{"id":105292,"date":"2026-09-15T07:56:55","date_gmt":"2026-09-14T23:56:55","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/105292.html"},"modified":"2026-09-15T07:56:55","modified_gmt":"2026-09-14T23:56:55","slug":"csp-j-%e5%88%9d%e8%b5%9b%ef%bc%88%e4%bb%a5%e6%bb%a1%e5%88%86%e4%b8%ba%e7%9b%ae%e6%a0%87%ef%bc%89%ef%bc%9a%e7%ac%ac%e5%9b%9b%e5%8d%81%e4%b8%89%e8%af%be%e3%80%8a%e9%9b%86%e5%90%88%e4%b8%8e%e5%ad%90","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/105292.html","title":{"rendered":"CSP-J \u521d\u8d5b\uff08\u4ee5\u6ee1\u5206\u4e3a\u76ee\u6807\uff09\uff1a\u7b2c\u56db\u5341\u4e09\u8bfe\u300a\u96c6\u5408\u4e0e\u5b50\u96c6\u2014\u2014\u4ece\u201c\u9009\u4e0d\u9009\u201d\u5230 2^n\u300b"},"content":{"rendered":"<p style=\"text-align:center\"><img decoding=\"async\" alt=\"\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235652-6aa889c46a8bf.png\" \/><\/p>\n<hr \/>\n<p>\u524d\u9762\u4e09\u8bfe\u5df2\u7ecf\u628a\u5206\u7c7b\u8ba1\u6570\u3001\u5206\u6b65\u8ba1\u6570\u3001\u6392\u5217\u7ec4\u5408\u3001\u6346\u7ed1\u6cd5\u3001\u63d2\u7a7a\u6cd5\u3001\u81f3\u5c11\/\u81f3\u591a\u3001\u8865\u96c6\u4e0e\u6392\u9664\u6cd5\u4e32\u4e86\u8d77\u6765\u3002<\/p>\n<p>\u672c\u8bfe\u6211\u4eec\u628a\u8fd9\u4e9b\u8ba1\u6570\u601d\u60f3\u8fdb\u4e00\u6b65\u63d0\u5347\u5230\u96c6\u5408\u4e0e\u5b50\u96c6\u3002\u8fd9\u4e00\u8bfe\u7684\u91cd\u70b9\u4e0d\u662f\u8ba9\u540c\u5b66\u4eec\u80cc\u5f88\u591a\u96c6\u5408\u7b26\u53f7&#xff0c;\u800c\u662f\u8ba9\u5927\u5bb6\u660e\u767d&#xff1a;<\/p>\n<p>\u96c6\u5408\u662f\u5728\u201c\u6570\u4e1c\u897f\u201d&#xff0c;\u5b50\u96c6\u662f\u5728\u201c\u505a\u9009\u62e9\u201d\u3002<\/p>\n<p>\u800c\u201c\u6bcf\u4e2a\u5143\u7d20\u9009\u4e0d\u9009\u201d&#xff0c;\u5c31\u4f1a\u4ea7\u751f&#xff1a;<\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\\\\boxed{2^n}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c51cbec.png\" \/><\/p>\n<h2>\u7b2c\u56db\u5341\u4e09\u8bfe&#xff1a;\u96c6\u5408\u4e0e\u5b50\u96c6\u2014\u2014\u4ece\u201c\u9009\u4e0d\u9009\u201d\u5230 2^n<\/h2>\n<hr \/>\n<h2>\u4e00\u3001\u5148\u4ece\u4e00\u4e2a\u201c\u9b54\u6cd5\u96c6\u5408\u201d\u5f00\u59cb<\/h2>\n<p>\u5c0f\u660e\u67094\u5f20\u5361\u7247&#xff1a;<\/p>\n<p>1\u53f7&#xff1a;&#x1f431;<br \/>\n2\u53f7&#xff1a;&#x1f436;<br \/>\n3\u53f7&#xff1a;&#x1f430;<br \/>\n4\u53f7&#xff1a;&#x1f43c;<\/p>\n<p>\u73b0\u5728\u8001\u5e08\u95ee&#xff1a;<\/p>\n<p>\u4ece\u8fd94\u5f20\u5361\u7247\u4e2d&#xff0c;\u4efb\u610f\u6311\u4e00\u4e9b\u51fa\u6765&#xff0c;\u53ef\u4ee5\u6709\u591a\u5c11\u79cd\u4e0d\u540c\u7684\u9009\u62e9&#xff1f;<\/p>\n<p>\u6ce8\u610f&#xff1a;<\/p>\n<p>\u53ef\u4ee5\u4e00\u5f20\u90fd\u4e0d\u9009&#xff0c;\u4e5f\u53ef\u4ee5\u5168\u90e8\u9009\u3002<\/p>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>\u4ec0\u4e48\u90fd\u4e0d\u9009<br \/>\n\u53ea\u9009&#x1f431;<br \/>\n\u53ea\u9009&#x1f436;<br \/>\n&#x1f431;&#x1f436;<br \/>\n&#x1f431;&#x1f430;<br \/>\n&#x1f436;&#x1f43c;<br \/>\n\u2026\u2026<br \/>\n\u56db\u5f20\u5168\u90e8\u9009<\/p>\n<p>\u95ee\u9898\u6765\u4e86&#xff1a;<\/p>\n<p>\u4e00\u5171\u6709\u591a\u5c11\u79cd&#xff1f;<\/p>\n<hr \/>\n<h2>\u4e8c\u3001\u4e0d\u8981\u4e00\u4e2a\u4e00\u4e2a\u5217&#xff01;<\/h2>\n<p>\u5982\u679c\u53ea\u67094\u4e2a\u5143\u7d20&#xff0c;\u53ef\u4ee5\u5217\u3002<\/p>\n<p>\u4f46\u662f\u5982\u679c\u6709&#xff1a;<\/p>\n<p>10\u4e2a<br \/>\n20\u4e2a<br \/>\n100\u4e2a<\/p>\n<p>\u8fd8\u80fd\u4e00\u4e2a\u4e00\u4e2a\u5217\u5417&#xff1f;<\/p>\n<p>\u5f53\u7136\u4e0d\u884c\u3002<\/p>\n<p>\u6240\u4ee5\u6211\u4eec\u9700\u8981\u627e\u5230\u89c4\u5f8b\u3002<\/p>\n<hr \/>\n<h2>\u4e09\u3001\u6bcf\u4e2a\u5143\u7d20\u53ea\u6709\u4e24\u4e2a\u9009\u62e9<\/h2>\n<p>\u5bf9\u4e8e&#x1f431;\u6765\u8bf4&#xff1a;<\/p>\n<p>\u9009<br \/>\n\u4e0d\u9009<\/p>\n<p>\u53ea\u67092\u79cd\u53ef\u80fd\u3002<\/p>\n<p>\u5bf9\u4e8e&#x1f436;&#xff1a;<\/p>\n<p>\u9009<br \/>\n\u4e0d\u9009<\/p>\n<p>\u4e5f\u662f2\u79cd\u3002<\/p>\n<p>\u5bf9\u4e8e&#x1f430;&#xff1a;<\/p>\n<p>\u9009<br \/>\n\u4e0d\u9009<\/p>\n<p>\u8fd8\u662f2\u79cd\u3002<\/p>\n<p>\u5bf9\u4e8e&#x1f43c;&#xff1a;<\/p>\n<p>\u9009<br \/>\n\u4e0d\u9009<\/p>\n<p>\u8fd8\u662f2\u79cd\u3002<\/p>\n<p>\u4e8e\u662f&#xff1a;<\/p>\n<p>\u7b2c1\u4e2a&#xff1a;2\u79cd<br \/>\n\u7b2c2\u4e2a&#xff1a;2\u79cd<br \/>\n\u7b2c3\u4e2a&#xff1a;2\u79cd<br \/>\n\u7b2c4\u4e2a&#xff1a;2\u79cd<\/p>\n<p>\u6839\u636e\u6211\u4eec\u7b2c42\u8bfe\u5b66\u8fc7\u7684&#xff1a;<\/p>\n<p>\u5206\u6b65\u8ba1\u6570 \u2192 \u76f8\u4e58<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>2\u00d72\u00d72\u00d72<\/p>\n<p>\u5373&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"\\\\boxed{2^4=16}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c5280ee.png\" \/><\/p>\n<hr \/>\n<h2>\u56db\u3001\u8fd9\u5c31\u662f\u201c\u5b50\u96c6\u4e2a\u6570\u201d<\/h2>\n<p>\u4e00\u4e2a\u96c6\u5408\u6709 n \u4e2a\u5143\u7d20\u3002<\/p>\n<p>\u5b83\u7684\u6240\u6709\u5b50\u96c6\u6570\u91cf\u662f&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"\\\\boxed{2^n}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c51cbec.png\" \/><\/p>\n<p>\u4e3a\u4ec0\u4e48&#xff1f;<\/p>\n<p>\u56e0\u4e3a&#xff1a;<\/p>\n<p>\u6bcf\u4e00\u4e2a\u5143\u7d20&#xff0c;\u90fd\u53ea\u6709\u201c\u9009\u201d\u548c\u201c\u4e0d\u9009\u201d\u4e24\u79cd\u72b6\u6001\u3002<\/p>\n<p>\u4e8e\u662f&#xff1a;<\/p>\n<p>2\u00d72\u00d7\u22ef\u00d72\u23dfn\u4e2a &#061;\u00a0 2^n<\/p>\n<hr \/>\n<h2>\u4e94\u3001\u6700\u91cd\u8981\u7684\u4e00\u4e2a\u95ee\u9898&#xff1a;\u7a7a\u96c6\u7b97\u4e0d\u7b97&#xff1f;<\/h2>\n<p>\u4f8b\u5982\u96c6\u5408&#xff1a;<\/p>\n<p>A &#061; {1,2,3}\u00a0<\/p>\n<p>\u5b83\u7684\u5b50\u96c6\u6709\u54ea\u4e9b&#xff1f;<\/p>\n<p>{}<br \/>\n{1}<br \/>\n{2}<br \/>\n{3}<br \/>\n{1,2}<br \/>\n{1,3}<br \/>\n{2,3}<br \/>\n{1,2,3}<\/p>\n<p>\u4e00\u5171&#xff1a;<\/p>\n<p>8<\/p>\n<p>\u4e2a\u3002<\/p>\n<p>\u4e5f\u5c31\u662f&#xff1a;<\/p>\n<p>2^3 &#061; 8<\/p>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<p>{}<\/p>\n<p>\u5c31\u662f&#xff1a;<\/p>\n<p>\u7a7a\u96c6<\/p>\n<hr \/>\n<p>\u7a7a\u96c6\u4e5f\u662f\u4efb\u4f55\u96c6\u5408\u7684\u5b50\u96c6\u3002<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>\u8ba1\u7b97\u5b50\u96c6\u6570\u91cf\u65f6&#xff0c;\u4e00\u5b9a\u8981\u628a\u7a7a\u96c6\u7b97\u8fdb\u53bb\u3002<\/p>\n<hr \/>\n<h2>\u516d\u3001\u521d\u5b66\u8005\u5bb9\u6613\u6df7\u6dc6&#xff1a;\u5b50\u96c6\u548c\u771f\u5b50\u96c6<\/h2>\n<p>\u8fd9\u662fCSP-J\u521d\u8d5b\u975e\u5e38\u503c\u5f97\u6ce8\u610f\u7684\u6982\u5ff5\u3002<\/p>\n<p>\u5047\u8bbe&#xff1a;<\/p>\n<p>A &#061; {1,2,3}<\/p>\n<p>\u90a3\u4e48&#xff1a;<\/p>\n<p>{1,2}<\/p>\n<p>\u662fA\u7684\u5b50\u96c6\u3002<\/p>\n<p>\u800c&#xff1a;<\/p>\n<p>{1,2,3}<\/p>\n<p>\u4e5f\u662fA\u7684\u5b50\u96c6\u3002<\/p>\n<p>\u56e0\u4e3a\u4e00\u4e2a\u96c6\u5408\u672c\u8eab\u4e5f\u662f\u81ea\u5df1\u7684\u5b50\u96c6\u3002<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>\u5b50\u96c6\u5305\u62ec\u96c6\u5408\u672c\u8eab<\/p>\n<hr \/>\n<h2>\u4e03\u3001\u4ec0\u4e48\u662f\u771f\u5b50\u96c6&#xff1f;<\/h2>\n<p>\u771f\u5b50\u96c6\u5c31\u662f&#xff1a;<\/p>\n<p>\u662f\u5b50\u96c6&#xff0c;\u4f46\u662f\u4e0d\u80fd\u548c\u539f\u96c6\u5408\u5b8c\u5168\u4e00\u6837\u3002<\/p>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>{1,2}<\/p>\n<p>\u662fA\u7684\u771f\u5b50\u96c6\u3002<\/p>\n<p>\u4f46\u662f&#xff1a;<\/p>\n<p>{1,2,3}<\/p>\n<p>\u4e0d\u662fA\u7684\u771f\u5b50\u96c6\u3002<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>\u5982\u679c\u96c6\u5408\u6709 n\u00a0\u4e2a\u5143\u7d20&#xff1a;<\/p>\n<h4>\u5b50\u96c6<\/h4>\n<p><img decoding=\"async\" alt=\"\\\\boxed{2^n}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c51cbec.png\" \/><\/p>\n<h4>\u771f\u5b50\u96c6<\/h4>\n<p>\u628a\u96c6\u5408\u81ea\u5df1\u53bb\u6389&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"\\\\boxed{2^n-1}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c53308b.png\" \/><\/p>\n<hr \/>\n<h2>\u516b\u3001\u7528\u201c\u5c0f\u76d2\u5b50\u201d\u7406\u89e3\u5b50\u96c6<\/h2>\n<p>\u53ef\u4ee5\u7ee7\u7eed\u4f7f\u7528\u6211\u4eec\u4e00\u76f4\u7ed9\u540c\u5b66\u4eec\u8bb2\u7684\u201c\u76d2\u5b50\u201d\u601d\u7ef4\u3002<\/p>\n<p>\u96c6\u5408&#xff1a;<\/p>\n<p>\u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510<br \/>\n\u2502 1   2   3   4 \u2502<br \/>\n\u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518<\/p>\n<p>\u6784\u9020\u4e00\u4e2a\u5b50\u96c6&#xff0c;\u5c31\u76f8\u5f53\u4e8e&#xff1a;<\/p>\n<p>\u5bf9\u6bcf\u4e2a\u6570\u5b57\u505a\u4e00\u6b21\u9009\u62e9\u3002<\/p>\n<p>1&#xff1a;\u62ff \/ \u4e0d\u62ff<br \/>\n2&#xff1a;\u62ff \/ \u4e0d\u62ff<br \/>\n3&#xff1a;\u62ff \/ \u4e0d\u62ff<br \/>\n4&#xff1a;\u62ff \/ \u4e0d\u62ff<\/p>\n<p>\u6bcf\u4e2a\u5143\u7d20&#xff1a;<\/p>\n<p>2\u79cd<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>2^4<\/p>\n<hr \/>\n<h2>\u4e5d\u3001\u5b50\u96c6\u4e3a\u4ec0\u4e48\u548c\u524d\u9762\u8bfe\u4e2d\u7684\u201c\u5206\u6b65\u8ba1\u6570\u201d\u6709\u5173\u7cfb&#xff1f;<\/h2>\n<p>\u56e0\u4e3a&#xff1a;<\/p>\n<p>\u9009\u62e9\u6bcf\u4e00\u4e2a\u5143\u7d20\u662f\u5426\u8fdb\u5165\u5b50\u96c6&#xff0c;\u5c31\u662f\u4e00\u4e2a\u6b65\u9aa4\u3002<\/p>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>\u51b3\u5b9a1\u8fdb\u4e0d\u8fdb<br \/>\n        \u2193<br \/>\n\u51b3\u5b9a2\u8fdb\u4e0d\u8fdb<br \/>\n        \u2193<br \/>\n\u51b3\u5b9a3\u8fdb\u4e0d\u8fdb<br \/>\n        \u2193<br \/>\n\u2026\u2026<\/p>\n<p>\u6bcf\u4e00\u6b65&#xff1a;<\/p>\n<p>2\u79cd<\/p>\n<p>\u56e0\u6b64&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"2\\\\times2\\\\times\\\\cdots\\\\times2\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c53e49b.png\" \/><\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"\\\\boxed{2^n}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c51cbec.png\" \/><\/p>\n<p>\u8fd9\u5c31\u662f\u6570\u5b66\u77e5\u8bc6\u4e4b\u95f4\u7684\u8fde\u63a5\u3002<\/p>\n<hr \/>\n<h2>\u5341\u3001\u5982\u679c\u8981\u6c42\u201c\u6070\u597d\u90092\u4e2a\u201d\u5462&#xff1f;<\/h2>\n<p>\u73b0\u5728\u96c6\u5408\u6709&#xff1a;<\/p>\n<p>{1,2,3,4,5}\u00a0<\/p>\n<p>\u95ee&#xff1a;<\/p>\n<p>\u6709\u591a\u5c11\u4e2a\u5b50\u96c6\u6070\u597d\u5305\u542b2\u4e2a\u5143\u7d20&#xff1f;<\/p>\n<p>\u8fd9\u65f6\u5019\u5c31\u4e0d\u662f 2^5 \u4e86\u3002<\/p>\n<p>\u56e0\u4e3a\u6211\u4eec\u8981\u6c42&#xff1a;<\/p>\n<p>\u6070\u597d\u90092\u4e2a\u3002<\/p>\n<p>\u4e5f\u5c31\u662f\u4ece5\u4e2a\u5143\u7d20\u4e2d&#xff1a;<\/p>\n<p>\u90092\u4e2a<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"C_5^2 =\\\\frac{5\\\\times4}{2} =\\\\boxed{10}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c54947d.png\" \/><\/p>\n<hr \/>\n<h2>\u5341\u4e00\u3001\u8fd9\u5c31\u628a\u201c\u5b50\u96c6\u201d\u548c\u201c\u7ec4\u5408\u201d\u8fde\u63a5\u8d77\u6765\u4e86<\/h2>\n<p>\u6240\u6709\u5b50\u96c6&#xff1a;\u6bcf\u4e2a\u5143\u7d20\u9009\/\u4e0d\u9009<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>2^n<\/p>\n<p>\u800c&#xff1a;<\/p>\n<p>\u6070\u597d\u9009k\u4e2a\u5143\u7d20&#xff1a;\u4ecen\u4e2a\u5143\u7d20\u4e2d\u9009\u62e9k\u4e2a<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"C_n^k\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c5542c2.png\" \/><\/p>\n<hr \/>\n<h2>\u5341\u4e8c\u3001\u4e3e\u4e00\u4e2a\u5b8c\u6574\u4f8b\u5b50<\/h2>\n<p>\u96c6\u5408&#xff1a;<\/p>\n<p>A&#061;{1,2,3,4}<\/p>\n<p>\u4e00\u5171\u67094\u4e2a\u5143\u7d20\u3002<\/p>\n<hr \/>\n<h4>\u6240\u6709\u5b50\u96c6<\/h4>\n<p>2^4&#061;16<\/p>\n<hr \/>\n<h4>\u6070\u597d\u67091\u4e2a\u5143\u7d20\u7684\u5b50\u96c6<\/h4>\n<p><img decoding=\"async\" alt=\"C_4^1=4\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c55f127.png\" \/><\/p>\n<hr \/>\n<h4>\u6070\u597d\u67092\u4e2a\u5143\u7d20\u7684\u5b50\u96c6<\/h4>\n<p><img decoding=\"async\" alt=\"C_4^2=6\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c56a745.png\" \/><\/p>\n<hr \/>\n<h4>\u6070\u597d\u67093\u4e2a\u5143\u7d20\u7684\u5b50\u96c6<\/h4>\n<p><img decoding=\"async\" alt=\"C_4^3=4\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c575df5.png\" \/><\/p>\n<hr \/>\n<h4>\u6070\u597d\u67094\u4e2a\u5143\u7d20\u7684\u5b50\u96c6<\/h4>\n<p><img