\u96c6\u667a\"<\/p>\n

\u592a\u6781\u9c7c\u56fe<\/span><\/strong><\/p>\n

<\/span><\/p>\n

\u5982\u4f55\u83b7\u5f97\u7a7a\u5462\uff1f\u7b54\u6848\u5c31\u5728\u4e8e\u201c\u5f52\u7eb3\u201d\u4e8c\u5b57\u3002\u5176\u5b9e\uff0c\u673a\u5668\u5b66\u4e60\u6b63\u662f\u8fd0\u7528\u4e86\u592a\u6781\u62f3\u4e2d\u7684\u5f52\u7eb3\u667a\u6167\uff0c\u56e0\u4e3a\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u6b63\u5728\u4ece\u5927\u91cf\u6570\u636e\u4e2d\u7684\u5177\u4f53\u62db\u5f0f\u4e0d\u65ad\u5f52\u7eb3\u51fa\u7c7b\u4f3c\u4e8e(n+1)x\u8fd9\u6837\u7684\u89c4\u5219\u51fa\u6765\u3002\u4eba\u5de5\u667a\u80fd\u7684\u7ec8\u6781\u76ee\u6807\u5c31\u662f\u8981\u5236\u9020\u51fa\u8fd9\u6837\u4e00\u53f0\u901a\u7528\u7684\u5f52\u7eb3\u673a\u5668\uff0c\u5b83\u80fd\u591f\u5728\u4e0d\u9700\u8981\u4efb\u4f55\u5148\u9a8c\u89c4\u5219\u7684\u60c5\u51b5\u4e0b\u81ea\u52a8\u4ece\u4e0e\u73af\u5883\u7684\u4e92\u52a8\u4e2d\u5f52\u7eb3\u51fa\u6240\u6709\u7684\u89c4\u5f8b\uff0c\u8fd9\u624d\u662f\u7a7a\u7684\u6700\u9ad8\u5883\u754c\u3002<\/span><\/p>\n


<\/span><\/strong><\/p>\n


<\/span><\/strong><\/p>\n

\u89c9\u609f\u5427\uff0c\u673a\u5668<\/span><\/strong><\/span><\/p>\n


<\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u96c6\u667a\u4ff1\u4e50\u90e8\u8d60\u4e66\u4eea\u5f0f<\/span><\/strong><\/p>\n

<\/span><\/p>\n

\u8ba8\u8bba\u5b8c\u6bd5\uff0c\u6211\u4eec\u6765\u5230\u4e86\u523b\u6709\u201c\u89c2\u81ea\u5728\u201d\u4e09\u5b57\u524d\u9762\u7684\u5bbd\u9614\u9732\u53f0\u4e0a\uff0c\u8fd9\u662f\u4e00\u4e2a\u5c0f\u5c0f\u7684\u8d60\u4e66\u4eea\u5f0f\uff0c\u96c6\u667a\u4ff1\u4e50\u90e8\u4e3a\u9f99\u6cc9\u5bfa\u8d60\u9001\u4e86\u51e0\u672c\u6709\u5173\u4eba\u5de5\u667a\u80fd\u7684\u79d1\u666e\u8bfb\u7269\u3002\u8fd9\u65f6\uff0c\u6211\u4e0e\u609f\u5149\u6cd5\u5e08\u5171\u540c\u6367\u8d77\u4e86\u90a3\u672c\u5f71\u54cd\u4e86\u6211\u4e00\u751f\u7684\u4e66\uff1a\u300a\u54e5\u5fb7\u5c14\u3001\u57c3\u820d\u5c14\u3001\u5df4\u8d6b\u2014\u2014\u96c6\u5f02\u74a7\u4e4b\u5927\u6210\u300b\uff08Godel, Escher, Bach: An Enternal Golden Braid, \u7b80\u79f0GEB\uff09\u2026\u2026<\/span>\"\u96c6\u667a\"<\/p>\n

\u300a\u54e5\u5fb7\u5c14\u3001\u57c3\u820d\u5c14\u3001\u5df4\u8d6b\u2014\u2014\u96c6\u5f02\u74a7\u4e4b\u5927\u6210\u300b<\/span><\/strong><\/span><\/p>\n

\u6211\u8fd8\u8bb0\u5f97\uff0c<\/span>13\u5e74\u524d\uff0c\u5f53\u6211\u7b2c\u4e00\u6b21\u6367\u8d77\u8fd9\u672c\u4e66\u65f6\u7684\u77db\u76fe\u5fc3\u7406\uff1a\u8fd9\u662f\u4ec0\u4e48\u9b3c\uff1f\u4e00\u4f1a\u8ba8\u8bba\u8d4b\u683c\u3001\u5361\u519c\uff0c\u4e00\u4f1a\u53c8\u662f\u54e5\u5fb7\u5c14\u5b9a\u7406\uff0c\u800c\u4e14\u53c8\u81ed\u53c8\u957f\uff0c\u7adf\u7136<\/span>1000\u591a\u9875<\/span>\u2026\u2026\u3002\u7136\u800c\uff0c\u5f53\u6211\u8bfb\u5230\u4e86\u4e4c\u9f9f\u4e0e\u963f\u57fa\u91cc\u65af\u7684\u7b2c\u4e00\u4e2a\u5bf9\u8bdd\uff0c<\/span>\u201c\u829d\u8bfa\u6096\u8bba<\/span>\u201d\u8fd9\u4e2a\u5343\u53e4\u96be\u9898\u5c31\u628a\u6211\u62c9\u8fdb\u4e86\u4e66\u4e2d\uff0c\u4ece\u6b64\u4e00\u53d1\u4e0d\u53ef\u6536\u62fe<\/span>\u2026\u2026<\/span><\/p>\n

