{"id":22539,"date":"2024-01-19T14:09:28","date_gmt":"2024-01-19T06:09:28","guid":{"rendered":"https:\/\/www.wukongsch.com\/blog\/?p=22539"},"modified":"2025-06-16T17:17:15","modified_gmt":"2025-06-16T09:17:15","slug":"amc-12-noledge-points","status":"publish","type":"post","link":"https:\/\/www.wukongsch.com\/blog\/zh\/amc-12-noledge-points-post-22539\/","title":{"rendered":"AMC 12\u8d85\u5168\u77e5\u8bc6\u70b9\u6c47\u603b\u30102025\u66f4\u65b0\u3011"},"content":{"rendered":"
<\/div>\n

AMC 12<\/strong>\uff08American Mathematics Competition\uff09\u753112\u5e74\u7ea7\u53ca12\u5e74\u7ea7\u4ee5\u4e0b\u5b66\u751f\u53c2\u52a0\uff0c\u53c2\u52a0AMC12\u8003\u8bd5\u7684\u5f53\u5929\u5e74\u9f84\u9700\u5c0f\u4e8e19.5\u5c81\u3002\u8fbe\u5230\u5206\u6570\u7ebf\u7684\u8003\u751f\u4f1a\u83b7\u5f97\u8363\u8a89\u8bc1\u4e66\uff0c\u5e76\u53d7\u9080\u53c2\u52a0\u7f8e\u56fd\u6570\u5b66\u9080\u8bf7\u8d5b\uff08AIME\uff09\uff0c\u6bcf\u5e74\u5206\u6570\u7ebf\u4f1a\u6839\u636e\u6574\u4f53\u60c5\u51b5\u6709\u6240\u8c03\u6574\u3002<\/p>\n\n\n\n

\u90a3\u4e48\uff0cAMC\u7684\u8003\u70b9\u6709\u54ea\u4e9b\uff1f\u80fd\u4ece\u54ea\u4e9b\u65b9\u9762\u4e0b\u624b\u5907\u8003\u5462\uff1f\u5feb\u8ddf\u5c0f\u609f\u7a7a\u4e00\u8d77\u770b\u770b\u5427\uff01<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

<\/span>\u4e00\u3001AMC 12\u8003\u70b9\u6709\u54ea\u4e9b\uff1f<\/strong><\/span><\/h2>\n\n\n\n

AMC10\u4e0eAMC12\u7684\u5dee\u5f02<\/strong><\/p>\n

\r\n
\r\n
<\/div>\r\n

\u609f\u7a7a\u56fd\u9645\u6570\u5b66
\n\u8ba9\u6570\u5b66\u4e4b\u5149\u7167\u4eae\u6bcf\u4e00\u4e2a\u5b69\u5b50\uff01<\/span><\/p>\n<\/h3>\r\n

\u9002\u5408\u5168\u74031-12\u5e74\u7ea7\u5b66\u751f<\/p>\r\n \r\n \u7acb\u5373\u514d\u8d39\u8bd5\u542c\r\n <\/a>\r\n <\/div>\r\n

<\/div>\r\n<\/div>\n\n\n

AMC12\u7684\u5927\u90e8\u5206\u8003\u70b9\u90fd\u662f\u4e0eAMC10\u4e00\u81f4\u7684\uff0c\u6574\u4efd\u8bd5\u5377\u4e2d\u4e5f\u4f1a\u670910\u9898\u5de6\u53f3\u662f\u5b8c\u5168\u76f8\u540c\u7684\u3002\u5dee\u5f02\u5728\u4e8e\uff0c\u4ee3\u6570\u6a21\u5757\u591a\u4e86\u5927\u91cf\u7684\u77e5\u8bc6\u70b9\uff0c\u8fd9\u4e9b\u77e5\u8bc6\u70b9\u57fa\u672c\u662f\u9ad8\u4e2d\u8bfe\u5185\u5185\u5bb9\uff1b\u6b64\u5916\u5728\u51e0\u4f55\u3001\u6570\u8bba\u3001\u7ec4\u5408\u6a21\u5757\u5404\u591a\u4e86\u5c11\u91cf\u7684\u77e5\u8bc6\u70b9\uff0c\u8fd9\u4e9b\u77e5\u8bc6\u70b9\u5927\u591a\u6bd4\u8f83\u590d\u6742\uff0c\u4e00\u822c\u51fa\u73b0\u5728\u540e10\u9898\u4e2d\uff0c\u638c\u63e1\u8fd9\u4e9b\u77e5\u8bc6\u70b9\u662f\u51b2\u51fb\u9ad8\u5206\u7684\u5173\u952e\u3002<\/p>\n\n\n\n

AMC12\u6db5\u76d6\u4e86AMC10\u7684\u6240\u6709\u77e5\u8bc6\u70b9\u4e4b\u5916\u8fd8\u5305\u62ec\u4e09\u89d2\u5b66\u3001\u9ad8\u7ea7\u4ee3\u6570\u548c\u9ad8\u7ea7\u51e0\u4f55\u5b66\uff0c\u4f46\u4e0d\u5305\u62ec\u5fae\u79ef\u5206\u3002<\/strong><\/p>\n\n\n\n

AMC12\u8003\u70b9<\/strong><\/p>\n\n\n\n

1\u3001\u4ee3\u6570<\/p>\n\n\n\n

\u672c\u90e8\u5206\u4e3b\u8981\u8003\u5bdf\uff1a\u5404\u79cd\u56e0\u5f0f\u5206\u89e3\u7684\u65b9\u6cd5\u53ca\u5176\u5e7f\u6cdb\u7684\u5e94\u7528\u3001\u6307\u6570\u8fd0\u7b97\u7684\u57fa\u672c\u6cd5\u5219\u53ca\u89e3\u65b9\u7a0b\u3001\u9ad8\u4e2d\u9636\u6bb5\u4ee3\u6570\u77e5\u8bc6\u3001\u4e0d\u7b49\u5f0f\u7406\u8bba\u3001\u591a\u9879\u5f0f\u7406\u8bba\u548c\u4e8c\u9879\u5f0f\u5b9a\u7406\u3002<\/p>\n\n\n\n

2\u3001\u5e73\u9762\u51e0\u4f55<\/p>\n\n\n\n

\u672c\u90e8\u5206\u4e3b\u8981\u8003\u5bdf\uff1a\u7b49\u8170\uff0c\u7b49\u8fb9\u548c\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u8ba1\u7b97\u3001\u7279\u6b8a\u89d2\u7684\u57fa\u672c\u4e09\u89d2\u51fd\u6570\u8ba1\u7b97\u3001\u76f8\u4f3c\u56fe\u5f62\u7684\u5224\u522b\u548c\u5468\u957f\u4e0e\u9762\u79ef\u7684\u8ba1\u7b97\u3001\u521d\u4e2d\u51e0\u4f55\u7684\u76f8\u5173\u7ed3\u8bba\u548c\u8bc1\u660e\u3001\u5185\u63a5\u5706\u3001\u5916\u5207\u56fe\u5f62\u7684\u7ed3\u8bba\u3002<\/p>\n\n\n\n

3\u3001\u6570\u8bba<\/p>\n\n\n\n

\u672c\u90e8\u5206\u4e3b\u8981\u8003\u5bdf\uff1a\u6574\u9664\u7406\u8bba\u3001\u540c\u4f59\u7406\u8bba\u3001\u8d39\u5c14\u9a6c\u5c0f\u5b9a\u7406\u548c\u7b97\u672f\u57fa\u672c\u5b9a\u7406\u7b49\u3001\u6570\u8bba\u8bc1\u660e\u3001\u4e86\u89e3Diophantineequations\u7684\u7c7b\u578b\u4ee5\u53ca\u4e0e\u6574\u9664\u7406\u8bba\u7684\u5173\u7cfb\u3001\u638c\u63e1\u7ebf\u6027Diophantineequations\u7684\u539f\u7406\uff0c\u89e3\u6cd5\u53ca\u5e94\u7528\u3002<\/p>\n\n\n\n

4\u3001\u6392\u5217\u7ec4\u5408<\/p>\n\n\n\n

\u672c\u90e8\u5206\u4e3b\u8981\u8003\u5bdf\uff1a\u8ba1\u6570\u539f\u7406\u3001\u638c\u63e1\u6392\u5217\u7ec4\u5408\u539f\u7406\u548c\u8ba1\u7b97\u3001Exclusion\u2013inclusionprinciple\u3001pigeon-holeprinciple\u89e3\u51b3\u5b9e\u9645\u95ee\u9898\u3001\u7ec4\u5408\u95ee\u9898\u7684\u5b9e\u9645\u5e94\u7528\u3001\u7edf\u8ba1\u521d\u6b65\uff1a\u5e73\u5747\u6570\uff0c\u4f17\u6570\uff0c\u4e2d\u4f4d\u6570\u53ca\u52a0\u6743\u5e73\u5747\u6570\u7684\u8ba1\u7b97\u3002<\/p>\n\n\n\n

5\u3001\u4e09\u89d2\u51fd\u6570<\/p>\n\n\n\n

\u672c\u90e8\u5206\u4e3b\u8981\u8003\u5bdf\uff1a\u4e09\u89d2\u57fa\u7840\u77e5\u8bc6\u548c\u516c\u5f0f\u3001\u4e09\u89d2\u51fd\u6570\u7684\u8ba1\u7b97\u548c\u5316\u7b80\u3001\u4e09\u89d2\u51fd\u6570\u7684\u7efc\u5408\u5e94\u7528\u3001\u638c\u63e1\u4e09\u89d2\u51fd\u6570\u548c\u4e09\u89d2\u65b9\u7a0b\u7684\u5b66\u672f\u6d3b\u52a8\u9898\u89e3\u6cd5\u3002<\/p>\n\n\n\n

6\u3001\u6570\u5217\u548c\u7ea7\u6570<\/p>\n\n\n\n

\u672c\u90e8\u5206\u4e3b\u8981\u8003\u5bdf\uff1a\u7b49\u5dee\u7b49\u6bd4\u6570\u5217\u89e3\u6cd5\u3001\u590d\u6742\u7684\u7b49\u5dee\u6570\u5217\u4e0e\u7b49\u6bd4\u6570\u5217\u7684\u5e94\u7528\u3001\u5b66\u4e60\u89e3\u7279\u6b8a\u6570\u5217\u548c\u7ea7\u6570\u7684\u76f8\u5173\u6280\u5de7\u3001\u4e09\u89d2\u3001\u4ee3\u6570\u548c\u7ec4\u5408\u76f8\u7ed3\u5408\u7684\u5b66\u672f\u6d3b\u52a8\u9898\u89e3\u6cd5\u3002<\/p>\n\n\n\n

7\u3001\u590d\u6570\u548c\u56fe\u8bba<\/p>\n\n\n\n

\u672c\u90e8\u5206\u4e3b\u8981\u8003\u5bdf\uff1a\u590d\u4e60\u590d\u6570\u77e5\u8bc6\u548c\u8bcd\u6c47\uff0c\u5b66\u4e60\u521d\u6b65\u56fe\u8bba\u3001\u8ba1\u6570\u548c\u7ec4\u5408\u7684\u8054\u7cfb\u3001\u91cd\u70b9\u8054\u7cfb\u4e0a\u8ff0\u4e0e\u5176\u4ed6\u77e5\u8bc6\u7684\u7efc\u5408\u9898\u7684\u89e3\u6cd5\u3002<\/p>\n\n\n\n