decoding=\"async\" alt=\"C_4^4=1\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c581153.png\" \/><\/p>\n<hr \/>\n<p>\u628a\u5b83\u4eec\u52a0\u8d77\u6765&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"C_4^0+C_4^1+C_4^2+C_4^3+C_4^4\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c58c1a8.png\" \/><\/p>\n<p>\u5f97\u5230&#xff1a;<\/p>\n<p>1 &#043; 4 &#043; 6 &#043; 4 &#043; 1&#061;16<\/p>\n<p>\u6070\u597d\u7b49\u4e8e&#xff1a;<\/p>\n<p>2^4<\/p>\n<hr \/>\n<h2>\u5341\u4e09\u3001\u8fd9\u5c31\u662f\u4e00\u4e2a\u975e\u5e38\u6f02\u4eae\u7684\u6570\u5b66\u89c4\u5f8b<\/h2>\n<p><img decoding=\"async\" alt=\"\\\\boxed{ C_n^0+C_n^1+C_n^2+\\\\cdots+C_n^n=2^n }\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c59836f.png\" \/><\/p>\n<p>\u8fd9\u5176\u5b9e\u5c31\u662f\u4e8c\u9879\u5f0f\u5b9a\u7406\u4e2d\u975e\u5e38\u91cd\u8981\u7684\u4e00\u79cd\u60c5\u51b5\u3002<\/p>\n<p>\u540c\u5b66\u4eec\u5df2\u7ecf\u5b66\u4e60\u8fc7\u6768\u8f89\u4e09\u89d2&#xff0c;\u8fd8\u53ef\u4ee5\u628a\u5b83\u8054\u7cfb\u8d77\u6765&#xff1a;<\/p>\n<p>             1<br \/>\n           1   1<br \/>\n         1   2   1<br \/>\n       1   3   3   1<br \/>\n     1   4   6   4   1<\/p>\n<p>\u7b2c\u56db\u884c&#xff1a;<\/p>\n<p>1&#043;4&#043;6&#043;4&#043;1&#061;16<\/p>\n<p>\u4e5f\u5c31\u662f&#xff1a;<\/p>\n<p>2^4<\/p>\n<hr \/>\n<h2>\u5341\u56db\u3001\u4ece\u201c\u5b50\u96c6\u201d\u8fdb\u5165\u96c6\u5408\u8fd0\u7b97<\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u5f00\u59cb\u5b66\u4e60\u96c6\u5408\u6700\u5e38\u89c1\u7684\u4e09\u4e2a\u64cd\u4f5c&#xff1a;<\/p>\n<p>\u4ea4\u96c6<br \/>\n\u5e76\u96c6<br \/>\n\u8865\u96c6<\/p>\n<p>\u53ef\u4ee5\u7528\u4e24\u4e2a\u201c\u9b54\u6cd5\u5708\u201d\u6765\u7406\u89e3\u3002<\/p>\n<hr \/>\n<h2>\u5341\u4e94\u3001\u5e76\u96c6&#xff1a;\u4e24\u4e2a\u96c6\u5408\u201c\u5408\u8d77\u6765\u201d<\/h2>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>A&#061;{1,2,3}\u00a0\u00a0\u00a0B&#061;{3,4,5}\u00a0<\/p>\n<p>\u628a\u4e24\u4e2a\u96c6\u5408\u653e\u5728\u4e00\u8d77&#xff1a;<\/p>\n<p>A&#xff1a;1 2 3<br \/>\nB&#xff1a;    3 4 5<\/p>\n<p>\u5e76\u96c6\u5c31\u662f&#xff1a;<\/p>\n<p>A\u6216B\u4e2d\u7684\u5143\u7d20\u90fd\u8981\u3002<\/p>\n<p>\u8bb0\u4f5c&#xff1a;<\/p>\n<p>A\u222aB<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>A\u222aB&#061;{1,2,3,4,5}\u00a0<\/p>\n<hr \/>\n<h2>\u5341\u516d\u3001\u4e3a\u4ec0\u4e483\u53ea\u80fd\u5199\u4e00\u6b21&#xff1f;<\/h2>\n<p>\u56e0\u4e3a\u96c6\u5408\u4e2d&#xff1a;<\/p>\n<p>\u76f8\u540c\u5143\u7d20\u4e0d\u80fd\u91cd\u590d\u8bb0\u5f55\u3002<\/p>\n<p>\u867d\u7136&#xff1a;<\/p>\n<p>A\u91cc\u67093<br \/>\nB\u91cc\u4e5f\u67093<\/p>\n<p>\u4f46\u662f\u5e76\u96c6\u4ecd\u7136\u53ea\u6709\u4e00\u4e2a3\u3002<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>A\u222aB&#061;{1,2,3,4,5}\u00a0<\/p>\n<p>\u800c\u4e0d\u662f&#xff1a;<\/p>\n<p>{1,2,3,3,4,5}<\/p>\n<hr \/>\n<h2>\u5341\u4e03\u3001\u4ea4\u96c6&#xff1a;\u4e24\u4e2a\u96c6\u5408\u201c\u5171\u540c\u62e5\u6709\u201d<\/h2>\n<p>\u8fd8\u662f&#xff1a;<\/p>\n<p>A&#061;{1,2,3}\u00a0\u00a0\u00a0B&#061;{3,4,5}\u00a0<\/p>\n<p>A\u548cB\u5171\u540c\u62e5\u6709&#xff1a;<\/p>\n<p>3<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>A\u2229B\u00a0<\/p>\n<p>\u8868\u793a\u4ea4\u96c6&#xff1a;<\/p>\n<p>A\u2229B &#061; {3}\u00a0<\/p>\n<p>\u8bb0\u5fc6&#xff1a;<\/p>\n<p>\u5e76\u96c6&#xff1a;\u6709\u4e00\u4e2a\u5c31\u884c\u3002<\/p>\n<p>\u4ea4\u96c6&#xff1a;\u4e24\u4e2a\u90fd\u8981\u6709\u3002<\/p>\n<hr \/>\n<h2>\u5341\u516b\u3001\u751f\u6d3b\u4e2d\u7684\u4f8b\u5b50<\/h2>\n<p>\u73ed\u7ea7\u91cc&#xff1a;<\/p>\n<p>A\u96c6\u5408&#xff1a;<\/p>\n<p>\u559c\u6b22\u8db3\u7403\u7684\u540c\u5b66<\/p>\n<p>B\u96c6\u5408&#xff1a;<\/p>\n<p>\u559c\u6b22\u7bee\u7403\u7684\u540c\u5b66<\/p>\n<p>\u90a3\u4e48&#xff1a;<\/p>\n<h4>A\u222aB<\/h4>\n<p>\u8868\u793a&#xff1a;<\/p>\n<p>\u559c\u6b22\u8db3\u7403\u6216\u8005\u7bee\u7403\u7684\u540c\u5b66\u3002<\/p>\n<h4>A\u2229B<\/h4>\n<p>\u8868\u793a&#xff1a;<\/p>\n<p>\u8db3\u7403\u3001\u7bee\u7403\u90fd\u559c\u6b22\u7684\u540c\u5b66\u3002<\/p>\n<p>\u8fd9\u548c\u524d\u9762\u8bfe\u7a0b\u4e2d\u7684&#xff1a;<\/p>\n<p>\u201c\u6216\u8005\u201d\u4e0e\u201c\u5e76\u4e14\u201d<\/p>\n<p>\u5176\u5b9e\u53c8\u8054\u7cfb\u8d77\u6765\u4e86\u3002<\/p>\n<hr \/>\n<h2>\u5341\u4e5d\u3001\u96c6\u5408\u4e2d\u7684\u201c\u8865\u96c6\u201d<\/h2>\n<p>\u5047\u8bbe\u5168\u96c6&#xff1a;<\/p>\n<p>U&#061;{1,2,3,4,5}\u00a0<\/p>\n<p>\u96c6\u5408&#xff1a;<\/p>\n<p>A&#061;{1,2,3}\u00a0<\/p>\n<p>\u90a3\u4e48&#xff1a;<\/p>\n<p>\u4e0d\u5c5e\u4e8eA&#xff0c;\u4f46\u5c5e\u4e8e\u5168\u96c6U\u7684\u5143\u7d20<\/p>\n<p>\u5c31\u662f&#xff1a;<\/p>\n<p>4 5<\/p>\n<p>\u8fd9\u53eb&#xff1a;<\/p>\n<p>A\u7684\u8865\u96c6\u00a0<\/p>\n<p>\u8bb0\u4f5c&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"A^c\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c5a55d3.png\" \/><\/p>\n<p>\u56e0\u6b64&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"\\\\boxed{ A^c=\\\\{4,5\\\\} }\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c5b0c70.png\" \/><\/p>\n<hr \/>\n<h2>\u4e8c\u5341\u3001\u8865\u96c6\u4e0e\u4e0a\u4e00\u8bfe\u201c\u81f3\u5c11\u3001\u6392\u9664\u6cd5\u201d\u518d\u6b21\u8fde\u63a5<\/h2>\n<p>\u4e0a\u4e00\u8bfe\u6211\u4eec\u5b66\u4e60&#xff1a;<\/p>\n<p>\u7b26\u5408\u6761\u4ef6 &#061; \u603b\u6570 \u2212 \u4e0d\u7b26\u5408\u6761\u4ef6<\/p>\n<p>\u73b0\u5728\u96c6\u5408\u4e2d&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"A^c\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c5a55d3.png\" \/><\/p>\n<p>\u5c31\u662f&#xff1a;<\/p>\n<p>A\u7684\u53cd\u9762\u3002<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>A      \u2192 \u6ee1\u8db3\u6761\u4ef6<br \/>\nA\u7684\u8865\u96c6 \u2192 \u4e0d\u6ee1\u8db3\u6761\u4ef6<\/p>\n<p>\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48&#xff1a;<\/p>\n<p>\u96c6\u5408\u8865\u96c6\u548c\u6392\u5217\u7ec4\u5408\u4e2d\u7684\u8865\u96c6\u601d\u60f3&#xff0c;\u672c\u8d28\u4e0a\u662f\u540c\u4e00\u4e2a\u601d\u7ef4\u3002<\/p>\n<hr \/>\n<h2>\u4e8c\u5341\u4e00\u3001\u96c6\u5408\u7684\u4e09\u4e2a\u57fa\u672c\u8fd0\u7b97<\/h2>\n<p>\u540c\u5b66\u4eec\u8981\u8bb0\u4f4f&#xff1a;<\/p>\n<table>\n<tr>\u7b26\u53f7\u540d\u79f0\u610f\u601d<\/tr>\n<tbody>\n<tr>\n<td>A\u222aB<\/td>\n<td>\u5e76\u96c6<\/td>\n<td>A\u6216B<\/td>\n<\/tr>\n<tr>\n<td>A\u2229B<\/td>\n<td>\u4ea4\u96c6<\/td>\n<td>A\u548cB\u90fd\u6709<\/td>\n<\/tr>\n<tr>\n<td><img decoding=\"async\" alt=\"A^c\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c5a55d3.png\" \/><\/td>\n<td>\u8865\u96c6<\/td>\n<td>\u4e0d\u5c5e\u4e8eA<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u53ef\u4ee5\u8bb0\u6210&#xff1a;<\/p>\n<p>\u5e76&#xff1a;\u5408\u8d77\u6765<\/p>\n<p>\u4ea4&#xff1a;\u5171\u540c\u90e8\u5206<\/p>\n<p>\u8865&#xff1a;\u5269\u4e0b\u7684<\/p>\n<hr \/>\n<h2>\u4e8c\u5341\u4e8c\u3001\u96c6\u5408\u6570\u91cf\u8ba1\u7b97&#xff1a;\u6700\u91cd\u8981\u7684\u516c\u5f0f<\/h2>\n<p>\u5047\u8bbe&#xff1a;<\/p>\n<p>\u2223A\u2223<\/p>\n<p>\u8868\u793aA\u4e2d\u5143\u7d20\u7684\u4e2a\u6570\u3002<\/p>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>A&#061;{1,2,3,4}\u00a0<\/p>\n<p>\u90a3\u4e48&#xff1a;<\/p>\n<p>\u2223A\u2223&#061;4\u00a0<\/p>\n<hr \/>\n<p>\u5982\u679c&#xff1a;<\/p>\n<p>\u2223A\u2223&#061;5\u00a0\u00a0\u2223B\u2223&#061;6<\/p>\n<p>\u800c\u4e14A\u3001B\u6ca1\u6709\u5171\u540c\u5143\u7d20\u3002<\/p>\n<p>\u90a3\u4e48&#xff1a;<\/p>\n<p>\u2223A\u222aB\u2223&#061; 5&#043;6 &#061; 11<\/p>\n<hr \/>\n<h2>\u4e8c\u5341\u4e09\u3001\u5982\u679cA\u3001B\u6709\u91cd\u590d\u5143\u7d20\u600e\u4e48\u529e&#xff1f;<\/h2>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>A&#061;{1,2,3,4}\u00a0 \u00a0B&#061;{3,4,5,6}\u00a0<\/p>\n<p>\u90a3\u4e48&#xff1a;<\/p>\n<p>\u2223A\u2223&#061;4\u00a0 \u00a0\u00a0\u2223B\u2223&#061;4\u00a0\u00a0<\/p>\n<p>\u4f46\u662f&#xff1a;<\/p>\n<p>\u2223A\u222aB\u2223<\/p>\n<p>\u4e0d\u662f8\u3002<\/p>\n<p>\u56e0\u4e3a3\u30014\u88ab\u91cd\u590d\u8ba1\u7b97\u4e86\u3002<\/p>\n<hr \/>\n<h2>\u4e8c\u5341\u56db\u3001\u8981\u51cf\u53bb\u91cd\u590d\u90e8\u5206<\/h2>\n<p>A\u548cB\u5171\u540c\u62e5\u6709&#xff1a;<\/p>\n<p>{3,4}<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>\u2223A\u2229B\u2223&#061;2\u00a0<\/p>\n<p>\u56e0\u6b64&#xff1a;<\/p>\n<p>\u2223A\u222aB\u2223&#061;\u2223A\u2223&#043;\u2223B\u2223\u2212\u2223A\u2229B\u2223<\/p>\n<p>\u4ee3\u5165&#xff1a;<\/p>\n<p>4&#043;4\u22122&#061;6\u00a0<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>\u2223A\u222aB\u2223&#061;6\u00a0<\/p>\n<hr \/>\n<h2>\u4e8c\u5341\u4e94\u3001\u4e3a\u4ec0\u4e48\u4e00\u5b9a\u8981\u51cf\u4e00\u6b21\u4ea4\u96c6&#xff1f;<\/h2>\n<p>\u53ef\u4ee5\u628a\u5b83\u60f3\u8c61\u6210\u70b9\u540d\u3002<\/p>\n<p>\u7b2c\u4e00\u6b21&#xff1a;<\/p>\n<p>\u70b9A\u96c6\u5408\u3002<\/p>\n<p>4\u4e2a\u4eba\u3002<\/p>\n<hr \/>\n<p>\u7b2c\u4e8c\u6b21&#xff1a;<\/p>\n<p>\u70b9B\u96c6\u5408\u3002<\/p>\n<p>4\u4e2a\u4eba\u3002<\/p>\n<hr \/>\n<p>\u603b\u5171\u70b9\u4e86&#xff1a;<\/p>\n<p>4&#043;4&#061;8<\/p>\n<p>\u4f46\u662f&#xff1a;<\/p>\n<p>3<br \/>\n4<\/p>\n<p>\u88ab\u70b9\u4e86\u4e24\u6b21\u3002<\/p>\n<hr \/>\n<p>\u6211\u4eec\u771f\u6b63\u9700\u8981&#xff1a;<\/p>\n<p>\u6bcf\u4e2a\u4eba\u53ea\u7b97\u4e00\u6b21\u3002<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>8\u22122 &#061; 6<\/p>\n<p>\u56e0\u6b64&#xff1a;<\/p>\n<p>\u2223A\u222aB\u2223&#061;\u2223A\u2223&#043;\u2223B\u2223\u2212\u2223A\u2229B\u2223<\/p>\n<hr \/>\n<h2>\u4e8c\u5341\u516d\u3001\u8fd9\u4e2a\u516c\u5f0f\u5728CSP-J\u975e\u5e38\u91cd\u8981<\/h2>\n<p>\u770b\u5230&#xff1a;<\/p>\n<p>\u559c\u6b22A\u9879\u76ee\u7684\u670930\u4eba&#xff1b;<\/p>\n<p>\u559c\u6b22B\u9879\u76ee\u7684\u670925\u4eba&#xff1b;<\/p>\n<p>\u4e24\u4e2a\u9879\u76ee\u90fd\u559c\u6b22\u7684\u670910\u4eba&#xff1b;<\/p>\n<p>\u81f3\u5c11\u559c\u6b22\u5176\u4e2d\u4e00\u4e2a\u7684\u6709\u591a\u5c11\u4eba&#xff1f;<\/p>\n<p>\u9a6c\u4e0a\u60f3\u5230&#xff1a;<\/p>\n<p>30&#043;25\u221210<\/p>\n<p>\u6240\u4ee5\u662f&#xff1a;<\/p>\n<p>45<\/p>\n<hr \/>\n<h2>\u4e8c\u5341\u4e03\u3001\u4e3a\u4ec0\u4e48\u4e0d\u662f30&#043;25&#061;55&#xff1f;<\/h2>\n<p>\u56e0\u4e3a&#xff1a;<\/p>\n<p>\u540c\u65f6\u559c\u6b22\u4e24\u4e2a\u9879\u76ee\u7684\u4eba&#xff0c;\u88ab\u8ba1\u7b97\u4e86\u4e24\u6b21\u3002<\/p>\n<p>\u6240\u4ee5\u8981\u51cf\u6389\u4e00\u6b21&#xff1a;<\/p>\n<p>55\u221210&#061;45<\/p>\n<p>\u8fd9\u5176\u5b9e\u4e5f\u662f&#xff1a;<\/p>\n<p>\u6392\u9664\u91cd\u590d\u8ba1\u6570\u3002<\/p>\n<hr \/>\n<h2>\u4e8c\u5341\u516b\u3001\u96c6\u5408\u548c\u201c\u81f3\u5c11\u4e00\u4e2a\u201d\u518d\u6b21\u8fde\u63a5<\/h2>\n<p>\u201c\u81f3\u5c11\u559c\u6b22\u4e00\u4e2a\u201d\u662f\u4ec0\u4e48\u610f\u601d&#xff1f;<\/p>\n<p>\u5c31\u662f&#xff1a;<\/p>\n<p>\u559c\u6b22A\u6216\u8005\u559c\u6b22B\u3002<\/p>\n<p>\u4e5f\u5c31\u662f&#xff1a;<\/p>\n<p>A\u222aB<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>\u81f3\u5c11\u4e00\u4e2a \u27fa \u5e76\u96c6<\/p>\n<hr \/>\n<p>\u800c&#xff1a;<\/p>\n<p>\u4e24\u4e2a\u90fd\u559c\u6b22<\/p>\n<p>\u5c31\u662f&#xff1a;<\/p>\n<p>A \u2229 B\u00a0<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>\u4e24\u4e2a\u90fd\u6ee1\u8db3 \u27fa \u4ea4\u96c6\u00a0<\/p>\n<hr \/>\n<h2>\u4e8c\u5341\u4e5d\u3001\u4e00\u4e2a\u7efc\u5408\u4f8b\u9898<\/h2>\n<p>\u73ed\u91cc\u670940\u540d\u540c\u5b66\u3002<\/p>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<ul>\n<li>\n<p>25\u4eba\u559c\u6b22\u6570\u5b66<\/p>\n<\/li>\n<li>\n<p>20\u4eba\u559c\u6b22\u7f16\u7a0b<\/p>\n<\/li>\n<li>\n<p>10\u4eba\u6570\u5b66\u548c\u7f16\u7a0b\u90fd\u559c\u6b22<\/p>\n<\/li>\n<\/ul>\n<p>\u95ee&#xff1a;<\/p>\n<p>\u81f3\u5c11\u559c\u6b22\u6570\u5b66\u548c\u7f16\u7a0b\u4e2d\u7684\u4e00\u4e2a\u7684\u6709\u591a\u5c11\u4eba&#xff1f;<\/p>\n<p>\u8bbe&#xff1a;<\/p>\n<p>A&#061;\u559c\u6b22\u6570\u5b66\u00a0 \u00a0\u00a0B&#061;\u559c\u6b22\u7f16\u7a0b\u00a0<\/p>\n<p>\u90a3\u4e48&#xff1a;<\/p>\n<p>\u2223A\u2223&#061;25\u00a0\u00a0\u00a0\u2223B\u2223&#061;20\u00a0 \u00a0\u00a0\u2223A\u2229B\u2223&#061;10\u00a0<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>\u2223A\u222aB\u2223&#061; 25 &#043; 