\u6211\u8fd8\u8bb0\u5f97\uff0c\u90a3\u5929\u665a\u4e0a\uff0c\u6211\u7b2c\u4e00\u6b21\u5c06\u5bb6\u91cc\u7684\u6444\u50cf\u673a\u63a5\u5230\u4e86\u7535\u89c6\u673a\u4e0a\u9a8c\u8bc1\u89c6\u9891\u53cd\u9988\u5b9e\u9a8c\uff0c\u770b\u5230\u4e86\u90a3\u4e9b\u7206\u70b8\u7684\u661f\u7cfb\u4e0e\u98de\u821e\u800c\u51fa\u7684\u5c9b\u5c7f\uff0c\u6211\u88ab\u81ea\u5df1\u4eb2\u81ea\u89c1\u8bc1\u5230\u7684\u8fd9\u4e2a<\/span>\u201c\u65e0\u4e2d\u751f\u6709<\/span>\u201d\u7684\u73b0\u8c61\u800c\u9707\u60ca\u4e86\u3002\u6211\u4e00\u4e2a\u4eba\u6765\u5230\u4e86\u5c0f\u6cb3\u65c1\uff0c\u611f\u53f9\u7740\u5b87\u5b99\u4f55\u5c1d\u4e0d\u662f\u4e00\u4e2a\u81ea\u5df1\u62cd\u6444\u81ea\u5df1\u7684\u6444\u50cf\u673a\uff1f<\/span>\u2026\u2026<\/span>\"\u96c6\u667a\"<\/p>\n

\u6444\u50cf\u673a\u63a5\u5230\u7535\u89c6\u673a\u4e0a\u9a8c\u8bc1\u89c6\u9891\u53cd\u9988\u5b9e\u9a8c<\/span><\/strong><\/span><\/p>\n

<\/span><\/p>\n

\u6211\u8fd8\u8bb0\u5f97\uff0c\u4e3a\u4e86\u89c1\u8bc1\u4e66\u4e2d\u6240\u63d0\u5230\u7684\u8682\u8681\u7fa4\u4f53\u667a\u6167\uff0c\u6211\u5df2\u7ecf\u7a9d\u5728\u5bbf\u820d\u91cc\u6574\u6574\u4e00\u4e2a\u6708\u4e86\uff0c\u4e3a\u4e86\u8c03\u901a\u90a3\u4e2a\u201c\u8681\u8ff9\u5bfb\u8e2a\u201d\u7684\u5c0f\u7a0b\u5e8f\u3002<\/span><\/p>\n

\u8fd9\u672c\u4e66\u6b63\u5728\u53cd\u590d\u5f3a\u8c03\u4e00\u70b9\uff1a\u8981\u60f3\u8d4b\u4e88\u673a\u5668\u667a\u6167\uff0c\u5c31\u5fc5\u987b\u8ba9\u673a\u5668\u5177\u5907\u81ea\u6211\u89c9\u5bdf\u80fd\u529b\uff0c\u5373\u602a\u5708\u3002<\/span><\/p>\n

\u6ca1\u9519\uff0c\u6b63\u662f\u8fd9\u4e2a\u602a\u5708\uff0c\u4ee4\u6211\u4eec\u4eba\u7c7b\u7684\u903b\u8f91\u548c\u8bed\u8a00\u5b58\u5728\u4e86\u4e0d\u53ef\u907f\u514d\u7684\u7455\u75b5\uff1a<\/span><\/p>\n

\n

\u8fd9\u53e5\u8bdd\u662f\u9519\u7684<\/span><\/strong><\/p>\n<\/blockquote>\n

\u5373\u6096\u8bba\u3002\u8fd9\u79cd\u65e2\u5bf9\u53c8\u9519\uff0c\u65e2\u4e0d\u5bf9\u53c8\u4e0d\u9519\u7684\u81ea\u7136\u8bed\u8a00\u5c06\u6c38\u8fdc\u6784\u6210\u7f20\u7ed5\u6211\u4eec\u610f\u8bc6\u7684\u68a6\u9b47\u3002\u7136\u800c\uff0c\u6b63\u662f\u8fd9\u4e2a\u602a\u5708\u8ba9\u4e0d\u673d\u7684\u6570\u5b66\u5bb6\u54e5\u5fb7\u5c14\u8bc1\u660e\u4e86\u54e5\u5fb7\u5c14\u4e0d\u5b8c\u5907\u6027\u5b9a\u7406\uff1b\u8ba9\u56fe\u7075\u6307\u8ba4\u51fa\u4e86\u673a\u5668\u6240\u4e0d\u53ef\u80fd\u89e3\u51b3\u7684\u505c\u673a\u95ee\u9898\u3002<\/span><\/p>\n