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

<\/span>\u4e8c\u3001AMC12 \u8003\u8bd5\u65f6\u95f4\u5206\u914d\u8868<\/span><\/h2>\n\n\n\n
\"\"<\/figure>\n\n\n\n

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

<\/span>\u4e09\u3001\u7b54\u9898\u516c\u5f0f\u4e0e\u53e3\u8bc0\uff08\u90e8\u5206\uff09<\/span><\/h2>\n\n\n\n

\u5f00\u5934\u6211\u4eec\u5c31\u8bf4\u4e86\uff0c\u5b66\u4f1a\u4e86\u77e5\u8bc6\u70b9\u8fd8\u4e0d\u591f\uff0c\u8fd8\u8981\u5b66\u4f1a\u7075\u6d3b\u8fd0\u7528\uff01\u54ea\u91cc\u80fd\u4f53\u73b0\u7075\u6d3b\u8fd0\u7528\uff0c\u90a3\u5c31\u662f\u5145\u5206\u4e86\u89e3\u3010\u5fc5\u8003\u9898\u578b\u3011<\/strong>\uff0c\u5c06\u77e5\u8bc6\u70b9\u4e0e\u9898\u8fdb\u884c\u7684\u5b8c\u7f8e\u7ed3\u5408\u3002\u8fd9\u65f6\u5019\u4e0e\u5927\u5bb6\u5206\u4eab\u51e0\u4e2a\u5173\u4e8e\u9898\u578b\u7684\u53e3\u8bc0\uff1a<\/p>\n\n\n\n

\u2460\u5728\u5e94\u7528\u9898\u3001\u51e0\u4f55\u9898\u3001\u6570\u5217\u9898\u3001\u51fd\u6570\u9898\u4e2d\uff0c\u5982\u679c\u9898\u76ee\u4e2d\u7684\u53d8\u91cf\u90fd\u662f\u6574\u6570\u65f6\uff0c\u5f88\u6709\u53ef\u80fd\u662f\u6570\u8bba\u9898\u3002<\/p>\n\n\n\n

\u89e3\u51b3\u65b9\u6848\uff1a\u9700\u8981\u7528\u5230\u6570\u8bba\u76f8\u5173\u77e5\u8bc6\uff0c\u4f8b\u5982\u5206\u6790\u56e0\u5b50\u548c\u500d\u6570\u5173\u7cfb\u6216\u8005\u5217\u51fa\u6574\u6570\u65b9\u7a0b\u518d\u6c42\u89e3\u3002<\/p>\n\n\n\n

\u2461\u6982\u7387\u7c7b\u9898\u76ee\u8981\u641e\u6e05\u695a\u662f\u5426\u4e3a\u51e0\u4f55\u578b\u6982\u7387\uff0c\u662f\u5426\u662f\u65e0\u7a77\u72b6\u6001\u7c7b\u95ee\u9898\uff0c\u662f\u5426\u662fequally likely outcome\u578b\u6982\u7387\uff0c\u7136\u540e\u518d\u9009\u62e9\u5bf9\u5e94\u7684\u65b9\u6cd5\u3002<\/p>\n\n\n\n

\u2462\u4e24\u4eba\u6e38\u620f\u7c7b\u95ee\u9898\uff0c\u7b80\u5355\u60c5\u51b5\u53ef\u4ee5\u76f4\u63a5\u679a\u4e3e\u8fdb\u884c\u8ba8\u8bba\uff1b\u590d\u6742\u60c5\u51b5\u53ef\u4ee5\u5148\u7528\u914d\u5bf9\u548c\u955c\u50cf\u7684\u65b9\u6cd5\u8fdb\u884c\u5c1d\u8bd5\uff0c\u82e5\u4e0d\u884c\u518d\u4ece\u7b80\u5355\u7684\u521d\u59cb\u6761\u4ef6\u51fa\u53d1\uff0c\u5bfb\u627ewinning position\u548closing position\uff0c\u5e76\u627e\u51fa\u4e00\u822c\u89c4\u5f8b\u3002<\/p>\n\n\n\n

\u2463\u5229\u7528\u5bf9\u79f0\u6027\u5316\u7b80\u95ee\u9898\uff0c\u7ec4\u5408\u8ba1\u6570\u9898\u76ee\u53ef\u4ee5\u6839\u636e\u5bf9\u79f0\u6027\u51cf\u5c11\u9700\u8981\u8ba1\u7b97\u7684\u60c5\u51b5\uff1b\u5177\u6709\u5bf9\u79f0\u6027\u7684\u65b9\u7a0b\u7ec4\u53ef\u4ee5\u5c1d\u8bd5\u76f8\u52a0\u6216\u8005\u76f8\u51cf\uff0c\u518d\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff1b\u5149\u7ebf\u4f20\u64ad\u7c7b\u95ee\u9898\u9700\u8981\u5bf9\u56fe\u5f62\u4f5c\u5bf9\u79f0\u8ba9\u5149\u7ebf\u6cbf\u76f4\u7ebf\u4f20\u64ad\u3002<\/p>\n\n\n\n

\u4e3e\u4f8b\u6765\u8bf4\uff1a\u4f8b\u5982\u7ed9\u6b63\u65b9\u4f53\u67d3\u62102\u9ed14\u767d\u548c2\u767d4\u9ed1\u7684\u60c5\u51b5\u662f\u4e00\u6837\u7684\u3002\u4f8b\u5982\u5149\u7ebf\u4f20\u64ad\u7c7b\u95ee\u9898\u9700\u8981\u5bf9\u56fe\u5f62\u4f5c\u5bf9\u79f0\u8ba9\u5149\u7ebf\u6cbf\u76f4\u7ebf\u4f20\u64ad\u3002<\/p>\n\n\n\n

\u2464\u719f\u6089\u51fd\u6570\u56fe\u50cf\u7684\u753b\u6cd5\uff1a\u57fa\u672c\u51fd\u6570\uff08\u7ebf\u6027\u3001\u4e8c\u6b21\u3001\u6307\u6570\u3001\u591a\u9879\u5f0f\u3001\u6709\u7406\u51fd\u6570\uff09\u3001\u7279\u6b8a\u51fd\u6570\uff08\u7edd\u5bf9\u503c\u3001\u53d6\u6574\u51fd\u6570\uff09\u3001\u590d\u5408\u51fd\u6570\u56fe\u50cf\u4ee5\u53ca\u56fe\u50cf\u7684\u5e73\u79fb\u3001\u4f38\u7f29\u548c\u5bf9\u79f0\u53d8\u6362\u3002<\/p>\n\n\n\n

\u2465\u540e\u9762\u51e0\u9053\u9898\u4e0d\u8981\u770b\u90fd\u4e0d\u770b\u76f4\u63a5\u8df3\u8fc7\uff0c\u8bf4\u4e0d\u5b9a\u67d0\u9053\u9898\u4f60\u6070\u597d\u5c31\u4f1a\uff01<\/p>\n\n\n\n

AMC12\u90e8\u5206\u9700\u8981\u8bb0\u4f4f\u7684\u516c\u5f0f\uff1a<\/strong><\/p>\n\n\n\n

\u4ee3\u6570\uff1a<\/strong>\u5404\u51fd\u6570\u7684\u56fe\u50cf\u7279\u5f81\uff08\u4e8c\u6b21 \u4e09\u89d2 \u6307\u5bf9\u6570 \u7edd\u5bf9\u503c \u53d6\u6574\u51fd\u6570 \u590d\u5408\u51fd\u6570 \u53cd\u51fd\u6570 \u5e73\u79fb\u3001\u4f38\u7f29\u3001\u5bf9\u79f0\u7b49\u56fe\u50cf\u53d8\u6362\uff09\uff0c\u4e09\u89d2\u6052\u7b49\u53d8\u6362\u516c\u5f0f\uff0c\u590d\u6570\u76f8\u5173\u516c\u5f0f\uff0c\u5bf9\u6570\u8fd0\u7b97\u516c\u5f0f\uff0c\u9012\u63a8\u6570\u5217\u6c42\u89e3\u901a\u9879\u65b9\u6cd5\uff0c\u5747\u503c\u4e0d\u7b49\u5f0f\uff0c\u9ad8\u6b21\u65b9\u7a0b\u97e6\u8fbe\u5b9a\u7406\uff0c\u5750\u6807\u7cfb\u4e2d\u8ddd\u79bb\u516c\u5f0f\uff08\u70b9-\u70b9\uff0c\u70b9-\u76f4\u7ebf\uff0c\u76f4\u7ebf-\u76f4\u7ebf\uff09\uff0c\u76f4\u7ebf\u5939\u89d2\u516c\u5f0f\uff0c\u978b\u5e26\u5b9a\u7406\uff1b<\/p>\n\n\n\n

\u51e0\u4f55\uff1a<\/strong>\u5e38\u89c1\u9762\u79ef\u548c\u4f53\u79ef\u516c\u5f0f\uff0c\u52fe\u80a1\u5b9a\u7406\uff0c\u89d2\u5e73\u5206\u7ebf\u5b9a\u7406\uff0c\u6b63\u4f59\u5f26\u5b9a\u7406\uff0c\u5706\u5e42\u8ba1\u7b97\u516c\u5f0f\uff0c\u4e09\u89d2\u5f62center\u7684\u76f8\u5173\u6027\u8d28\uff0c\u5706\u5185\u63a5\u56db\u8fb9\u5f62\u7684\u76f8\u5173\u6027\u8d28\uff0c\u6258\u52d2\u5bc6\u5b9a\u7406\uff0cStewart\u5b9a\u7406\uff1b<\/p>\n\n\n\n

\u6570\u8bba\uff1a<\/strong>\u56e0\u5f0f\u5206\u89e3\u516c\u5f0f\uff0c\u56e0\u6570\u76f8\u5173\u516c\u5f0f\uff08\u4e2a\u6570\u3001\u548c\u3001\u4e58\u79ef\uff09\uff0c\u8fdb\u5236\u8f6c\u5316\u516c\u5f0f\uff0c\u540c\u4f59\u8ba1\u7b97\u6cd5\u5219\u4e0e\u540c\u4f59\u65b9\u7a0b\u89e3\u6cd5\uff0c\u4e2d\u56fd\u5269\u4f59\u5b9a\u7406\uff1b<\/p>\n\n\n\n

\u7ec4\u5408\uff1a<\/strong>\u63d2\u677f\u6cd5\u516c\u5f0f\uff0c\u4e8c\u9879\u5f0f\u5b9a\u7406\uff0c\u5bb9\u65a5\u539f\u7406\u516c\u5f0f\uff1b<\/p>\n\n\n\n

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

<\/span>\u56db\u3001\u7b54\u9898\u6ce8\u610f\u4e8b\u9879\uff08Tips\uff09<\/strong><\/span><\/h2>\n\n\n\n

\u2776<\/strong>\u505a\u9898\u8fc7\u7a0b\u4e2d\u7684\u6ce8\u610f\u4e8b\u9879<\/strong><\/p>\n\n\n\n