20\u221210 &#061; 35<\/p>\n<hr \/>\n<h2>\u4e09\u5341\u3001\u90a3\u4e24\u6837\u90fd\u4e0d\u559c\u6b22\u7684\u6709\u591a\u5c11\u4eba&#xff1f;<\/h2>\n<p>\u5168\u73ed40\u4eba\u3002<\/p>\n<p>\u81f3\u5c11\u559c\u6b22\u4e00\u4e2a&#xff1a;<\/p>\n<p>35<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>40\u221235 &#061; 5<\/p>\n<p>\u8fd9\u53c8\u4e00\u6b21\u7528\u5230\u4e86&#xff1a;<\/p>\n<p>\u8865\u96c6\u601d\u60f3\u3002<\/p>\n<p>\u4e5f\u5c31\u662f&#xff1a;<\/p>\n<p>\u90fd\u4e0d\u559c\u6b22 &#061; \u603b\u4eba\u6570 \u2212 \u81f3\u5c11\u559c\u6b22\u4e00\u4e2a<\/p>\n<hr \/>\n<h2>\u4e09\u5341\u4e00\u3001\u628a\u6574\u4e2a\u601d\u8def\u4e32\u8d77\u6765<\/h2>\n<p>\u96c6\u5408<br \/>\n \u2502<br \/>\n \u251c\u2500\u2500 \u5e76\u96c6 A\u222aB<br \/>\n \u2502      \u2193<br \/>\n \u2502   \u81f3\u5c11\u4e00\u4e2a<br \/>\n \u2502<br \/>\n \u251c\u2500\u2500 \u4ea4\u96c6 A\u2229B<br \/>\n \u2502      \u2193<br \/>\n \u2502   \u4e24\u4e2a\u90fd\u6709<br \/>\n \u2502<br \/>\n \u2514\u2500\u2500 \u8865\u96c6 A\u1d9c<br \/>\n        \u2193<br \/>\n      \u53cd\u9762<br \/>\n        \u2193<br \/>\n     \u603b\u6570-\u6ee1\u8db3<\/p>\n<p>\u5927\u5bb6\u4f1a\u53d1\u73b0&#xff1a;<\/p>\n<p>\u4e0a\u4e00\u8bfe\u7684\u8865\u96c6\u601d\u60f3&#xff0c;\u5728\u672c\u8bfe\u518d\u6b21\u51fa\u73b0\u3002<\/p>\n<hr \/>\n<h2>\u4e09\u5341\u4e8c\u3001\u96c6\u5408\u4e0e\u6392\u5217\u7ec4\u5408\u53c8\u8fde\u63a5\u8d77\u6765\u4e86<\/h2>\n<p>\u73b0\u5728\u518d\u770b\u4e00\u4e2a\u95ee\u9898&#xff1a;<\/p>\n<p>\u96c6\u5408\u67095\u4e2a\u5143\u7d20\u3002<\/p>\n<p>\u95ee&#xff1a;<\/p>\n<p>\u5b83\u6709\u591a\u5c11\u4e2a\u5b50\u96c6&#xff1f;<\/p>\n<p>\u7b54\u6848&#xff1a;<\/p>\n<p>2^5<\/p>\n<hr \/>\n<p>\u5982\u679c\u95ee&#xff1a;<\/p>\n<p>\u6070\u597d\u67092\u4e2a\u5143\u7d20\u7684\u5b50\u96c6\u6709\u591a\u5c11\u4e2a&#xff1f;<\/p>\n<p>\u7b54\u6848&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"C_5^2\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c5bc30f.png\" \/><\/p>\n<hr \/>\n<p>\u5982\u679c\u95ee&#xff1a;<\/p>\n<p>\u81f3\u5c11\u67091\u4e2a\u5143\u7d20\u7684\u5b50\u96c6\u6709\u591a\u5c11\u4e2a&#xff1f;<\/p>\n<p>\u6240\u6709\u5b50\u96c6&#xff1a;<\/p>\n<p>2^5<\/p>\n<p>\u4f46\u662f\u7a7a\u96c6\u4e0d\u7b26\u5408\u3002<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p>2^5 &#8211; 1 &#061;31<\/p>\n<hr \/>\n<h2>\u4e09\u5341\u4e09\u3001\u5982\u679c\u95ee\u201c\u81f3\u5c112\u4e2a\u5143\u7d20\u201d\u5462&#xff1f;<\/h2>\n<p>\u5168\u96c6\u5b50\u96c6\u6570\u91cf&#xff1a;<\/p>\n<p>2^5<\/p>\n<p>\u4e0d\u6ee1\u8db3&#xff1a;<\/p>\n<p>0\u4e2a<br \/>\n1\u4e2a<\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"2^5-C_5^0-C_5^1\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c5c76c4.png\" \/><\/p>\n<p>&#061; 32\u22121\u22125 &#061; 26<\/p>\n<hr \/>\n<p>\u8fd9\u6b63\u597d\u628a&#xff1a;<\/p>\n<p>\u7ec4\u5408<\/p>\n<ul>\n<li><\/li>\n<\/ul>\n<p>\u81f3\u5c11\/\u8865\u96c6<\/p>\n<ul>\n<li><\/li>\n<\/ul>\n<p>\u5b50\u96c6<\/p>\n<p>\u5168\u90e8\u8fde\u63a5\u8d77\u6765\u3002<\/p>\n<hr \/>\n<h2>\u4e09\u5341\u56db\u3001CSP-J\u521d\u8d5b\u7684\u5178\u578b\u8003\u6cd5<\/h2>\n<p>\u4ee5\u540e\u770b\u5230&#xff1a;<\/p>\n<p>\u4e00\u4e2a\u96c6\u5408\u6709 n\u00a0\u4e2a\u5143\u7d20&#xff0c;\u5b83\u7684\u5b50\u96c6\u6709\u591a\u5c11\u4e2a&#xff1f;<\/p>\n<p>\u7b54\u6848&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"\\\\boxed{2^n}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c51cbec.png\" \/><\/p>\n<hr \/>\n<p>\u770b\u5230&#xff1a;<\/p>\n<p>\u771f\u5b50\u96c6\u6709\u591a\u5c11\u4e2a&#xff1f;<\/p>\n<p>\u7b54\u6848&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"\\\\boxed{2^n-1}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c53308b.png\" \/><\/p>\n<hr \/>\n<p>\u770b\u5230&#xff1a;<\/p>\n<p>\u6070\u597d\u5305\u542b k\u00a0\u4e2a\u5143\u7d20\u7684\u5b50\u96c6\u6709\u591a\u5c11\u4e2a&#xff1f;<\/p>\n<p>\u7b54\u6848&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"\\\\boxed{C_n^k}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c5d2940.png\" \/><\/p>\n<hr \/>\n<p>\u770b\u5230&#xff1a;<\/p>\n<p>\u81f3\u5c11\u5305\u542b\u4e00\u4e2a\u5143\u7d20\u7684\u5b50\u96c6\u6709\u591a\u5c11\u4e2a&#xff1f;<\/p>\n<p>\u7b54\u6848&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"\\\\boxed{2^n-1}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c53308b.png\" \/><\/p>\n<hr \/>\n<p>\u770b\u5230&#xff1a;<\/p>\n<p>\u81f3\u5c11\u5305\u542b2\u4e2a\u5143\u7d20&#xff1f;<\/p>\n<p>\u7b54\u6848&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"\\\\boxed{ 2^n-C_n^0-C_n^1 }\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c5ddadb.png\" \/><\/p>\n<hr \/>\n<h2>\u4e09\u5341\u4e94\u3001\u4e00\u4e2a\u521d\u5b66\u8005\u5bb9\u6613\u9519\u7684\u5730\u65b9<\/h2>\n<p>\u9898\u76ee&#xff1a;<\/p>\n<p>\u4e00\u4e2a\u96c6\u5408\u67095\u4e2a\u5143\u7d20&#xff0c;\u6709\u591a\u5c11\u4e2a\u5b50\u96c6&#xff1f;<\/p>\n<p>\u7b54\u6848&#xff1a;<\/p>\n<p>2^5&#061;32<\/p>\n<p>\u6709\u4eba\u4f1a\u5199&#xff1a;<\/p>\n<p>5!<\/p>\n<p>\u8fd9\u662f\u9519\u7684\u3002<\/p>\n<p>\u4e3a\u4ec0\u4e48&#xff1f;<\/p>\n<p>\u56e0\u4e3a&#xff1a;<\/p>\n<p>5!<\/p>\n<p>\u662f\u5728\u8003\u8651&#xff1a;<\/p>\n<p>5\u4e2a\u5143\u7d20\u600e\u4e48\u6392\u5217\u3002<\/p>\n<p>\u800c&#xff1a;<\/p>\n<p>2^5<\/p>\n<p>\u662f\u5728\u8003\u8651&#xff1a;<\/p>\n<p>5\u4e2a\u5143\u7d20\u6bcf\u4e00\u4e2a\u9009\u8fd8\u662f\u4e0d\u9009\u3002<\/p>\n<p>\u4e24\u8005\u89e3\u51b3\u7684\u95ee\u9898\u5b8c\u5168\u4e0d\u540c\u3002<\/p>\n<hr \/>\n<h2>\u4e09\u5341\u516d\u3001\u201c\u6392\u5217\u201d\u548c\u201c\u5b50\u96c6\u201d\u6709\u4ec0\u4e48\u533a\u522b&#xff1f;<\/h2>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>{A,B,C}\u00a0<\/p>\n<p>\u9009\u62e9\u4e24\u4e2a\u5143\u7d20\u3002<\/p>\n<p>\u5982\u679c\u95ee&#xff1a;<\/p>\n<p>\u9009\u51fa\u4e24\u4e2a\u5143\u7d20\u3002<\/p>\n<p>\u90a3\u4e48&#xff1a;<\/p>\n<p>AB<br \/>\nAC<br \/>\nBC<\/p>\n<p>\u4e00\u5171&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"C_3^2=3\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c5e8eb2.png\" \/><\/p>\n<p>\u56e0\u4e3a&#xff1a;<\/p>\n<p>AB\u548cBA\u662f\u540c\u4e00\u79cd\u9009\u62e9\u3002<\/p>\n<p>\u4f46\u662f\u5982\u679c\u95ee&#xff1a;<\/p>\n<p>\u4eceA\u3001B\u3001C\u4e2d\u90092\u4e2a\u6392\u6210\u4e00\u6392\u3002<\/p>\n<p>\u90a3\u4e48&#xff1a;<\/p>\n<p>AB<br \/>\nBA<br \/>\nAC<br \/>\nCA<br \/>\nBC<br \/>\nCB<\/p>\n<p>\u4e00\u5171&#xff1a;<\/p>\n<p>3\u00d72 &#061; 6<\/p>\n<p>\u56e0\u4e3a&#xff1a;<\/p>\n<p>AB\u548cBA\u662f\u4e0d\u540c\u987a\u5e8f\u3002<\/p>\n<hr \/>\n<h2>\u4e09\u5341\u4e03\u3001\u6240\u4ee5\u5927\u5bb6\u5fc5\u987b\u8bb0\u4f4f<\/h2>\n<p>\u96c6\u5408\u5173\u6ce8\u201c\u6709\u6ca1\u6709\u201d\u3002<\/p>\n<p>\u6392\u5217\u5173\u6ce8\u201c\u987a\u5e8f\u201d\u3002<\/p>\n<p>\u4f8b\u5982&#xff1a;<\/p>\n<p>{A,B}<\/p>\n<p>\u548c&#xff1a;<\/p>\n<p>{B,A}<\/p>\n<p>\u5b83\u4eec\u662f\u540c\u4e00\u4e2a\u96c6\u5408\u3002<\/p>\n<p>\u4f46\u662f\u6392\u5217&#xff1a;<\/p>\n<p>AB<\/p>\n<p>\u548c&#xff1a;<\/p>\n<p>BA<\/p>\n<p>\u662f\u4e24\u79cd\u4e0d\u540c\u7684\u6392\u5217\u3002<\/p>\n<hr \/>\n<h2>\u4e09\u5341\u516b\u3001\u672c\u8bfe\u201c\u53cd\u7c97\u5fc3\u201d\u8bad\u7ec3<\/h2>\n<p>\u505a\u96c6\u5408\u9898\u7684\u65f6\u5019&#xff0c;\u540c\u5b66\u4eec\u5f3a\u5236\u68c0\u67e5&#xff1a;<\/p>\n<h4>\u2460 \u5b50\u96c6\u5305\u62ec\u96c6\u5408\u672c\u8eab\u5417&#xff1f;<\/h4>\n<p>\u5305\u62ec\u3002<\/p>\n<hr \/>\n<h4>\u2461 \u7a7a\u96c6\u7b97\u4e0d\u7b97&#xff1f;<\/h4>\n<p>\u7b97\u3002<\/p>\n<hr \/>\n<h4>\u2462 \u771f\u5b50\u96c6\u5305\u62ec\u96c6\u5408\u672c\u8eab\u5417&#xff1f;<\/h4>\n<p>\u4e0d\u5305\u62ec\u3002<\/p>\n<hr \/>\n<h4>\u2463 \u96c6\u5408\u4e2d\u7684\u5143\u7d20\u6709\u987a\u5e8f\u5417&#xff1f;<\/h4>\n<p>\u6ca1\u6709\u3002<\/p>\n<hr \/>\n<h4>\u2464 \u5e76\u96c6\u4e2d\u7684\u91cd\u590d\u5143\u7d20\u600e\u4e48\u7b97&#xff1f;<\/h4>\n<p>\u53ea\u7b97\u4e00\u6b21\u3002<\/p>\n<hr \/>\n<h4>\u2465 \u4ea4\u96c6\u8868\u793a\u4ec0\u4e48&#xff1f;<\/h4>\n<p>\u5171\u540c\u90e8\u5206\u3002<\/p>\n<hr \/>\n<h4>\u2466 \u201c\u81f3\u5c11\u4e00\u4e2a\u201d\u5bf9\u5e94\u4ec0\u4e48&#xff1f;<\/h4>\n<p>\u5e76\u96c6\u3002<\/p>\n<hr \/>\n<h4>\u2467 \u201c\u90fd\u4e0d\u6ee1\u8db3\u201d\u600e\u4e48\u529e&#xff1f;<\/h4>\n<p>\u8003\u8651\u8865\u96c6\u3002<\/p>\n<hr \/>\n<h2>\u4e09\u5341\u4e5d\u3001\u672c\u8bfe\u77e5\u8bc6\u5730\u56fe<\/h2>\n<p>                       \u96c6\u5408<br \/>\n                        \u2502<br \/>\n             \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510<br \/>\n             \u2193          \u2193          \u2193<br \/>\n           \u5e76\u96c6        \u4ea4\u96c6        \u8865\u96c6<br \/>\n          A\u222aB         A\u2229B         A\u1d9c<br \/>\n             \u2502          \u2502           \u2502<br \/>\n          \u6216\u8005        \u90fd\u6709        \u53cd\u9762<br \/>\n             \u2502          \u2502           \u2502<br \/>\n          \u81f3\u5c11\u4e00\u4e2a    \u540c\u65f6\u6ee1\u8db3     \u603b\u6570-\u6ee1\u8db3<br \/>\n                        \u2502<br \/>\n                        \u2193<br \/>\n                      \u5b50\u96c6<br \/>\n                        \u2502<br \/>\n              \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510<br \/>\n              \u2193         \u2193         \u2193<br \/>\n           \u6240\u6709\u5b50\u96c6   \u6070\u597dk\u4e2a    \u771f\u5b50\u96c6<br \/>\n              \u2193         \u2193         \u2193<br \/>\n             2\u207f       C(n,k)    2\u207f-1<\/p>\n<hr \/>\n<h2>\u56db\u5341\u3001\u6211\u4eec\u5df2\u7ecf\u5f62\u6210\u4e00\u6761\u5b8c\u6574\u7684\u6570\u5b66\u94fe<\/h2>\n<p>\u73b0\u5728\u56de\u5934\u770b\u524d\u9762\u56db\u8bfe&#xff1a;<\/p>\n<p>\u7b2c40\u8bfe<br \/>\n\u5206\u7c7b\u3001\u5206\u6b65<br \/>\n   \u2193<br \/>\n\u52a0\u6cd5\u3001\u4e58\u6cd5<br \/>\n   \u2193<br \/>\n\u6392\u5217\u3001\u7ec4\u5408<\/p>\n<p>\u7b2c41\u8bfe<br \/>\n\u7279\u6b8a\u9650\u5236<br \/>\n   \u2193<br \/>\n\u6346\u7ed1\u3001\u63d2\u7a7a\u3001\u56fa\u5b9a\u4f4d\u7f6e<\/p>\n<p>\u7b2c42\u8bfe<br \/>\n\u81f3\u5c11\u3001\u81f3\u591a<br \/>\n   \u2193<br \/>\n\u8865\u96c6\u3001\u6392\u9664\u3001\u907f\u514d\u91cd\u590d<\/p>\n<p>\u7b2c43\u8bfe<br \/>\n\u96c6\u5408\u4e0e\u5b50\u96c6<br \/>\n   \u2193<br \/>\n\u5e76\u96c6\u3001\u4ea4\u96c6\u3001\u8865\u96c6<br \/>\n   \u2193<br \/>\n2\u207f\u3001C(n,k)<br \/>\n   \u2193<br \/>\n\u518d\u6b21\u8fde\u63a5\u6392\u5217\u7ec4\u5408<\/p>\n<p>\u6240\u4ee5\u6211\u4eec\u4e0d\u662f\u5728\u201c\u5806\u77e5\u8bc6\u70b9\u201d&#xff0c;\u800c\u662f\u5728\u4e0d\u65ad\u628a\u524d\u9762\u7684\u77e5\u8bc6\u91cd\u65b0\u7ec4\u5408\u8d77\u6765\u3002<\/p>\n<hr \/>\n<h2>\u56db\u5341\u4e00\u3001\u672c\u8bfe\u7ed9\u540c\u5b66\u4eec\u7684\u201c\u9b54\u6cd5\u53e3\u8bc0\u201d<\/h2>\n<h4>&#x1fa84; \u96c6\u5408\u4e0e\u5b50\u96c6\u56db\u53e5\u53e3\u8bc0<\/h4>\n<p>\u96c6\u5408\u6ca1\u6709\u987a\u5e8f&#xff0c;\u91cd\u590d\u5143\u7d20\u4e0d\u7b97&#xff1b;<\/p>\n<p>\u5e76\u96c6\u5c31\u662f\u5408\u8d77\u6765&#xff0c;\u4ea4\u96c6\u5c31\u662f\u5171\u540c\u90e8\u5206&#xff1b;<\/p>\n<p>\u6bcf\u4e2a\u5143\u7d20\u9009\u4e0d\u9009&#xff0c;\u4e24\u79cd\u9009\u62e9\u4e58\u8d77\u6765&#xff1b;<\/p>\n<p>n\u4e2a\u5143\u7d20\u7684\u5b50\u96c6&#xff0c;\u4e00\u5171\u5c31\u662f 2n2^n\u3002<\/p>\n<p>\u7a7a\u96c6\u4e5f\u7b97\u5b50\u96c6&#xff0c;\u771f\u5b50\u96c6\u8981\u51cf\u6389\u81ea\u5df1&#xff01;<\/p>\n<p>\u518d\u52a0\u4e00\u53e5&#xff1a;<\/p>\n<h4>\u201c\u81f3\u5c11\u201d\u60f3\u5e76\u96c6&#xff0c;\u201c\u90fd\u4e0d\u201d\u60f3\u8865\u96c6&#xff0c;\u201c\u6070\u597dk\u4e2a\u201d\u60f3\u7ec4\u5408\u3002<\/h4>\n<hr \/>\n<h2>\u56db\u5341\u4e8c\u3001\u8bfe\u540e\u7ec3\u4e60<\/h2>\n<h4>1<\/h4>\n<p>\u96c6\u5408 A&#061;{1,2,3}\u00a0 &#xff0c;\u4e00\u5171\u6709\u591a\u5c11\u4e2a\u5b50\u96c6&#xff1f;<\/p>\n<p>8<\/p>\n<hr \/>\n<h4>2<\/h4>\n<p>\u96c6\u5408 A&#061;{1,2,3,4,5}\u00a0 &#xff0c;\u6709\u591a\u5c11\u4e2a\u5b50\u96c6&#xff1f;<\/p>\n<p>32<\/p>\n<hr \/>\n<h4>3<\/h4>\n<p>\u4e00\u4e2a\u67096\u4e2a\u5143\u7d20\u7684\u96c6\u5408&#xff0c;\u6709\u591a\u5c11\u4e2a\u771f\u5b50\u96c6&#xff1f;<\/p>\n<p>2^6 \u22121 &#061; 63\u00a0<\/p>\n<hr \/>\n<h4>4<\/h4>\n<p>\u4e00\u4e2a\u67095\u4e2a\u5143\u7d20\u7684\u96c6\u5408&#xff0c;\u6709\u591a\u5c11\u4e2a\u6070\u597d\u5305\u542b2\u4e2a\u5143\u7d20\u7684\u5b50\u96c6&#xff1f;<\/p>\n<p><img decoding=\"async\" alt=\"C_5^2 = \\\\boxed{10}\" class=\"mathcode\" src=\"2026-09-15jic3nqbkd4a.png\" \/><\/p>\n<hr \/>\n<h4>5<\/h4>\n<p>\u4e00\u4e2a\u67095\u4e2a\u5143\u7d20\u7684\u96c6\u5408&#xff0c;\u6709\u591a\u5c11\u4e2a\u81f3\u5c11\u5305\u542b1\u4e2a\u5143\u7d20\u7684\u5b50\u96c6&#xff1f;<\/p>\n<p><img decoding=\"async\" alt=\"2^5-1 = \\\\boxed{31}\" class=\"mathcode\" src=\"2026-09-15q1jy3o3ubtl.png\" \/><\/p>\n<hr \/>\n<h4>6<\/h4>\n<p>\u4e00\u4e2a\u67095\u4e2a\u5143\u7d20\u7684\u96c6\u5408&#xff0c;\u6709\u591a\u5c11\u4e2a\u81f3\u5c11\u5305\u542b2\u4e2a\u5143\u7d20\u7684\u5b50\u96c6&#xff1f;<\/p>\n<p><img decoding=\"async\" alt=\"2^5-C_5^0-C_5^1\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235653-6aa889c5c76c4.png\" \/><\/p>\n<p>&#061; 32\u22121\u22125\u00a0\u00a0&#061;26<\/p>\n<hr \/>\n<h4>7<\/h4>\n<p>\u5982\u679c&#xff1a;<\/p>\n<p>A&#061;{1,2,3}\u00a0 \u00a0\u00a0B&#061;{3,4,5}\u00a0\u00a0<\/p>\n<p>\u90a3\u4e48&#xff1a;<\/p>\n<p>A\u222aB\u00a0\u00a0<\/p>\n<p>\u662f\u4ec0\u4e48&#xff1f;<\/p>\n<p>\u7b54\u6848&#xff1a;<\/p>\n<p>{1,2,3,4,5}<\/p>\n<hr \/>\n<h4>8<\/h4>\n<p>\u524d\u9898\u4e2d&#xff0c;\u540c\u6837\u7684A\u3001B&#xff1a;<\/p>\n<p>A \u2229 B<\/p>\n<p>\u662f\u4ec0\u4e48&#xff1f;<\/p>\n<p>\u7b54\u6848&#xff1a;<\/p>\n<p>{3}\u00a0<\/p>\n<hr \/>\n<h4>9<\/h4>\n<p>\u67d0\u73ed\u670930\u4eba\u559c\u6b22C&#043;&#043;&#xff0c;20\u4eba\u559c\u6b22\u6570\u5b66&#xff0c;\u5176\u4e2d10\u4eba\u4e24\u8005\u90fd\u559c\u6b22\u3002<\/p>\n<p>\u81f3\u5c11\u559c\u6b22\u5176\u4e2d\u4e00\u95e8\u7684\u6709\u591a\u5c11\u4eba&#xff1f;<\/p>\n<p>30 &#043; 20 \u2212 10 &#061; 40<\/p>\n<hr \/>\n<h4>10<\/h4>\n<p>\u5168\u73ed50\u4eba&#xff0c;\u81f3\u5c11\u559c\u6b22C&#043;&#043;\u6216\u6570\u5b66\u7684\u670940\u4eba&#xff0c;\u90a3\u4e48\u4e24\u95e8\u90fd\u4e0d\u559c\u6b22\u7684\u6709\u591a\u5c11\u4eba&#xff1f;<\/p>\n<p>50\u221240 &#061; 10<\/p>\n<hr \/>\n<h3><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>\u524d\u9762\u4e09\u8bfe\u5df2\u7ecf\u628a\u5206\u7c7b\u8ba1\u6570\u3001\u5206\u6b65\u8ba1\u6570\u3001\u6392\u5217\u7ec4\u5408\u3001\u6346\u7ed1\u6cd5\u3001\u63d2\u7a7a\u6cd5\u3001\u81f3\u5c11\/\u81f3\u591a\u3001\u8865\u96c6\u4e0e\u6392\u9664\u6cd5\u4e32\u4e86\u8d77\u6765\u3002\u672c\u8bfe\u6211\u4eec\u628a\u8fd9\u4e9b\u8ba1\u6570\u601d\u60f3\u8fdb\u4e00\u6b65\u63d0\u5347\u5230\u96c6\u5408\u4e0e\u5b50\u96c6\u3002\u8fd9\u4e00\u8bfe\u7684\u91cd\u70b9\u4e0d\u662f\u8ba9\u540c\u5b66\u4eec\u80cc\u5f88\u591a\u96c6\u5408\u7b26\u53f7&#xff0c;\u800c\u662f\u8ba9\u5927\u5bb6\u660e\u767d&#xff1a;\u96c6\u5408\u662f\u5728\u201c\u6570\u4e1c\u897f\u201d&#xff0c;\u5b50\u96c6\u662f\u5728\u201c\u505a\u9009\u62e9\u201d\u3002\u800c\u201c\u6bcf\u4e2a\u5143\u7d20\u9009\u4e0d\u9009\u201d&#xff0c;\u5c31\u4f1a\u4ea7\u751f&#xff1a;\u7b2c\u56db\u5341\u4e09\u8bfe&#xff1a;\u96c6\u5408\u4e0e\u5b50\u96c6\u2014\u2014\u4ece\u201c\u9009\u4e0d\u9009\u201d\u5230 2^n\u4e00\u3001\u5148\u4ece\u4e00\u4e2a\u201c\u9b54\u6cd5\u96c6\u5408\u201d\u5f00\u59cb\u5c0f\u660e\u67094\u5f20\u5361\u7247&#xff1a;1\u53f7&#xff1a;&amp;<\/p>\n","protected":false},"author":2,"featured_media":105272,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[10494,10493,55,5184],"topic":[],"class_list":["post-105292","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-c","tag-10493","tag-csp-j"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>CSP-J \u521d\u8d5b\uff08\u4ee5\u6ee1\u5206\u4e3a\u76ee\u6807\uff09\uff1a\u7b2c\u56db\u5341\u4e09\u8bfe\u300a\u96c6\u5408\u4e0e\u5b50\u96c6\u2014\u2014\u4ece\u201c\u9009\u4e0d\u9009\u201d\u5230 2^n\u300b - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/105292.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"CSP-J \u521d\u8d5b\uff08\u4ee5\u6ee1\u5206\u4e3a\u76ee\u6807\uff09\uff1a\u7b2c\u56db\u5341\u4e09\u8bfe\u300a\u96c6\u5408\u4e0e\u5b50\u96c6\u2014\u2014\u4ece\u201c\u9009\u4e0d\u9009\u201d\u5230 2^n\u300b - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u524d\u9762\u4e09\u8bfe\u5df2\u7ecf\u628a\u5206\u7c7b\u8ba1\u6570\u3001\u5206\u6b65\u8ba1\u6570\u3001\u6392\u5217\u7ec4\u5408\u3001\u6346\u7ed1\u6cd5\u3001\u63d2\u7a7a\u6cd5\u3001\u81f3\u5c11\/\u81f3\u591a\u3001\u8865\u96c6\u4e0e\u6392\u9664\u6cd5\u4e32\u4e86\u8d77\u6765\u3002\u672c\u8bfe\u6211\u4eec\u628a\u8fd9\u4e9b\u8ba1\u6570\u601d\u60f3\u8fdb\u4e00\u6b65\u63d0\u5347\u5230\u96c6\u5408\u4e0e\u5b50\u96c6\u3002\u8fd9\u4e00\u8bfe\u7684\u91cd\u70b9\u4e0d\u662f\u8ba9\u540c\u5b66\u4eec\u80cc\u5f88\u591a\u96c6\u5408\u7b26\u53f7&#xff0c;\u800c\u662f\u8ba9\u5927\u5bb6\u660e\u767d&#xff1a;\u96c6\u5408\u662f\u5728\u201c\u6570\u4e1c\u897f\u201d&#xff0c;\u5b50\u96c6\u662f\u5728\u201c\u505a\u9009\u62e9\u201d\u3002\u800c\u201c\u6bcf\u4e2a\u5143\u7d20\u9009\u4e0d\u9009\u201d&#xff0c;\u5c31\u4f1a\u4ea7\u751f&#xff1a;\u7b2c\u56db\u5341\u4e09\u8bfe&#xff1a;\u96c6\u5408\u4e0e\u5b50\u96c6\u2014\u2014\u4ece\u201c\u9009\u4e0d\u9009\u201d\u5230 2^n\u4e00\u3001\u5148\u4ece\u4e00\u4e2a\u201c\u9b54\u6cd5\u96c6\u5408\u201d\u5f00\u59cb\u5c0f\u660e\u67094\u5f20\u5361\u7247&#xff1a;1\u53f7&#xff1a;&amp;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/105292.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-09-14T23:56:55+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235652-6aa889c46a8bf.png\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/105292.