{"id":303,"date":"2012-02-14T00:46:59","date_gmt":"2012-02-13T15:46:59","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=303"},"modified":"2021-09-16T06:48:12","modified_gmt":"2021-09-15T21:48:12","slug":"ngr200804a","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ngr200804a\/","title":{"rendered":"\u540d\u53e4\u5c4b\u5927\u7406\u7cfb2008\uff1a\u7b2c4\u554f(A)"},"content":{"rendered":"
\n

\u6b21\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(3x+2y \\leqq 2008\\) \u3092\u6e80\u305f\u3059 \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570\u306e\u7d44 \\((x,y)\\) \u306e\u500b\u6570\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(\\dfrac{x}{2} +\\dfrac{y}{3} +\\dfrac{z}{6} \\leqq 10\\) \u3092\u6e80\u305f\u3059 \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570\u306e\u7d44 \\((x,y,z)\\) \u306e\u500b\u6570\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n

    \u6761\u4ef6\u3088\u308a\r\n\\[\r\n0 \\leqq x \\leqq 669 , \\ 0 \\leqq y \\leqq 1004\n\\]\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(x = 2k \\ ( 0 \\leqq k \\leqq 334 )\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\n0 & \\leqq 2y \\leqq 2008 -6k \\\\\r\n\\text{\u2234} \\quad 0 & \\leqq y \\leqq 1004 -3k\n\\end{align}\\]\r\n\u3053\u306e\u3068\u304d \\((x,y)\\) \u306e\u7d44\u306f, \\(1005 -3k\\) \u901a\u308a.<\/p><\/li>\r\n

    2. 2*<\/strong>\u3000\\(x = 2k+1 \\ ( 0 \\leqq k \\leqq 334 )\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\n0 & \\leqq 2y \\leqq 2005 -6k \\\\\r\n\\text{\u2234} \\quad 0 & \\leqq y \\leqq 1002 -3k\n\\end{align}\\]\r\n\u3053\u306e\u3068\u304d \\((x,y)\\) \u306e\u7d44\u306f, \\(1003 -3k\\) \u901a\u308a.<\/p><\/li>\r\n<\/ol>\r\n

      \u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u500b\u6570\u306f\r\n\\[\\begin{align}\r\n\\textstyle\\sum\\limits _ {k=0}^{334} & \\left\\{ (1005-3k) +(1003-3k) \\right\\} \\\\\r\n& = 2008 \\cdot 335 -6 \\cdot \\dfrac{334 \\cdot 335}{2} \\\\\r\n& = 335 (2008-1002) \\\\\r\n& = \\underline{337010}\n\\end{align}\\]\r\n

      (2)<\/strong><\/p>\r\n

      \u4e0e\u5f0f\u3092\u5909\u5f62\u3059\u308b\u3068\r\n\\[\r\n3x +2y +z \\leqq 60\n\\]\r\n\u3053\u306e\u3068\u304d\r\n\\[\r\n0 \\leqq x \\leqq 20 , \\ 0 \\leqq y \\leqq 30 , \\ 0 \\leqq z \\leqq 60\n\\]\r\n

        \r\n

      1. 1*<\/strong>\u3000\\(x = 2m \\ ( 0 \\leqq m \\leqq 10 )\\) \u306e\u3068\u304d\r\n\\[\r\n0 \\leqq 2y+z \\leqq 60 -6m\n\\]\r\n\u3053\u306e\u3068\u304d, \\(0 \\leqq y \\leqq 30-3m\\) .\r\n\\(y = \\ell \\ ( 0 \\leqq \\ell \\leqq 30-3m )\\) \u306e\u3068\u304d\r\n\\[\r\n0 \\leqq z \\leqq 60- 6m -2 \\ell\n\\]\r\n\u3053\u306e\u3068\u304d \\((x,y,z)\\) \u306e\u7d44\u306f, \\(61 -6m -2 \\ell\\) \u901a\u308a.<\/p><\/li>\r\n

      2. 2*<\/strong>\u3000\\(x = 2m+1 \\ ( 0 \\leqq m \\leqq 9 )\\) \u306e\u3068\u304d\r\n\\[\r\n0 \\leqq 2y+z \\leqq 57 -6m\n\\]\r\n\u3053\u306e\u3068\u304d, \\(0 \\leqq y \\leqq 28-3m\\) .\r\n\\(y = \\ell \\ ( 0 \\leqq \\ell \\leqq 28-3m )\\) \u306e\u3068\u304d\r\n\\[\r\n0 \\leqq z \\leqq 57- 6m -2 \\ell\n\\]\r\n\u3053\u306e\u3068\u304d \\((x,y,z)\\) \u306e\u7d44\u306f, \\(58 -6m -2 \\ell\\) \u901a\u308a.<\/p><\/li>\r\n<\/ol>\r\n

        \u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u500b\u6570\u306f\r\n\\[\\begin{align}\r\n\\textstyle\\sum\\limits _ {m=0}^{10} & \\textstyle\\sum\\limits _ {\\ell =0}^{30 -3m} ( 61-6m-2\\ell ) +\\textstyle\\sum\\limits _ {m=0}^{9} \\textstyle\\sum\\limits _ {\\ell =0}^{28 -3m} ( 58-6m-2\\ell ) \\\\\r\n& = \\displaystyle\\sum _ {m=0}^{10} \\left\\{ ( 31-3m )( 61-6m ) -( 30-3m )( 31-3m ) \\right\\} \\\\\r\n& \\qquad +\\displaystyle\\sum _ {m=0}^{9} \\left\\{ ( 29-3m )( 58-6m ) -( 28-3m )( 29-3m ) \\right\\} \\\\\r\n& = \\displaystyle\\sum _ {m=0}^{10} ( 31-3m )^2 +\\displaystyle\\sum _ {m=0}^{9} ( 30-3m )( 29-3m ) \\\\\r\n& = \\displaystyle\\sum _ {m=0}^{10} \\left\\{ ( 3m+1 )^2 +3m ( 3m-1 ) \\right\\} \\\\\r\n& = \\displaystyle\\sum _ {m=0}^{10} ( 18m^2 +3m +1 ) \\\\\r\n& = 18 \\cdot \\dfrac{10 \\cdot 11 \\cdot 21}{6} +3 \\cdot \\dfrac{10 \\cdot 11}{2} +11 \\\\\r\n& = 6930 +165 +11 \\\\\r\n& =\\underline{7106}\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u6b21\u306e\u554f\u306b\u7b54\u3048\u3088. (1)\u3000\\(3x+2y \\leqq 2008\\) \u3092\u6e80\u305f\u3059 \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570\u306e\u7d44 \\((x,y)\\) \u306e\u500b\u6570\u3092\u6c42\u3081\u3088. (2)\u3000\\(\\dfrac{x}{2} +\\dfrac{y}{3} +\\dfr … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[53],"tags":[143,16],"class_list":["post-303","post","type-post","status-publish","format-standard","hentry","category-nagoya_r_2008","tag-nagoya_r","tag-16"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/303","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=303"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/303\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=303"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=303"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=303"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}