AMC\u4e2d\u6709\u4e9b\u9898\u76ee\u6587\u5b57\u8f83\u591a\uff0c\u57fa\u672c\u4e0a\u6570\u5b66\u9898\u4e2d\u4e0d\u4f1a\u6709\u6ca1\u7528\u7684\u4fe1\u606f\uff0c\u56e0\u6b64\u4e00\u5b9a\u8981\u4ed4\u7ec6\u8bfb\u9898\u770b\u56fe\uff0c\u5982\u679c\u7ebf\u4e0b\u8003\u8bd5\u7684\u8bdd\u5728\u4e0a\u5377\u4e0a\u6807\u8bb0\u51fa\u91cd\u8981\u4fe1\u606f\uff0c\u5982\u679c\u7ebf\u4e0a\u8003\u8bd5\u5219\u5728\u8349\u7a3f\u7eb8\u4e0a\u5199\u4e0b\u9898\u76ee\u7684\u91cd\u70b9\u4fe1\u606f\uff1b<\/p>\n\n\n\n

\u7ebf\u4e0a\u8003\u8bd5\u7684\u540c\u5b66\uff0c\u51e0\u4f55\u9898\u65e0\u8bba\u6709\u6ca1\u6709\u7ed9\u56fe\uff0c\u90fd\u5728\u8349\u7a3f\u7eb8\u4e0a\u753b\u4e00\u904d\u56fe\uff08\u5efa\u8bae\u591a\u51c6\u5907\u51e0\u652f\u4e0d\u540c\u989c\u8272\u7684\u7b14\uff09\uff1b<\/p>\n\n\n\n

\u8349\u7a3f\u4e5f\u4e0d\u8981\u5199\u5f97\u592a\u4e71\uff0c\u8981\u8ba9\u81ea\u5df1\u68c0\u67e5\u7684\u65f6\u5019\u5f88\u5feb\u80fd\u627e\u5230\u6bcf\u4e00\u6b65\u7684\u8ba1\u7b97\u7ed3\u679c\uff1b<\/p>\n\n\n\n

\u53cc\u8bed\u8bd5\u5377\u8bfb\u9898\u65f6\uff0c\u5148\u770b\u81ea\u5df1\u719f\u6089\u7684\u8bed\u8a00\uff0c\u5982\u679c\u89c9\u5f97\u9898\u76ee\u6709\u6b67\u4e49\uff0c\u518d\u770b\u53e6\u4e00\u79cd\u8bed\u8a00\u6765\u786e\u8ba4\uff1b\u5982\u679c\u6709\u914d\u56fe\u7684\uff0c\u53ef\u4ee5\u5148\u770b\u56fe\u518d\u770b\u6587\u5b57\uff1b<\/p>\n\n\n\n

\u2777<\/strong>\u89e3\u9898\u524d\uff0c\u5148\u60f3\u4e00\u60f3\uff1a<\/strong><\/p>\n\n\n\n

\u27a4 <\/strong>\u51e0\u4f55\u9898\u53ef\u4ee5\u60f3\u60f3\u80fd\u4e0d\u80fd\u5efa\u7cfb\u505a\uff1f\u5982\u679c\u5efa\u7cfb\u7684\u8bdd\uff0c\u8ba1\u7b97\u91cf\u662f\u5426\u5408\u9002\uff1f\u6700\u540e\u51b3\u5b9a\u7528\u4ec0\u4e48\u65b9\u6cd5\uff1b<\/p>\n\n\n\n

\u27a4 <\/strong>\u4e09\u89d2\u51fd\u6570\u5316\u7b80\u95ee\u9898\uff0c\u53ef\u4ee5\u8003\u8651\u80fd\u4e0d\u80fd\u7528\u590d\u6570\u8868\u793a\u540e\u518d\u5316\u7b80\uff1b\u5750\u6807\u7cfb\u4e2d\u6d89\u53ca\u70b9\u65cb\u8f6c\u7684\u95ee\u9898\uff0c\u53ef\u4ee5\u8003\u8651\u7528\u590d\u6570\u8868\u793a\uff1b<\/p>\n\n\n\n

\u27a4 <\/strong>\u9012\u63a8\u6570\u5217\u95ee\u9898\uff0c\u5148\u7b97\u51e0\u9879\u627e\u627e\u89c4\u5f8b\uff0c\u770b\u770b\u662f\u4e0d\u662f\u5468\u671f\u6570\u5217\uff1b\u518d\u601d\u8003\u80fd\u4e0d\u80fd\u7528\u7d2f\u52a0\u7d2f\u4e58\u6216\u8005\u7279\u5f81\u65b9\u7a0b\u6c42\u89e3\u901a\u9879\uff1b\u5982\u679c\u4e0d\u53ef\u4ee5\u6c42\u901a\u9879\uff0c\u53ef\u4ee5\u8003\u8651\u76f8\u90bb\u4e24\u4e2a\u5f0f\u5b50\u76f8\u51cf\uff0c\u6d88\u5e38\u6570\u540e\u56e0\u5f0f\u5206\u89e3\u6216\u8005\u6784\u9020\u65b0\u6570\u5217\uff1b\u5982\u679c\u9012\u63a8\u5173\u7cfb\u660e\u663e\u4e0e\u6574\u6570\u6709\u5173\uff0c\u9700\u8981\u4ece\u6570\u8bba\u7684\u89d2\u5ea6\u6765\u8003\u8651\uff1b<\/p>\n\n\n\n

\u27a4 <\/strong>\u5728\u5e94\u7528\u9898\u3001\u51e0\u4f55\u9898\u3001\u6570\u5217\u9898\u3001\u51fd\u6570\u9898\u4e2d\uff0c\u5982\u679c\u9898\u76ee\u4e2d\u7684\u53d8\u91cf\u90fd\u662f\u6574\u6570\u65f6\uff0c\u5f88\u6709\u53ef\u80fd\u662f\u6570\u8bba\u9898\u76ee\uff0c\u9700\u8981\u7528\u5230\u6570\u8bba\u76f8\u5173\u77e5\u8bc6\uff0c\u4f8b\u5982\u5206\u6790\u56e0\u6570\u548c\u500d\u6570\u5173\u7cfb\u6216\u8005\u5217\u51fa\u6574\u6570\u65b9\u7a0b\u518d\u6c42\u89e3\u3002<\/p>\n\n\n\n

\u27a4 <\/strong>\u7ec4\u5408\u9898\u8981\u5206\u6e05\u695a\u9898\u76ee\u7c7b\u578b\uff0c\u662f\u8ba1\u6570\u95ee\u9898\uff0c\u6982\u7387\u95ee\u9898\uff0c2\u4eba\u6e38\u620f\u95ee\u9898\uff0c\u7ec4\u5408\u6781\u503c\u95ee\u9898\uff0c\u5b83\u4eec\u7684\u89e3\u9898\u65b9\u6cd5\u662f\u6709\u5dee\u5f02\u7684\uff1b<\/p>\n\n\n\n

\u27a4 <\/strong>\u6982\u7387\u7c7b\u9898\u76ee\u8981\u641e\u6e05\u695a\u9898\u76ee\u7c7b\u578b\uff0c\u7b49\u53ef\u80fd\u6027\u7ed3\u679c\u7684\u6982\u7387\uff0c\u975e\u7b49\u53ef\u80fd\u6027\u7ed3\u679c\u7684\u6982\u7387\uff0c\u6761\u4ef6\u6982\u7387\uff0c\u51e0\u4f55\u578b\u6982\u7387\uff0c\u65e0\u7a77\u65f6\u95f4\u72b6\u6001\u7c7b\u95ee\u9898\uff0c\u7136\u540e\u518d\u9009\u62e9\u5bf9\u5e94\u7684\u65b9\u6cd5\u3002<\/p>\n\n\n\n

\u27a4 <\/strong>\u7ec4\u5408\u8ba1\u6570\u9898\u4e2d\uff0c\u201c\u81f3\u5c11\u5b58\u5728\uff08at least\uff09\u201d\u7c7b\u95ee\u9898\u548c\u201c\u90fd\u4e0d\u6ee1\u8db3\u201d\u7c7b\u95ee\u9898\uff0c\u53ef\u4ee5\u8003\u8651\u7b97\u53cd\u9762\uff08complementary counting\uff09\u548c\u5bb9\u65a5\u539f\u7406\uff08PIE\uff09\uff1b\u95f4\u9694\u4e0e\u76f8\u90bb\u7c7b\u95ee\u9898\uff0c\u5206\u914d\u4e0e\u9009\u62e9\u95ee\u9898\uff0c\u53ef\u4ee5\u8003\u8651\u63d2\u677f\u6cd5\uff1b\u7ecf\u8fc7\u5206\u7c7b\u8ba8\u8bba\uff0c \u80fd\u628a\u60c5\u51b5n\u53d8\u4e3an-1\u6216n-2\u6216\u8005\u66f4\u5c0f\u7684\u60c5\u51b5\uff0c\u53ef\u4ee5\u8003\u8651\u9012\u63a8\u65b9\u6cd5\uff1b<\/p>\n\n\n\n

\u27a4 <\/strong>\u89c2\u5bdf\u9898\u76ee\u4e2d\u662f\u5426\u6709\u5bf9\u79f0\u6027\uff0c\u4ece\u800c\u5316\u7b80\u95ee\u9898\uff1a\u7ec4\u5408\u8ba1\u6570\u9898\u76ee\u53ef\u4ee5\u6839\u636e\u5bf9\u79f0\u6027\u51cf\u5c11\u9700\u8981\u8ba1\u7b97\u7684\u60c5\u51b5\uff08\u4f8b\u5982\u7ed9\u6b63\u65b9\u4f53\u67d3\u62102\u9ed14\u767d\u548c2\u767d4\u9ed1\u7684\u60c5\u51b5\u662f\u4e00\u6837\u7684\uff09\uff1b\u5177\u6709\u5bf9\u79f0\u6027\u7684\u65b9\u7a0b\u7ec4\u53ef\u4ee5\u5c1d\u8bd5\u76f8\u52a0\u6216\u8005\u76f8\u51cf\u518d\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff1b\u5149\u7ebf\u4f20\u64ad\u7c7b\u95ee\u9898\u9700\u8981\u5bf9\u56fe\u5f62\u4f5c\u5bf9\u79f0\u8ba9\u5149\u7ebf\u6cbf\u76f4\u7ebf\u4f20\u64ad\u3002<\/p>\n\n\n\n

\u2778<\/strong>\u9009\u62e9\u9898\u7b54\u9898\u6280\u5de7<\/strong><\/p>\n\n\n\n

\u27a4 \u8bbe\u6570\u6cd5\uff1a<\/strong>\u90e8\u5206\u9898\u76ee\u53ef\u4ee5\u81ea\u884c\u5047\u8bbe\u4e00\u4e9b\u4fbf\u4e8e\u89e3\u9898\u7684\u6761\u4ef6<\/p>\n\n\n\n

\u2460 \u65b9\u7a0b\u4e2a\u6570\u5c11\u4e8e\u53d8\u91cf\u7684\u65f6\u5019\uff0c\u53ef\u4ee5\u5047\u8bbe\u5176\u4e2d\u67d0\u4e9b\u53d8\u91cf\u4e3a\u7279\u5b9a\u503c\u3002\uff08\u4e0d\u9002\u7528\u4e8e\u6574\u6570\u65b9\u7a0b\uff09\uff1b<\/p>\n\n\n\n