\u300aGEB\u300b\u7684\u4f5c\u8005\u5927\u58f0\u75be\u547c\uff0c\u602a\u5708\u751a\u81f3\u5f88\u53ef\u80fd\u662f\u6784\u9020\u751f\u547d\u4e43\u81f3\u667a\u6167\u7684\u91cd\u8981\u57fa\u77f3\uff01\u6bd4\u5982\uff0c\u751f\u547d\u7684\u65b0\u9648\u4ee3\u8c22\u5c31\u662f\u8981\u6784\u6210\u5982\u57c3\u820d\u5c14\u7684\u201c\u753b\u624b\u201d\u6240\u8868\u8ff0\u7684\u8fd9\u79cd\u201c\u81ea\u6211\u521b\u9020\u201d\u7684\u602a\u5708\u3002<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u57c3\u820d\u5c14\u7684\u300a\u753b\u624b\u300b\u63cf\u8ff0\u4e86\u4e24\u4e2a\u4e92\u76f8\u521b\u5efa\u7684\u624b<\/span><\/strong><\/span><\/p>\n

\u800c\u751f\u547d\u7684\u81ea\u6211\u7e41\u6b96\u5219\u662f\u5229\u7528\u590d\u6742\u7684\u5316\u5b66\u53cd\u5e94\u5b9e\u73b0\u4e86\u4e00\u4e2a\u300c\u84af\u6069\u300d\uff0c\u5373\u5f62\u5982\u4e0b\u5217\u5f62\u5f0f\u7684\u5947\u602a\u8bed\u53e5\uff1a<\/span><\/p>\n

\n

\u201c\u653e\u5728\u5f15\u6587\u540e\u9762\u5f97\u5230\u4e00\u4e2a\u53e5\u5b50\u201d\u653e\u5728\u5f15\u6587\u540e\u9762\u5f97\u5230\u4e00\u4e2a\u53e5\u5b50<\/span><\/em><\/strong><\/span><\/span><\/p>\n<\/blockquote>\n

\u800c\u6211\u4eec\u7684\u610f\u8bc6\u4e5f\u6b63\u50cf\u57c3\u820d\u5c14\u7684\u540d\u753b\u300a\u753b\u5eca\u300b\u6240\u63cf\u8ff0\u7684\u90a3\u6837\uff1a<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u57c3\u820d\u5c14\u7684\u300a\u753b\u5eca\u300b\u63cf\u8ff0\u4e86\u4e00\u4e2a\u81ea\u6211\u5305\u542b\u7684\u4e16\u754c\uff0c\u5c0f\u4f19\u5b50\u6b63\u5728\u81ea\u5df1\u770b\u7684\u753b\u4e2d<\/span><\/strong><\/span><\/p>\n

<\/span><\/p>\n

\u5728\u4f5b\u6559\u4e2d\u6709\u5f88\u591a\u81ea\u6211\u89c2\u60f3\u7684\u6cd5\u95e8\u5c31\u662f\u8981\u8bad\u7ec3\u6bcf\u4e2a\u4eba\u7684\u81ea\u6211\u89c2\u5bdf\u80fd\u529b\u3002\u53cd\u8fc7\u6765\uff0c\u4e5f\u8bb8\u6211\u4eec\u4e5f\u8981\u8bad\u7ec3\u673a\u5668\u5177\u5907\u8fd9\u6837\u7684\u81ea\u6211\u89c2\u5bdf\u3001\u81ea\u6211\u6307\u6d89\uff08self-reference\uff09\u7684\u80fd\u529b\u3002\u4e5f\u8bb8\u8fd9\u5c31\u662f\u5c5e\u4e8e\u4eba\u5de5\u667a\u80fd\u7684\u822c\u82e5\u667a\u6167\u2026\u2026<\/span><\/p>\n


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<\/span><\/p>\n

\u5c3e\u58f0<\/span><\/strong><\/span><\/p>\n


<\/span><\/strong><\/span><\/p>\n

\u6211\u4e00\u76f4\u975e\u5e38\u597d\u5947\uff0c\u4f5b\u6559\u4eba\u58eb\u662f\u5982\u4f55\u770b\u5f85\u602a\u5708\u8fd9\u4e2a\u95ee\u9898\u7684\uff0c\u4e8e\u662f\u5c31\u6709\u4e86\u548c\u609f\u5149\u6cd5\u5e08\u5982\u4e0b\u8fd9\u6bb5\u5bf9\u8bdd\uff1a<\/span>\"\u96c6\u667a\"<\/p>\n

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<\/span><\/strong><\/span><\/p>\n

\u63a2\u7d22\u4e4b\u65c5\u8bf7\u7ee7\u7eed<\/span><\/strong><\/span><\/p>\n


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