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/105292.html\",\"name\":\"CSP-J \u521d\u8d5b\uff08\u4ee5\u6ee1\u5206\u4e3a\u76ee\u6807\uff09\uff1a\u7b2c\u56db\u5341\u4e09\u8bfe\u300a\u96c6\u5408\u4e0e\u5b50\u96c6\u2014\u2014\u4ece\u201c\u9009\u4e0d\u9009\u201d\u5230 2^n\u300b - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"isPartOf\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\"},\"datePublished\":\"2026-09-14T23:56:55+00:00\",\"dateModified\":\"2026-09-14T23:56:55+00:00\",\"author\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\"},\"breadcrumb\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/105292.html#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.wsisp.com\/helps\/105292.html\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/105292.html#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u9996\u9875\",\"item\":\"https:\/\/www.wsisp.com\/helps\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"CSP-J \u521d\u8d5b\uff08\u4ee5\u6ee1\u5206\u4e3a\u76ee\u6807\uff09\uff1a\u7b2c\u56db\u5341\u4e09\u8bfe\u300a\u96c6\u5408\u4e0e\u5b50\u96c6\u2014\u2014\u4ece\u201c\u9009\u4e0d\u9009\u201d\u5230 2^n\u300b\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\",\"url\":\"https:\/\/www.wsisp.com\/helps\/\",\"name\":\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"description\":\"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"contentUrl\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"caption\":\"admin\"},\"sameAs\":[\"http:\/\/wp.wsisp.com\"],\"url\":\"https:\/\/www.wsisp.com\/helps\/author\/admin\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"CSP-J \u521d\u8d5b\uff08\u4ee5\u6ee1\u5206\u4e3a\u76ee\u6807\uff09\uff1a\u7b2c\u56db\u5341\u4e09\u8bfe\u300a\u96c6\u5408\u4e0e\u5b50\u96c6\u2014\u2014\u4ece\u201c\u9009\u4e0d\u9009\u201d\u5230 2^n\u300b - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.wsisp.com\/helps\/105292.html","og_locale":"zh_CN","og_type":"article","og_title":"CSP-J \u521d\u8d5b\uff08\u4ee5\u6ee1\u5206\u4e3a\u76ee\u6807\uff09\uff1a\u7b2c\u56db\u5341\u4e09\u8bfe\u300a\u96c6\u5408\u4e0e\u5b50\u96c6\u2014\u2014\u4ece\u201c\u9009\u4e0d\u9009\u201d\u5230 2^n\u300b - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","og_description":"\u524d\u9762\u4e09\u8bfe\u5df2\u7ecf\u628a\u5206\u7c7b\u8ba1\u6570\u3001\u5206\u6b65\u8ba1\u6570\u3001\u6392\u5217\u7ec4\u5408\u3001\u6346\u7ed1\u6cd5\u3001\u63d2\u7a7a\u6cd5\u3001\u81f3\u5c11\/\u81f3\u591a\u3001\u8865\u96c6\u4e0e\u6392\u9664\u6cd5\u4e32\u4e86\u8d77\u6765\u3002\u672c\u8bfe\u6211\u4eec\u628a\u8fd9\u4e9b\u8ba1\u6570\u601d\u60f3\u8fdb\u4e00\u6b65\u63d0\u5347\u5230\u96c6\u5408\u4e0e\u5b50\u96c6\u3002\u8fd9\u4e00\u8bfe\u7684\u91cd\u70b9\u4e0d\u662f\u8ba9\u540c\u5b66\u4eec\u80cc\u5f88\u591a\u96c6\u5408\u7b26\u53f7&#xff0c;\u800c\u662f\u8ba9\u5927\u5bb6\u660e\u767d&#xff1a;\u96c6\u5408\u662f\u5728\u201c\u6570\u4e1c\u897f\u201d&#xff0c;\u5b50\u96c6\u662f\u5728\u201c\u505a\u9009\u62e9\u201d\u3002\u800c\u201c\u6bcf\u4e2a\u5143\u7d20\u9009\u4e0d\u9009\u201d&#xff0c;\u5c31\u4f1a\u4ea7\u751f&#xff1a;\u7b2c\u56db\u5341\u4e09\u8bfe&#xff1a;\u96c6\u5408\u4e0e\u5b50\u96c6\u2014\u2014\u4ece\u201c\u9009\u4e0d\u9009\u201d\u5230 2^n\u4e00\u3001\u5148\u4ece\u4e00\u4e2a\u201c\u9b54\u6cd5\u96c6\u5408\u201d\u5f00\u59cb\u5c0f\u660e\u67094\u5f20\u5361\u7247&#xff1a;1\u53f7&#xff1a;&amp;","og_url":"https:\/\/www.wsisp.com\/helps\/105292.html","og_site_name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","article_published_time":"2026-09-14T23:56:55+00:00","og_image":[{"url":"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260914235652-6aa889c46a8bf.png"}],"author":"admin","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005":"admin","\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4":"4 \u5206"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.wsisp.com\/helps\/105292.html","url":"https:\/\/www.wsisp.com\/helps\/105292.html","name":"CSP-J \u521d\u8d5b\uff08\u4ee5\u6ee1\u5206\u4e3a\u76ee\u6807\uff09\uff1a\u7b2c\u56db\u5341\u4e09\u8bfe\u300a\u96c6\u5408\u4e0e\u5b50\u96c6\u2014\u2014\u4ece\u201c\u9009\u4e0d\u9009\u201d\u5230 2^n\u300b - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","isPartOf":{"@id":"https:\/\/www.wsisp.com\/helps\/#website"},"datePublished":"2026-09-14T23:56:55+00:00","dateModified":"2026-09-14T23:56:55+00:00","author":{"@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41"},"breadcrumb":{"@id":"https:\/\/www.wsisp.com\/helps\/105292.html#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.wsisp.com\/helps\/105292.html"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.wsisp.com\/helps\/105292.html#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u9996\u9875","item":"https:\/\/www.wsisp.com\/helps"},{"@type":"ListItem","position":2,"name":"CSP-J \u521d\u8d5b\uff08\u4ee5\u6ee1\u5206\u4e3a\u76ee\u6807\uff09\uff1a\u7b2c\u56db\u5341\u4e09\u8bfe\u300a\u96c6\u5408\u4e0e\u5b50\u96c6\u2014\u2014\u4ece\u201c\u9009\u4e0d\u9009\u201d\u5230 2^n\u300b"}]},{"@type":"WebSite","@id":"https:\/\/www.wsisp.com\/helps\/#website","url":"https:\/\/www.wsisp.com\/helps\/","name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","description":"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"zh-Hans"},{"@type":"Person","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41","name":"admin","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/","url":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","contentUrl":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","caption":"admin"},"sameAs":["http:\/\/wp.wsisp.com"],"url":"https:\/\/www.wsisp.com\/helps\/author\/admin"}]}},"_links":{"self":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/105292","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/comments?post=105292"}],"version-history":[{"count":0,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/105292\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media\/105272"}],"wp:attachment":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media?parent=105292"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/categories?post=105292"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/tags?post=105292"},{"taxonomy":"topic","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/topic?post=105292"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}