\u2461 \u9012\u63a8\u6570\u5217\u7684\u524d\u51e0\u9879\u662f\u6bd4\u8f83\u5927\u6216\u8005\u590d\u6742\u7684\u6570\u65f6\uff0c\u53ef\u4ee5\u81ea\u5df1\u5047\u8bbe\u4e00\u4e9b\u7b80\u5355\u503c\u6216\u8005\u76f4\u63a5\u5047\u8bbe\u53d8\u91cf\u8fdb\u884c\u9012\u63a8\uff0c\u53ef\u80fd\u4f1a\u6709\u5468\u671f\u6027\u6216\u8005\u660e\u663e\u7684\u89c4\u5f8b\uff1b<\/p>\n\n\n\n

\u2462 \u51e0\u4f55\u9898\u4e2d\u7ed9\u51fa\u7684\u4fe1\u606f\u4e0d\u8db3\u4ee5\u786e\u5b9a\u4e00\u4e2a\u56fe\u5f62\u65f6\uff0c\u53ef\u4ee5\u81ea\u5df1\u5047\u8bbe\u4e00\u4e9b\u989d\u5916\u7684\u89d2\u5ea6\u6216\u8005\u8fb9\u957f\u6761\u4ef6\uff1b<\/p>\n\n\n\n

\u27a4 \u5ea6\u91cf\u6cd5\uff1a<\/strong>\u5bf9\u4e8e\u90e8\u5206\u51e0\u4f55\u9898\uff0c\u5982\u679c\u9898\u76ee\u6761\u4ef6\u80fd\u591f\u552f\u4e00\u786e\u5b9a\u56fe\u5f62\u65f6\uff0c\u53ef\u4ee5\u4f5c\u51fa\u6807\u51c6\u56fe\uff1b\u5f53\u9898\u76ee\u6761\u4ef6\u4e0d\u80fd\u552f\u4e00\u786e\u5b9a\u56fe\u5f62\u65f6\uff0c\u53ef\u4ee5\u753b\u51fa\u67d0\u79cd\u7279\u6b8a\u60c5\u51b5\u4e0b\u7684\u56fe\u5f62\u3002\u800c\u540e\u53ef\u4ee5\u901a\u8fc7\u5ea6\u91cf\u8fb9\u957f\u6216\u8005\u89d2\u5ea6\u76f4\u63a5\u5f97\u5230\u7b54\u6848\uff08\u4f46\u662f\u8fd1\u5e74\u6765\u51fa\u9898\u4eba\u4f1a\u6709\u610f\u89c4\u907f\u8fd9\u79cd\u53ef\u80fd\uff0c\u6240\u4ee5\u80fd\u7528\u5230\u7684\u673a\u4f1a\u4e0d\u5927\uff09<\/p>\n\n\n\n

\u27a4 \u627e\u89c4\u5f8b\uff1a<\/strong>\u9012\u63a8\u6570\u5217\u3001\u9012\u63a8\u51fd\u6570\u3001\u65b0\u5b9a\u4e49\u7684\u6570\u8bba\u51fd\u6570\u3001\u7ec4\u5408\u9012\u63a8\u95ee\u9898\u3001\u4e8c\u4eba\u6e38\u620f\u95ee\u9898\uff0c\u90fd\u53ef\u4ee5\u5148\u4ece\u6700\u7b80\u5355\u7684\u521d\u59cb\u60c5\u51b5\u5f00\u59cb\u7814\u7a76\uff0c\u4e89\u53d6\u53d1\u73b0\u89c4\u5f8b\u3002<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

<\/span>\u603b\u7ed3<\/span><\/h2>\n\n\n\n

AMC12\u8003\u8bd5\u6db5\u76d6\u4e86\u4ee3\u6570\u3001\u51e0\u4f55\u3001\u6570\u8bba\u3001\u6392\u5217\u7ec4\u5408\u7b49\u591a\u4e2a\u6570\u5b66\u9886\u57df\uff0c\u9700\u8981\u8003\u751f\u719f\u7ec3\u638c\u63e1\u5404\u77e5\u8bc6\u70b9\u3002\u540c\u65f6\uff0c\u7b54\u9898\u65f6\u9700\u6ce8\u610f\u65f6\u95f4\u5206\u914d\uff0c\u786e\u4fdd\u6bcf\u9053\u9898\u90fd\u6709\u8db3\u591f\u7684\u65f6\u95f4\u53bb\u601d\u8003\u548c\u89e3\u7b54\u3002\u6b64\u5916\uff0c\u7b54\u9898\u6280\u5de7\u4e5f\u975e\u5e38\u91cd\u8981\uff0c\u5982\u638c\u63e1\u5e38\u89c1\u7684\u89e3\u9898\u53e3\u8bc0\u548c\u516c\u5f0f\uff0c\u80fd\u591f\u63d0\u9ad8\u89e3\u9898\u6548\u7387\u3002\u6700\u540e\uff0c\u8981\u7279\u522b\u6ce8\u610f\u505a\u9898\u8fc7\u7a0b\u4e2d\u7684\u7ec6\u8282\u95ee\u9898\uff0c\u5982\u4ed4\u7ec6\u8bfb\u9898\u3001\u68c0\u67e5\u7b54\u6848\u7b49\u3002\u53ea\u6709\u77e5\u8bc6\u70b9\u548c\u6280\u5de7\u76f8\u7ed3\u5408\uff0c\u624d\u80fd\u53d6\u5f97\u66f4\u597d\u7684\u6210\u7ee9\u3002<\/p>\n\n\n\n

\u60f3\u8981\u4e86\u89e3\u66f4\u591a\u6570\u5b66\u5907\u8003\u8d44\u8baf\uff0c\u70b9\u51fb\u4e0b\u65b9\u5361\u7247\uff0c\u9886\u53d6\u8bfe\u7a0b\u5427~<\/p>\n

\r\n
\r\n
<\/div>\r\n

\u609f\u7a7a\u56fd\u9645\u6570\u5b66
\n\u8ba9\u6570\u5b66\u4e4b\u5149\u7167\u4eae\u6bcf\u4e00\u4e2a\u5b69\u5b50\uff01<\/span><\/p>\n<\/h3>\r\n

\u9002\u5408\u5168\u74031-12\u5e74\u7ea7\u5b66\u751f<\/p>\r\n \r\n \u7acb\u5373\u514d\u8d39\u8bd5\u542c\r\n <\/a>\r\n <\/div>\r\n

<\/div>\r\n<\/div>","protected":false},"excerpt":{"rendered":"

AMC 12\uff08American Mathematics Competition\uff09\u753112\u5e74\u7ea7\u53ca12\u5e74\u7ea7\u4ee5\u4e0b\u5b66\u751f\u53c2\u52a0\uff0c\u53c2\u52a0AMC12\u8003\u8bd5\u7684\u5f53\u5929\u5e74\u9f84\u9700\u5c0f\u4e8e19.5\u5c81\u3002\u8fbe\u5230\u5206\u6570\u7ebf\u7684\u8003\u751f\u4f1a\u83b7\u5f97\u8363\u8a89\u8bc1\u4e66\uff0c\u5e76\u53d7\u9080\u53c2\u52a0\u7f8e\u56fd\u6570\u5b66\u9080\u8bf7\u8d5b\uff08AIME\uff09\uff0c\u6bcf\u5e74\u5206\u6570\u7ebf\u4f1a\u6839\u636e\u6574\u4f53\u60c5\u51b5\u6709\u6240\u8c03\u6574\u3002 \u90a3\u4e48\uff0cAMC\u7684\u8003\u70b9\u6709\u54ea\u4e9b\uff1f\u80fd\u4ece\u54ea\u4e9b\u65b9\u9762\u4e0b\u624b\u5907\u8003\u5462\uff1f\u5feb\u8ddf\u5c0f\u609f\u7a7a\u4e00\u8d77\u770b\u770b\u5427\uff01 \u4e00\u3001AMC 12\u8003\u70b9\u6709\u54ea\u4e9b\uff1f AMC10\u4e0eAMC12\u7684\u5dee\u5f02 AMC12\u7684\u5927\u90e8\u5206\u8003\u70b9\u90fd\u662f\u4e0eAMC10\u4e00\u81f4\u7684\uff0c\u6574\u4efd\u8bd5\u5377\u4e2d\u4e5f\u4f1a\u670910\u9898\u5de6\u53f3\u662f\u5b8c\u5168\u76f8\u540c\u7684\u3002\u5dee\u5f02\u5728\u4e8e\uff0c\u4ee3\u6570\u6a21\u5757\u591a\u4e86\u5927\u91cf\u7684\u77e5\u8bc6\u70b9\uff0c\u8fd9\u4e9b\u77e5\u8bc6\u70b9\u57fa\u672c\u662f\u9ad8\u4e2d\u8bfe\u5185\u5185\u5bb9\uff1b\u6b64\u5916\u5728\u51e0\u4f55\u3001\u6570\u8bba\u3001\u7ec4\u5408\u6a21\u5757\u5404\u591a\u4e86\u5c11\u91cf\u7684\u77e5\u8bc6\u70b9\uff0c\u8fd9\u4e9b\u77e5\u8bc6\u70b9\u5927\u591a\u6bd4\u8f83\u590d\u6742\uff0c\u4e00\u822c\u51fa\u73b0\u5728\u540e10\u9898\u4e2d\uff0c\u638c\u63e1\u8fd9\u4e9b\u77e5\u8bc6\u70b9\u662f\u51b2\u51fb\u9ad8\u5206\u7684\u5173\u952e\u3002 AMC12\u6db5\u76d6\u4e86AMC10\u7684\u6240\u6709\u77e5\u8bc6\u70b9\u4e4b\u5916\u8fd8\u5305\u62ec\u4e09\u89d2\u5b66\u3001\u9ad8\u7ea7\u4ee3\u6570\u548c\u9ad8\u7ea7\u51e0\u4f55\u5b66\uff0c\u4f46\u4e0d\u5305\u62ec\u5fae\u79ef\u5206\u3002 AMC12\u8003\u70b9 1\u3001\u4ee3\u6570 \u672c\u90e8\u5206\u4e3b\u8981\u8003\u5bdf\uff1a\u5404\u79cd\u56e0\u5f0f\u5206\u89e3\u7684\u65b9\u6cd5\u53ca\u5176\u5e7f\u6cdb\u7684\u5e94\u7528\u3001\u6307\u6570\u8fd0\u7b97\u7684\u57fa\u672c\u6cd5\u5219\u53ca\u89e3\u65b9\u7a0b\u3001\u9ad8\u4e2d\u9636\u6bb5\u4ee3\u6570\u77e5\u8bc6\u3001\u4e0d\u7b49\u5f0f\u7406\u8bba\u3001\u591a\u9879\u5f0f\u7406\u8bba\u548c\u4e8c\u9879\u5f0f\u5b9a\u7406\u3002 2\u3001\u5e73\u9762\u51e0\u4f55 \u672c\u90e8\u5206\u4e3b\u8981\u8003\u5bdf\uff1a\u7b49\u8170\uff0c\u7b49\u8fb9\u548c\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u8ba1\u7b97\u3001\u7279\u6b8a\u89d2\u7684\u57fa\u672c\u4e09\u89d2\u51fd\u6570\u8ba1\u7b97\u3001\u76f8\u4f3c\u56fe\u5f62\u7684\u5224\u522b\u548c\u5468\u957f\u4e0e\u9762\u79ef\u7684\u8ba1\u7b97\u3001\u521d\u4e2d\u51e0\u4f55\u7684\u76f8\u5173\u7ed3\u8bba\u548c\u8bc1\u660e\u3001\u5185\u63a5\u5706\u3001\u5916\u5207\u56fe\u5f62\u7684\u7ed3\u8bba\u3002 3\u3001\u6570\u8bba \u672c\u90e8\u5206\u4e3b\u8981\u8003\u5bdf\uff1a\u6574\u9664\u7406\u8bba\u3001\u540c\u4f59\u7406\u8bba\u3001\u8d39\u5c14\u9a6c\u5c0f\u5b9a\u7406\u548c\u7b97\u672f\u57fa\u672c\u5b9a\u7406\u7b49\u3001\u6570\u8bba\u8bc1\u660e\u3001\u4e86\u89e3Diophantineequations\u7684\u7c7b\u578b\u4ee5\u53ca\u4e0e\u6574\u9664\u7406\u8bba\u7684\u5173\u7cfb\u3001\u638c\u63e1\u7ebf\u6027Diophantineequations\u7684\u539f\u7406\uff0c\u89e3\u6cd5\u53ca\u5e94\u7528\u3002 4\u3001\u6392\u5217\u7ec4\u5408 \u672c\u90e8\u5206\u4e3b\u8981\u8003\u5bdf\uff1a\u8ba1\u6570\u539f\u7406\u3001\u638c\u63e1\u6392\u5217\u7ec4\u5408\u539f\u7406\u548c\u8ba1\u7b97\u3001Exclusion\u2013inclusionprinciple\u3001pigeon-holeprinciple\u89e3\u51b3\u5b9e\u9645\u95ee\u9898\u3001\u7ec4\u5408\u95ee\u9898\u7684\u5b9e\u9645\u5e94\u7528\u3001\u7edf\u8ba1\u521d\u6b65\uff1a\u5e73\u5747\u6570\uff0c\u4f17\u6570\uff0c\u4e2d\u4f4d\u6570\u53ca\u52a0\u6743\u5e73\u5747\u6570\u7684\u8ba1\u7b97\u3002 5\u3001\u4e09\u89d2\u51fd\u6570 \u672c\u90e8\u5206\u4e3b\u8981\u8003\u5bdf\uff1a\u4e09\u89d2\u57fa\u7840\u77e5\u8bc6\u548c\u516c\u5f0f\u3001\u4e09\u89d2\u51fd\u6570\u7684\u8ba1\u7b97\u548c\u5316\u7b80\u3001\u4e09\u89d2\u51fd\u6570\u7684\u7efc\u5408\u5e94\u7528\u3001\u638c\u63e1\u4e09\u89d2\u51fd\u6570\u548c\u4e09\u89d2\u65b9\u7a0b\u7684\u5b66\u672f\u6d3b\u52a8\u9898\u89e3\u6cd5\u3002 6\u3001\u6570\u5217\u548c\u7ea7\u6570 \u672c\u90e8\u5206\u4e3b\u8981\u8003\u5bdf\uff1a\u7b49\u5dee\u7b49\u6bd4\u6570\u5217\u89e3\u6cd5\u3001\u590d\u6742\u7684\u7b49\u5dee\u6570\u5217\u4e0e\u7b49\u6bd4\u6570\u5217\u7684\u5e94\u7528\u3001\u5b66\u4e60\u89e3\u7279\u6b8a\u6570\u5217\u548c\u7ea7\u6570\u7684\u76f8\u5173\u6280\u5de7\u3001\u4e09\u89d2\u3001\u4ee3\u6570\u548c\u7ec4\u5408\u76f8\u7ed3\u5408\u7684\u5b66\u672f\u6d3b\u52a8\u9898\u89e3\u6cd5\u3002 7\u3001\u590d\u6570\u548c\u56fe\u8bba \u672c\u90e8\u5206\u4e3b\u8981\u8003\u5bdf\uff1a\u590d\u4e60\u590d\u6570\u77e5\u8bc6\u548c\u8bcd\u6c47\uff0c\u5b66\u4e60\u521d\u6b65\u56fe\u8bba\u3001\u8ba1\u6570\u548c\u7ec4\u5408\u7684\u8054\u7cfb\u3001\u91cd\u70b9\u8054\u7cfb\u4e0a\u8ff0\u4e0e\u5176\u4ed6\u77e5\u8bc6\u7684\u7efc\u5408\u9898\u7684\u89e3\u6cd5\u3002 \u4e8c\u3001AMC12 \u8003\u8bd5\u65f6\u95f4\u5206\u914d\u8868 \u4e09\u3001\u7b54\u9898\u516c\u5f0f\u4e0e\u53e3\u8bc0\uff08\u90e8\u5206\uff09 \u5f00\u5934\u6211\u4eec\u5c31\u8bf4\u4e86\uff0c\u5b66\u4f1a\u4e86\u77e5\u8bc6\u70b9\u8fd8\u4e0d\u591f\uff0c\u8fd8\u8981\u5b66\u4f1a\u7075\u6d3b\u8fd0\u7528\uff01\u54ea\u91cc\u80fd\u4f53\u73b0\u7075\u6d3b\u8fd0\u7528\uff0c\u90a3\u5c31\u662f\u5145\u5206\u4e86\u89e3\u3010\u5fc5\u8003\u9898\u578b\u3011\uff0c\u5c06\u77e5\u8bc6\u70b9\u4e0e\u9898\u8fdb\u884c\u7684\u5b8c\u7f8e\u7ed3\u5408\u3002\u8fd9\u65f6\u5019\u4e0e\u5927\u5bb6\u5206\u4eab\u51e0\u4e2a\u5173\u4e8e\u9898\u578b\u7684\u53e3\u8bc0\uff1a \u2460\u5728\u5e94\u7528\u9898\u3001\u51e0\u4f55\u9898\u3001\u6570\u5217\u9898\u3001\u51fd\u6570\u9898\u4e2d\uff0c\u5982\u679c\u9898\u76ee\u4e2d\u7684\u53d8\u91cf\u90fd\u662f\u6574\u6570\u65f6\uff0c\u5f88\u6709\u53ef\u80fd\u662f\u6570\u8bba\u9898\u3002 \u89e3\u51b3\u65b9\u6848\uff1a\u9700\u8981\u7528\u5230\u6570\u8bba\u76f8\u5173\u77e5\u8bc6\uff0c\u4f8b\u5982\u5206\u6790\u56e0\u5b50\u548c\u500d\u6570\u5173\u7cfb\u6216\u8005\u5217\u51fa\u6574\u6570\u65b9\u7a0b\u518d\u6c42\u89e3\u3002 \u2461\u6982\u7387\u7c7b\u9898\u76ee\u8981\u641e\u6e05\u695a\u662f\u5426\u4e3a\u51e0\u4f55\u578b\u6982\u7387\uff0c\u662f\u5426\u662f\u65e0\u7a77\u72b6\u6001\u7c7b\u95ee\u9898\uff0c\u662f\u5426\u662fequally likely outcome\u578b\u6982\u7387\uff0c\u7136\u540e\u518d\u9009\u62e9\u5bf9\u5e94\u7684\u65b9\u6cd5\u3002 \u2462\u4e24\u4eba\u6e38\u620f\u7c7b\u95ee\u9898\uff0c\u7b80\u5355\u60c5\u51b5\u53ef\u4ee5\u76f4\u63a5\u679a\u4e3e\u8fdb\u884c\u8ba8\u8bba\uff1b\u590d\u6742\u60c5\u51b5\u53ef\u4ee5\u5148\u7528\u914d\u5bf9\u548c\u955c\u50cf\u7684\u65b9\u6cd5\u8fdb\u884c\u5c1d\u8bd5\uff0c\u82e5\u4e0d\u884c\u518d\u4ece\u7b80\u5355\u7684\u521d\u59cb\u6761\u4ef6\u51fa\u53d1\uff0c\u5bfb\u627ewinning position\u548closing position\uff0c\u5e76\u627e\u51fa\u4e00\u822c\u89c4\u5f8b\u3002 \u2463\u5229\u7528\u5bf9\u79f0\u6027\u5316\u7b80\u95ee\u9898\uff0c\u7ec4\u5408\u8ba1\u6570\u9898\u76ee\u53ef\u4ee5\u6839\u636e\u5bf9\u79f0\u6027\u51cf\u5c11\u9700\u8981\u8ba1\u7b97\u7684\u60c5\u51b5\uff1b\u5177\u6709\u5bf9\u79f0\u6027\u7684\u65b9\u7a0b\u7ec4\u53ef\u4ee5\u5c1d\u8bd5\u76f8\u52a0\u6216\u8005\u76f8\u51cf\uff0c\u518d\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff1b\u5149\u7ebf\u4f20\u64ad\u7c7b\u95ee\u9898\u9700\u8981\u5bf9\u56fe\u5f62\u4f5c\u5bf9\u79f0\u8ba9\u5149\u7ebf\u6cbf\u76f4\u7ebf\u4f20\u64ad\u3002 \u4e3e\u4f8b\u6765\u8bf4\uff1a\u4f8b\u5982\u7ed9\u6b63\u65b9\u4f53\u67d3\u62102\u9ed14\u767d\u548c2\u767d4\u9ed1\u7684\u60c5\u51b5\u662f\u4e00\u6837\u7684\u3002\u4f8b\u5982\u5149\u7ebf\u4f20\u64ad\u7c7b\u95ee\u9898\u9700\u8981\u5bf9\u56fe\u5f62\u4f5c\u5bf9\u79f0\u8ba9\u5149\u7ebf\u6cbf\u76f4\u7ebf\u4f20\u64ad\u3002 \u2464\u719f\u6089\u51fd\u6570\u56fe\u50cf\u7684\u753b\u6cd5\uff1a\u57fa\u672c\u51fd\u6570\uff08\u7ebf\u6027\u3001\u4e8c\u6b21\u3001\u6307\u6570\u3001\u591a\u9879\u5f0f\u3001\u6709\u7406\u51fd\u6570\uff09\u3001\u7279\u6b8a\u51fd\u6570\uff08\u7edd\u5bf9\u503c\u3001\u53d6\u6574\u51fd\u6570\uff09\u3001\u590d\u5408\u51fd\u6570\u56fe\u50cf\u4ee5\u53ca\u56fe\u50cf\u7684\u5e73\u79fb\u3001\u4f38\u7f29\u548c\u5bf9\u79f0\u53d8\u6362\u3002 \u2465\u540e\u9762\u51e0\u9053\u9898\u4e0d\u8981\u770b\u90fd\u4e0d\u770b\u76f4\u63a5\u8df3\u8fc7\uff0c\u8bf4\u4e0d\u5b9a\u67d0\u9053\u9898\u4f60\u6070\u597d\u5c31\u4f1a\uff01 AMC12\u90e8\u5206\u9700\u8981\u8bb0\u4f4f\u7684\u516c\u5f0f\uff1a \u4ee3\u6570\uff1a\u5404\u51fd\u6570\u7684\u56fe\u50cf\u7279\u5f81\uff08\u4e8c\u6b21 \u4e09\u89d2 \u6307\u5bf9\u6570 \u7edd\u5bf9\u503c \u53d6\u6574\u51fd\u6570 \u590d\u5408\u51fd\u6570 \u53cd\u51fd\u6570 \u5e73\u79fb\u3001\u4f38\u7f29\u3001\u5bf9\u79f0\u7b49\u56fe\u50cf\u53d8\u6362\uff09\uff0c\u4e09\u89d2\u6052\u7b49\u53d8\u6362\u516c\u5f0f\uff0c\u590d\u6570\u76f8\u5173\u516c\u5f0f\uff0c\u5bf9\u6570\u8fd0\u7b97\u516c\u5f0f\uff0c\u9012\u63a8\u6570\u5217\u6c42\u89e3\u901a\u9879\u65b9\u6cd5\uff0c\u5747\u503c\u4e0d\u7b49\u5f0f\uff0c\u9ad8\u6b21\u65b9\u7a0b\u97e6\u8fbe\u5b9a\u7406\uff0c\u5750\u6807\u7cfb\u4e2d\u8ddd\u79bb\u516c\u5f0f\uff08\u70b9-\u70b9\uff0c\u70b9-\u76f4\u7ebf\uff0c\u76f4\u7ebf-\u76f4\u7ebf\uff09\uff0c\u76f4\u7ebf\u5939\u89d2\u516c\u5f0f\uff0c\u978b\u5e26\u5b9a\u7406\uff1b \u51e0\u4f55\uff1a\u5e38\u89c1\u9762\u79ef\u548c\u4f53\u79ef\u516c\u5f0f\uff0c\u52fe\u80a1\u5b9a\u7406\uff0c\u89d2\u5e73\u5206\u7ebf\u5b9a\u7406\uff0c\u6b63\u4f59\u5f26\u5b9a\u7406\uff0c\u5706\u5e42\u8ba1\u7b97\u516c\u5f0f\uff0c\u4e09\u89d2\u5f62center\u7684\u76f8\u5173\u6027\u8d28\uff0c\u5706\u5185\u63a5\u56db\u8fb9\u5f62\u7684\u76f8\u5173\u6027\u8d28\uff0c\u6258\u52d2\u5bc6\u5b9a\u7406\uff0cStewart\u5b9a\u7406\uff1b \u6570\u8bba\uff1a\u56e0\u5f0f\u5206\u89e3\u516c\u5f0f\uff0c\u56e0\u6570\u76f8\u5173\u516c\u5f0f\uff08\u4e2a\u6570\u3001\u548c\u3001\u4e58\u79ef\uff09\uff0c\u8fdb\u5236\u8f6c\u5316\u516c\u5f0f\uff0c\u540c\u4f59\u8ba1\u7b97\u6cd5\u5219\u4e0e\u540c\u4f59\u65b9\u7a0b\u89e3\u6cd5\uff0c\u4e2d\u56fd\u5269\u4f59\u5b9a\u7406\uff1b \u7ec4\u5408\uff1a\u63d2\u677f\u6cd5\u516c\u5f0f\uff0c\u4e8c\u9879\u5f0f\u5b9a\u7406\uff0c\u5bb9\u65a5\u539f\u7406\u516c\u5f0f\uff1b \u56db\u3001\u7b54\u9898\u6ce8\u610f\u4e8b\u9879\uff08Tips\uff09 \u2776\u505a\u9898\u8fc7\u7a0b\u4e2d\u7684\u6ce8\u610f\u4e8b\u9879 AMC\u4e2d\u6709\u4e9b\u9898\u76ee\u6587\u5b57\u8f83\u591a\uff0c\u57fa\u672c\u4e0a\u6570\u5b66\u9898\u4e2d\u4e0d\u4f1a\u6709\u6ca1\u7528\u7684\u4fe1\u606f\uff0c\u56e0\u6b64\u4e00\u5b9a\u8981\u4ed4\u7ec6\u8bfb\u9898\u770b\u56fe\uff0c\u5982\u679c\u7ebf\u4e0b\u8003\u8bd5\u7684\u8bdd\u5728\u4e0a\u5377\u4e0a\u6807\u8bb0\u51fa\u91cd\u8981\u4fe1\u606f\uff0c\u5982\u679c\u7ebf\u4e0a\u8003\u8bd5\u5219\u5728\u8349\u7a3f\u7eb8\u4e0a\u5199\u4e0b\u9898\u76ee\u7684\u91cd\u70b9\u4fe1\u606f\uff1b \u7ebf\u4e0a\u8003\u8bd5\u7684\u540c\u5b66\uff0c\u51e0\u4f55\u9898\u65e0\u8bba\u6709\u6ca1\u6709\u7ed9\u56fe\uff0c\u90fd\u5728\u8349\u7a3f\u7eb8\u4e0a\u753b\u4e00\u904d\u56fe\uff08\u5efa\u8bae\u591a\u51c6\u5907\u51e0\u652f\u4e0d\u540c\u989c\u8272\u7684\u7b14\uff09\uff1b \u8349\u7a3f\u4e5f\u4e0d\u8981\u5199\u5f97\u592a\u4e71\uff0c\u8981\u8ba9\u81ea\u5df1\u68c0\u67e5\u7684\u65f6\u5019\u5f88\u5feb\u80fd\u627e\u5230\u6bcf\u4e00\u6b65\u7684\u8ba1\u7b97\u7ed3\u679c\uff1b \u53cc\u8bed\u8bd5\u5377\u8bfb\u9898\u65f6\uff0c\u5148\u770b\u81ea\u5df1\u719f\u6089\u7684\u8bed\u8a00\uff0c\u5982\u679c\u89c9\u5f97\u9898\u76ee\u6709\u6b67\u4e49\uff0c\u518d\u770b\u53e6\u4e00\u79cd\u8bed\u8a00\u6765\u786e\u8ba4\uff1b\u5982\u679c\u6709\u914d\u56fe\u7684\uff0c\u53ef\u4ee5\u5148\u770b\u56fe\u518d\u770b\u6587\u5b57\uff1b \u2777\u89e3\u9898\u524d\uff0c\u5148\u60f3\u4e00\u60f3\uff1a \u27a4 \u51e0\u4f55\u9898\u53ef\u4ee5\u60f3\u60f3\u80fd\u4e0d\u80fd\u5efa\u7cfb\u505a\uff1f\u5982\u679c\u5efa\u7cfb\u7684\u8bdd\uff0c\u8ba1\u7b97\u91cf\u662f\u5426\u5408\u9002\uff1f\u6700\u540e\u51b3\u5b9a\u7528\u4ec0\u4e48\u65b9\u6cd5\uff1b \u27a4 \u4e09\u89d2\u51fd\u6570\u5316\u7b80\u95ee\u9898\uff0c\u53ef\u4ee5\u8003\u8651\u80fd\u4e0d\u80fd\u7528\u590d\u6570\u8868\u793a\u540e\u518d\u5316\u7b80\uff1b\u5750\u6807\u7cfb\u4e2d\u6d89\u53ca\u70b9\u65cb\u8f6c\u7684\u95ee\u9898\uff0c\u53ef\u4ee5\u8003\u8651\u7528\u590d\u6570\u8868\u793a\uff1b \u27a4 \u9012\u63a8\u6570\u5217\u95ee\u9898\uff0c\u5148\u7b97\u51e0\u9879\u627e\u627e\u89c4\u5f8b\uff0c\u770b\u770b\u662f\u4e0d\u662f\u5468\u671f\u6570\u5217\uff1b\u518d\u601d\u8003\u80fd\u4e0d\u80fd\u7528\u7d2f\u52a0\u7d2f\u4e58\u6216\u8005\u7279\u5f81\u65b9\u7a0b\u6c42\u89e3\u901a\u9879\uff1b\u5982\u679c\u4e0d\u53ef\u4ee5\u6c42\u901a\u9879\uff0c\u53ef\u4ee5\u8003\u8651\u76f8\u90bb\u4e24\u4e2a\u5f0f\u5b50\u76f8\u51cf\uff0c\u6d88\u5e38\u6570\u540e\u56e0\u5f0f\u5206\u89e3\u6216\u8005\u6784\u9020\u65b0\u6570\u5217\uff1b\u5982\u679c\u9012\u63a8\u5173\u7cfb\u660e\u663e\u4e0e\u6574\u6570\u6709\u5173\uff0c\u9700\u8981\u4ece\u6570\u8bba\u7684\u89d2\u5ea6\u6765\u8003\u8651\uff1b \u27a4 \u5728\u5e94\u7528\u9898\u3001\u51e0\u4f55\u9898\u3001\u6570\u5217\u9898\u3001\u51fd\u6570\u9898\u4e2d\uff0c\u5982\u679c\u9898\u76ee\u4e2d\u7684\u53d8\u91cf\u90fd\u662f\u6574\u6570\u65f6\uff0c\u5f88\u6709\u53ef\u80fd\u662f\u6570\u8bba\u9898\u76ee\uff0c\u9700\u8981\u7528\u5230\u6570\u8bba\u76f8\u5173\u77e5\u8bc6\uff0c\u4f8b\u5982\u5206\u6790\u56e0\u6570\u548c\u500d\u6570\u5173\u7cfb\u6216\u8005\u5217\u51fa\u6574\u6570\u65b9\u7a0b\u518d\u6c42\u89e3\u3002 \u27a4 \u7ec4\u5408\u9898\u8981\u5206\u6e05\u695a\u9898\u76ee\u7c7b\u578b\uff0c\u662f\u8ba1\u6570\u95ee\u9898\uff0c\u6982\u7387\u95ee\u9898\uff0c2\u4eba\u6e38\u620f\u95ee\u9898\uff0c\u7ec4\u5408\u6781\u503c\u95ee\u9898\uff0c\u5b83\u4eec\u7684\u89e3\u9898\u65b9\u6cd5\u662f\u6709\u5dee\u5f02\u7684\uff1b \u27a4 \u6982\u7387\u7c7b\u9898\u76ee\u8981\u641e\u6e05\u695a\u9898\u76ee\u7c7b\u578b\uff0c\u7b49\u53ef\u80fd\u6027\u7ed3\u679c\u7684\u6982\u7387\uff0c\u975e\u7b49\u53ef\u80fd\u6027\u7ed3\u679c\u7684\u6982\u7387\uff0c\u6761\u4ef6\u6982\u7387\uff0c\u51e0\u4f55\u578b\u6982\u7387\uff0c\u65e0\u7a77\u65f6\u95f4\u72b6\u6001\u7c7b\u95ee\u9898\uff0c\u7136\u540e\u518d\u9009\u62e9\u5bf9\u5e94\u7684\u65b9\u6cd5\u3002 \u27a4 \u7ec4\u5408\u8ba1\u6570\u9898\u4e2d\uff0c\u201c\u81f3\u5c11\u5b58\u5728\uff08at least\uff09\u201d\u7c7b\u95ee\u9898\u548c\u201c\u90fd\u4e0d\u6ee1\u8db3\u201d\u7c7b\u95ee\u9898\uff0c\u53ef\u4ee5\u8003\u8651\u7b97\u53cd\u9762\uff08complementary counting\uff09\u548c\u5bb9\u65a5\u539f\u7406\uff08PIE\uff09\uff1b\u95f4\u9694\u4e0e\u76f8\u90bb\u7c7b\u95ee\u9898\uff0c\u5206\u914d\u4e0e\u9009\u62e9\u95ee\u9898\uff0c\u53ef\u4ee5\u8003\u8651\u63d2\u677f\u6cd5\uff1b\u7ecf\u8fc7\u5206\u7c7b\u8ba8\u8bba\uff0c \u80fd\u628a\u60c5\u51b5n\u53d8\u4e3an-1\u6216n-2\u6216\u8005\u66f4\u5c0f\u7684\u60c5\u51b5\uff0c\u53ef\u4ee5\u8003\u8651\u9012\u63a8\u65b9\u6cd5\uff1b \u27a4 \u89c2\u5bdf\u9898\u76ee\u4e2d\u662f\u5426\u6709\u5bf9\u79f0\u6027\uff0c\u4ece\u800c\u5316\u7b80\u95ee\u9898\uff1a\u7ec4\u5408\u8ba1\u6570\u9898\u76ee\u53ef\u4ee5\u6839\u636e\u5bf9\u79f0\u6027\u51cf\u5c11\u9700\u8981\u8ba1\u7b97\u7684\u60c5\u51b5\uff08\u4f8b\u5982\u7ed9\u6b63\u65b9\u4f53\u67d3\u62102\u9ed14\u767d\u548c2\u767d4\u9ed1\u7684\u60c5\u51b5\u662f\u4e00\u6837\u7684\uff09\uff1b\u5177\u6709\u5bf9\u79f0\u6027\u7684\u65b9\u7a0b\u7ec4\u53ef\u4ee5\u5c1d\u8bd5\u76f8\u52a0\u6216\u8005\u76f8\u51cf\u518d\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff1b\u5149\u7ebf\u4f20\u64ad\u7c7b\u95ee\u9898\u9700\u8981\u5bf9\u56fe\u5f62\u4f5c\u5bf9\u79f0\u8ba9\u5149\u7ebf\u6cbf\u76f4\u7ebf\u4f20\u64ad\u3002 \u2778\u9009\u62e9\u9898\u7b54\u9898\u6280\u5de7 \u27a4 \u8bbe\u6570\u6cd5\uff1a\u90e8\u5206\u9898\u76ee\u53ef\u4ee5\u81ea\u884c\u5047\u8bbe\u4e00\u4e9b\u4fbf\u4e8e\u89e3\u9898\u7684\u6761\u4ef6 \u2460 \u65b9\u7a0b\u4e2a\u6570\u5c11\u4e8e\u53d8\u91cf\u7684\u65f6\u5019\uff0c\u53ef\u4ee5\u5047\u8bbe\u5176\u4e2d\u67d0\u4e9b\u53d8\u91cf\u4e3a\u7279\u5b9a\u503c\u3002\uff08\u4e0d\u9002\u7528\u4e8e\u6574\u6570\u65b9\u7a0b\uff09\uff1b \u2461 \u9012\u63a8\u6570\u5217\u7684\u524d\u51e0\u9879\u662f\u6bd4\u8f83\u5927\u6216\u8005\u590d\u6742\u7684\u6570\u65f6\uff0c\u53ef\u4ee5\u81ea\u5df1\u5047\u8bbe\u4e00\u4e9b\u7b80\u5355\u503c\u6216\u8005\u76f4\u63a5\u5047\u8bbe\u53d8\u91cf\u8fdb\u884c\u9012\u63a8\uff0c\u53ef\u80fd\u4f1a\u6709\u5468\u671f\u6027\u6216\u8005\u660e\u663e\u7684\u89c4\u5f8b\uff1b \u2462 \u51e0\u4f55\u9898\u4e2d\u7ed9\u51fa\u7684\u4fe1\u606f\u4e0d\u8db3\u4ee5\u786e\u5b9a\u4e00\u4e2a\u56fe\u5f62\u65f6\uff0c\u53ef\u4ee5\u81ea\u5df1\u5047\u8bbe\u4e00\u4e9b\u989d\u5916\u7684\u89d2\u5ea6\u6216\u8005\u8fb9\u957f\u6761\u4ef6\uff1b \u27a4 \u5ea6\u91cf\u6cd5\uff1a\u5bf9\u4e8e\u90e8\u5206\u51e0\u4f55\u9898\uff0c\u5982\u679c\u9898\u76ee\u6761\u4ef6\u80fd\u591f\u552f\u4e00\u786e\u5b9a\u56fe\u5f62\u65f6\uff0c\u53ef\u4ee5\u4f5c\u51fa\u6807\u51c6\u56fe\uff1b\u5f53\u9898\u76ee\u6761\u4ef6\u4e0d\u80fd\u552f\u4e00\u786e\u5b9a\u56fe\u5f62\u65f6\uff0c\u53ef\u4ee5\u753b\u51fa\u67d0\u79cd\u7279\u6b8a\u60c5\u51b5\u4e0b\u7684\u56fe\u5f62\u3002\u800c\u540e\u53ef\u4ee5\u901a\u8fc7\u5ea6\u91cf\u8fb9\u957f\u6216\u8005\u89d2\u5ea6\u76f4\u63a5\u5f97\u5230\u7b54\u6848\uff08\u4f46\u662f\u8fd1\u5e74\u6765\u51fa\u9898\u4eba\u4f1a\u6709\u610f\u89c4\u907f\u8fd9\u79cd\u53ef\u80fd\uff0c\u6240\u4ee5\u80fd\u7528\u5230\u7684\u673a\u4f1a\u4e0d\u5927\uff09 \u27a4 \u627e\u89c4\u5f8b\uff1a\u9012\u63a8\u6570\u5217\u3001\u9012\u63a8\u51fd\u6570\u3001\u65b0\u5b9a\u4e49\u7684\u6570\u8bba\u51fd\u6570\u3001\u7ec4\u5408\u9012\u63a8\u95ee\u9898\u3001\u4e8c\u4eba\u6e38\u620f\u95ee\u9898\uff0c\u90fd\u53ef\u4ee5\u5148\u4ece\u6700\u7b80\u5355\u7684\u521d\u59cb\u60c5\u51b5\u5f00\u59cb\u7814\u7a76\uff0c\u4e89\u53d6\u53d1\u73b0\u89c4\u5f8b\u3002 \u603b\u7ed3 AMC12\u8003\u8bd5\u6db5\u76d6\u4e86\u4ee3\u6570\u3001\u51e0\u4f55\u3001\u6570\u8bba\u3001\u6392\u5217\u7ec4\u5408\u7b49\u591a\u4e2a\u6570\u5b66\u9886\u57df\uff0c\u9700\u8981\u8003\u751f\u719f\u7ec3\u638c\u63e1\u5404\u77e5\u8bc6\u70b9\u3002\u540c\u65f6\uff0c\u7b54\u9898\u65f6\u9700\u6ce8\u610f\u65f6\u95f4\u5206\u914d\uff0c\u786e\u4fdd\u6bcf\u9053\u9898\u90fd\u6709\u8db3\u591f\u7684\u65f6\u95f4\u53bb\u601d\u8003\u548c\u89e3\u7b54\u3002\u6b64\u5916\uff0c\u7b54\u9898\u6280\u5de7\u4e5f\u975e\u5e38\u91cd\u8981\uff0c\u5982\u638c\u63e1\u5e38\u89c1\u7684\u89e3\u9898\u53e3\u8bc0\u548c\u516c\u5f0f\uff0c\u80fd\u591f\u63d0\u9ad8\u89e3\u9898\u6548\u7387\u3002\u6700\u540e\uff0c\u8981\u7279\u522b\u6ce8\u610f\u505a\u9898\u8fc7\u7a0b\u4e2d\u7684\u7ec6\u8282\u95ee\u9898\uff0c\u5982\u4ed4\u7ec6\u8bfb\u9898\u3001\u68c0\u67e5\u7b54\u6848\u7b49\u3002\u53ea\u6709\u77e5\u8bc6\u70b9\u548c\u6280\u5de7\u76f8\u7ed3\u5408\uff0c\u624d\u80fd\u53d6\u5f97\u66f4\u597d\u7684\u6210\u7ee9\u3002 \u60f3\u8981\u4e86\u89e3\u66f4\u591a\u6570\u5b66\u5907\u8003\u8d44\u8baf\uff0c\u70b9\u51fb\u4e0b\u65b9\u5361\u7247\uff0c\u9886\u53d6\u8bfe\u7a0b\u5427~<\/p>\n","protected":false},"author":211806805,"featured_media":47297,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","footnotes":""},"categories":[132672,135358],"tags":[],"class_list":["post-22539","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math-learning-zh","category-math-education-info"],"acf":[],"yoast_head":"\nAMC 12\u8d85\u5168\u77e5\u8bc6\u70b9\u6c47\u603b\u30102025\u66f4\u65b0\u3011 - WuKong Edu Blog<\/title>\n<meta name=\"description\" content=\"AMC12\u8003\u8bd5\u662f\u9488\u5bf912\u5e74\u7ea7\u53ca\u4ee5\u4e0b\u5b66\u751f\u7684\u4e00\u9879\u6570\u5b66\u7ade\u8d5b\uff0c\u8003\u751f\u9700\u719f\u7ec3\u638c\u63e1\u77e5\u8bc6\u70b9\uff0c\u5e76\u6ce8\u610f\u7b54\u9898\u6280\u5de7\u548c\u65f6\u95f4\u5206\u914d\u3002AMC12\u7684\u77e5\u8bc6\u70b9\u90fd\u6709\u54ea\u4e9b\u5462\uff1f\u6709\u4ec0\u4e48\u516c\u5f0f\u9700\u8981\u80cc\u8bf5\uff1f\u4e00\u8d77\u6765\u770b\u770b\uff01\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"AMC 12\u8d85\u5168\u77e5\u8bc6\u70b9\u6c47\u603b\u30102025\u66f4\u65b0\u3011 - WuKong Edu Blog\" \/>\n<meta property=\"og:description\" content=\"AMC12\u8003\u8bd5\u662f\u9488\u5bf912\u5e74\u7ea7\u53ca\u4ee5\u4e0b\u5b66\u751f\u7684\u4e00\u9879\u6570\u5b66\u7ade\u8d5b\uff0c\u8003\u751f\u9700\u719f\u7ec3\u638c\u63e1\u77e5\u8bc6\u70b9\uff0c\u5e76\u6ce8\u610f\u7b54\u9898\u6280\u5de7\u548c\u65f6\u95f4\u5206\u914d\u3002AMC12\u7684\u77e5\u8bc6\u70b9\u90fd\u6709\u54ea\u4e9b\u5462\uff1f\u6709\u4ec0\u4e48\u516c\u5f0f\u9700\u8981\u80cc\u8bf5\uff1f\u4e00\u8d77\u6765\u770b\u770b\uff01\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wukongsch.com\/blog\/zh\/amc-12-noledge-points-post-22539\/\" \/>\n<meta property=\"og:site_name\" content=\"WuKong Edu Blog\" \/>\n<meta property=\"article:published_time\" content=\"2024-01-19T06:09:28+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-06-16T09:17:15+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2024\/01\/\u8be2\u95ee\u4e2d\u6587\u65e9\u4e0a\u597d\u7684\u8bf4\u6cd5-21-1024x1024.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1024\" \/>\n\t<meta property=\"og:image:height\" content=\"1024\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"James | WuKong Math Teacher\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"James | WuKong Math Teacher\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wukongsch.com\/blog\/zh\/amc-12-noledge-points-post-22539\/\",\"url\":\"https:\/\/www.wukongsch.com\/blog\/zh\/amc-12-noledge-points-post-22539\/\",\"name\":\"AMC 12\u8d85\u5168\u77e5\u8bc6\u70b9\u6c47\u603b\u30102025\u66f4\u65b0\u3011 - WuKong Edu Blog\",\"isPartOf\":{\"@id\":\"https:\/\/www.wukongsch.com\/blog\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.wukongsch.com\/blog\/zh\/amc-12-noledge-points-post-22539\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/www.wukongsch.com\/blog\/zh\/amc-12-noledge-points-post-22539\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2024\/01\/\u8be2\u95ee\u4e2d\u6587\u65e9\u4e0a\u597d\u7684\u8bf4\u6cd5-21.png\",\"datePublished\":\"2024-01-19T06:09:28+00:00\",\"dateModified\":\"2025-06-16T09:17:15+00:00\",\"author\":{\"@id\":\"https:\/\/www.wukongsch.com\/blog\/#\/schema\/person\/577c4f1bd6e736f4ad808618c36f30c6\"},\"description\":\"AMC12\u8003\u8bd5\u662f\u9488\u5bf912\u5e74\u7ea7\u53ca\u4ee5\u4e0b\u5b66\u751f\u7684\u4e00\u9879\u6570\u5b66\u7ade\u8d5b\uff0c\u8003\u751f\u9700\u719f\u7ec3\u638c\u63e1\u77e5\u8bc6\u70b9\uff0c\u5e76\u6ce8\u610f\u7b54\u9898\u6280\u5de7\u548c\u65f6\u95f4\u5206\u914d\u3002AMC12\u7684\u77e5\u8bc6\u70b9\u90fd\u6709\u54ea\u4e9b\u5462\uff1f\u6709\u4ec0\u4e48\u516c\u5f0f\u9700\u8981\u80cc\u8bf5\uff1f\u4e00\u8d77\u6765\u770b\u770b\uff01\",\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.wukongsch.com\/blog\/zh\/amc-12-noledge-points-post-22539\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.wukongsch.com\/blog\/zh\/amc-12-noledge-points-post-22539\/#primaryimage\",\"url\":\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2024\/01\/\u8be2\u95ee\u4e2d\u6587\u65e9\u4e0a\u597d\u7684\u8bf4\u6cd5-21.png\",\"contentUrl\":\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2024\/01\/\u8be2\u95ee\u4e2d\u6587\u65e9\u4e0a\u597d\u7684\u8bf4\u6cd5-21.png\",\"width\":1328,\"height\":1328},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.wukongsch.com\/blog\/#website\",\"url\":\"https:\/\/www.wukongsch.com\/blog\/\",\"name\":\"WuKong Edu Blog\",\"description\":\"Get latest news of WuKong Education and Tips of WuKong Chinese, Math & English ELA. We also share useful tips for Chinese learning & International Math & English reading, writing learning for 3-18 students.\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.wukongsch.com\/blog\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.wukongsch.com\/blog\/#\/schema\/person\/577c4f1bd6e736f4ad808618c36f30c6\",\"name\":\"James | WuKong Math Teacher\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.wukongsch.com\/blog\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/litespeed\/avatar\/e3888295fb9b47750d9ad85a5a9bf15d.jpg?ver=1777966723\",\"contentUrl\":\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/litespeed\/avatar\/e3888295fb9b47750d9ad85a5a9bf15d.jpg?ver=1777966723\",\"caption\":\"James | WuKong Math Teacher\"},\"description\":\"Graduated from Columbia University in the United States and has rich practical experience in mathematics competitions' teaching, including Math Kangaroo, AMC... He teaches students the ways to flexible thinking and quick thinking in sloving math questions, and he is good at inspiring and guiding students to think about mathematical problems and find solutions.\",\"url\":\"https:\/\/www.wukongsch.com\/blog\/author\/james\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"AMC 12\u8d85\u5168\u77e5\u8bc6\u70b9\u6c47\u603b\u30102025\u66f4\u65b0\u3011 - WuKong Edu Blog","description":"AMC12\u8003\u8bd5\u662f\u9488\u5bf912\u5e74\u7ea7\u53ca\u4ee5\u4e0b\u5b66\u751f\u7684\u4e00\u9879\u6570\u5b66\u7ade\u8d5b\uff0c\u8003\u751f\u9700\u719f\u7ec3\u638c\u63e1\u77e5\u8bc6\u70b9\uff0c\u5e76\u6ce8\u610f\u7b54\u9898\u6280\u5de7\u548c\u65f6\u95f4\u5206\u914d\u3002AMC12\u7684\u77e5\u8bc6\u70b9\u90fd\u6709\u54ea\u4e9b\u5462\uff1f\u6709\u4ec0\u4e48\u516c\u5f0f\u9700\u8981\u80cc\u8bf5\uff1f\u4e00\u8d77\u6765\u770b\u770b\uff01","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"og_locale":"en_US","og_type":"article","og_title":"AMC 12\u8d85\u5168\u77e5\u8bc6\u70b9\u6c47\u603b\u30102025\u66f4\u65b0\u3011 - WuKong Edu Blog","og_description":"AMC12\u8003\u8bd5\u662f\u9488\u5bf912\u5e74\u7ea7\u53ca\u4ee5\u4e0b\u5b66\u751f\u7684\u4e00\u9879\u6570\u5b66\u7ade\u8d5b\uff0c\u8003\u751f\u9700\u719f\u7ec3\u638c\u63e1\u77e5\u8bc6\u70b9\uff0c\u5e76\u6ce8\u610f\u7b54\u9898\u6280\u5de7\u548c\u65f6\u95f4\u5206\u914d\u3002AMC12\u7684\u77e5\u8bc6\u70b9\u90fd\u6709\u54ea\u4e9b\u5462\uff1f\u6709\u4ec0\u4e48\u516c\u5f0f\u9700\u8981\u80cc\u8bf5\uff1f\u4e00\u8d77\u6765\u770b\u770b\uff01","og_url":"https:\/\/www.wukongsch.com\/blog\/zh\/amc-12-noledge-points-post-22539\/","og_site_name":"WuKong Edu Blog","article_published_time":"2024-01-19T06:09:28+00:00","article_modified_time":"2025-06-16T09:17:15+00:00","og_image":[{"width":1024,"height":1024,"url":"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2024\/01\/\u8be2\u95ee\u4e2d\u6587\u65e9\u4e0a\u597d\u7684\u8bf4\u6cd5-21-1024x1024.png","type":"image\/png"}],"author":"James | WuKong Math Teacher","twitter_card":"summary_large_image","twitter_misc":{"Written by":"James | WuKong Math Teacher","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.wukongsch.com\/blog\/zh\/amc-12-noledge-points-post-22539\/","url":"https:\/\/www.wukongsch.com\/blog\/zh\/amc-12-noledge-points-post-22539\/","name":"AMC 12\u8d85\u5168\u77e5\u8bc6\u70b9\u6c47\u603b\u30102025\u66f4\u65b0\u3011 - WuKong Edu Blog","isPartOf":{"@id":"https:\/\/www.wukongsch.com\/blog\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.wukongsch.com\/blog\/zh\/amc-12-noledge-points-post-22539\/#primaryimage"},"image":{"@id":"https:\/\/www.wukongsch.com\/blog\/zh\/amc-12-noledge-points-post-22539\/#primaryimage"},"thumbnailUrl":"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2024\/01\/\u8be2\u95ee\u4e2d\u6587\u65e9\u4e0a\u597d\u7684\u8bf4\u6cd5-21.png","datePublished":"2024-01-19T06:09:28+00:00","dateModified":"2025-06-16T09:17:15+00:00","author":{"@id":"https:\/\/www.wukongsch.com\/blog\/#\/schema\/person\/577c4f1bd6e736f4ad808618c36f30c6"},"description":"AMC12\u8003\u8bd5\u662f\u9488\u5bf912\u5e74\u7ea7\u53ca\u4ee5\u4e0b\u5b66\u751f\u7684\u4e00\u9879\u6570\u5b66\u7ade\u8d5b\uff0c\u8003\u751f\u9700\u719f\u7ec3\u638c\u63e1\u77e5\u8bc6\u70b9\uff0c\u5e76\u6ce8\u610f\u7b54\u9898\u6280\u5de7\u548c\u65f6\u95f4\u5206\u914d\u3002AMC12\u7684\u77e5\u8bc6\u70b9\u90fd\u6709\u54ea\u4e9b\u5462\uff1f\u6709\u4ec0\u4e48\u516c\u5f0f\u9700\u8981\u80cc\u8bf5\uff1f\u4e00\u8d77\u6765\u770b\u770b\uff01","inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.wukongsch.com\/blog\/zh\/amc-12-noledge-points-post-22539\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.wukongsch.com\/blog\/zh\/amc-12-noledge-points-post-22539\/#primaryimage","url":"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2024\/01\/\u8be2\u95ee\u4e2d\u6587\u65e9\u4e0a\u597d\u7684\u8bf4\u6cd5-21.png","contentUrl":"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2024\/01\/\u8be2\u95ee\u4e2d\u6587\u65e9\u4e0a\u597d\u7684\u8bf4\u6cd5-21.png","width":1328,"height":1328},{"@type":"WebSite","@id":"https:\/\/www.wukongsch.com\/blog\/#website","url":"https:\/\/www.wukongsch.com\/blog\/","name":"WuKong Edu Blog","description":"Get latest news of WuKong Education and Tips of WuKong Chinese, Math & English ELA. We also share useful tips for Chinese learning & International Math & English reading, writing learning for 3-18 students.","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.wukongsch.com\/blog\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/www.wukongsch.com\/blog\/#\/schema\/person\/577c4f1bd6e736f4ad808618c36f30c6","name":"James | WuKong Math Teacher","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.wukongsch.com\/blog\/#\/schema\/person\/image\/","url":"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/litespeed\/avatar\/e3888295fb9b47750d9ad85a5a9bf15d.jpg?ver=1777966723","contentUrl":"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/litespeed\/avatar\/e3888295fb9b47750d9ad85a5a9bf15d.jpg?ver=1777966723","caption":"James | WuKong Math Teacher"},"description":"Graduated from Columbia University in the United States and has rich practical experience in mathematics competitions' teaching, including Math Kangaroo, AMC... He teaches students the ways to flexible thinking and quick thinking in sloving math questions, and he is good at inspiring and guiding students to think about mathematical problems and find solutions.","url":"https:\/\/www.wukongsch.com\/blog\/author\/james\/"}]}},"amp_enabled":false,"read_time":"5","_links":{"self":[{"href":"https:\/\/wp-more.wukongedu.net\/blog\/wp-json\/wp\/v2\/posts\/22539","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp-more.wukongedu.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp-more.wukongedu.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp-more.wukongedu.net\/blog\/wp-json\/wp\/v2\/users\/211806805"}],"replies":[{"embeddable":true,"href":"https:\/\/wp-more.wukongedu.net\/blog\/wp-json\/wp\/v2\/comments?post=22539"}],"version-history":[{"count":1,"href":"https:\/\/wp-more.wukongedu.net\/blog\/wp-json\/wp\/v2\/posts\/22539\/revisions"}],"predecessor-version":[{"id":47298,"href":"https:\/\/wp-more.wukongedu.net\/blog\/wp-json\/wp\/v2\/posts\/22539\/revisions\/47298"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wp-more.wukongedu.net\/blog\/wp-json\/wp\/v2\/media\/47297"}],"wp:attachment":[{"href":"https:\/\/wp-more.wukongedu.net\/blog\/wp-json\/wp\/v2\/media?parent=22539"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp-more.wukongedu.net\/blog\/wp-json\/wp\/v2\/categories?post=22539"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp-more.wukongedu.net\/blog\/wp-json\/wp\/v2\/tags?post=22539"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}