{"id":2043,"date":"2021-12-18T02:22:20","date_gmt":"2021-12-17T17:22:20","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=2043"},"modified":"2021-12-18T02:22:20","modified_gmt":"2021-12-17T17:22:20","slug":"tkb202102","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkb202102\/","title":{"rendered":"\u6771\u5927\u6587\u7cfb2021\uff1a\u7b2c2\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(N\\) \u3092 \\(5\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b.\r\n\\(1\\) \u4ee5\u4e0a \\(2N\\) \u4ee5\u4e0b\u306e\u6574\u6570\u304b\u3089, \u76f8\u7570\u306a\u308b \\(N\\) \u500b\u306e\u6574\u6570\u3092\u9078\u3076.\r\n\u305f\u3060\u3057 \\(1\\) \u306f\u5fc5\u305a\u9078\u3076\u3053\u3068\u3068\u3059\u308b.\r\n\u9078\u3093\u3060\u6570\u306e\u96c6\u5408\u3092 \\(S\\) \u3068\u3057, \\(S\\) \u306b\u95a2\u3059\u308b\u4ee5\u4e0b\u306e\u6761\u4ef6\u3092\u8003\u3048\u308b.<\/p>\r\n<ol>\r\n<li><p>\u6761\u4ef6 1 : \\(S\\) \u306f\u9023\u7d9a\u3059\u308b \\(2\\) \u500b\u306e\u6574\u6570\u304b\u3089\u306a\u308b\u96c6\u5408\u3092 \\(1\\) \u3064\u3082\u542b\u307e\u306a\u3044.<\/p><\/li>\r\n<li><p>\u6761\u4ef6 2 : \\(S\\) \u306f\u9023\u7d9a\u3059\u308b \\(N-2\\) \u500b\u306e\u6574\u6570\u304b\u3089\u306a\u308b\u96c6\u5408\u3092\u5c11\u306a\u304f\u3068\u3082 \\(1\\) \u3064\u542b\u3080.<\/p><\/li>\r\n<\/ol>\r\n<p>\u305f\u3060\u3057, \\(2\\) \u4ee5\u4e0a\u306e\u6574\u6570 \\(k\\) \u306b\u5bfe\u3057\u3066, \u9023\u7d9a\u3059\u308b \\(k\\) \u500b\u306e\u6574\u6570\u304b\u3089\u306a\u308b\u96c6\u5408\u3068\u306f, \u3042\u308b\u6574\u6570 \\(l\\) \u3092\u7528\u3044\u3066 \\(\\{ l , l+1 , \\cdots , l+k-1 \\}\\) \u3068\u8868\u3055\u308c\u308b\u96c6\u5408\u3092\u6307\u3059.\r\n\u4f8b\u3048\u3070 \\(\\{ 1 , 2 , 3 , 5 , 7 , 8 , 9 , 10 \\}\\) \u306f\u9023\u7d9a\u3059\u308b \\(3\\) \u500b\u306e\u6574\u6570\u304b\u3089\u306a\u308b\u96c6\u5408 \\(\\{ 1 , 2 , 3 \\}\\) , \\(\\{ 7 , 8 , 9 \\}\\) , \\(\\{ 8 , 9 , 10 \\}\\) \u3092\u542b\u3080.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\u6761\u4ef6 1 \u3092\u6e80\u305f\u3059\u3088\u3046\u306a\u9078\u3073\u65b9\u306f\u4f55\u901a\u308a\u3042\u308b\u304b.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\u6761\u4ef6 2 \u3092\u6e80\u305f\u3059\u3088\u3046\u306a\u9078\u3073\u65b9\u306f\u4f55\u901a\u308a\u3042\u308b\u304b.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\u9078\u3076\u6570\u5b57\u3092 \u25cb , \u9078\u3070\u306a\u3044\u6570\u5b57\u3092 \u00d7 \u306b\u7f6e\u304d\u304b\u3048\u308b\u3068, \u25cb \u304c\u96a3\u308a\u5408\u308f\u306a\u3044\u4e26\u3079\u65b9\u3092\u8003\u3048\u308c\u3070\u3088\u3044.<br \/>\r\n\\(1\\) \u306f\u5fc5\u305a\u9078\u3076\u306e\u3067, \\(N\\) \u500b\u306e \u25cb \u306b\u5bfe\u3057\u3066, \u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4e26\u3079\u308c\u3070\u6761\u4ef6\u3092\u307f\u305f\u3059.<\/p>\r\n<ul>\r\n<li><p>\\(N-1\\) \u304b\u6240\u306e\u9593\u3068\u53f3\u7aef\u306b \u00d7 \u3092 \\(1\\) \u3064\u305a\u3064\u4e26\u3079\u308b.<\/p><\/li>\r\n<li><p>\\(N-1\\) \u304b\u6240\u306e\u9593\u306e\u3046\u3061 \\(1\\) \u304b\u6240\u306b \\(2\\) \u3064, \u6b8b\u308a\u306b \\(1\\) \u3064\u305a\u3064 \u00d7 \u3092\u4e26\u3079\u308b.<\/p><\/li>\r\n<\/ul>\r\n<p>\u3088\u3063\u3066, \u6c42\u3081\u308b\u9078\u3073\u65b9\u306f\r\n\\[\r\n1 +( N-1 ) = \\underline{N} \\text{\u901a\u308a}\r\n\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\u25cb \u304c \\(K\\) \u500b\u4e26\u3076\u90e8\u5206\u3092 \\(\\underbrace{\\text{\u25cb \u2026 \u25cb}} _ K\\) \u3068\u8868\u3059.<br \/>\r\n\\(N \\geqq 5\\) \u3088\u308a \\(N-2 \\gt 2\\) \u306a\u306e\u3067, \u6761\u4ef6\u3092\u307f\u305f\u3059\u9078\u3073\u65b9\u306f, \u4ee5\u4e0b\u306e\u901a\u308a.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\u300c \\(\\underbrace{\\text{\u25cb \u2026 \u25cb}} _ N\\) \u00d7 \u300d\u3067\u59cb\u307e\u308b\u3068\u304d<br \/>\r\n\u6b8b\u308a\u306f\u3059\u3079\u3066 \u00d7 \u3067, \\(1\\) \u901a\u308a.<\/p><\/li>\r\n<li><p><strong>2*<\/strong>\u3000\u300c \\(\\underbrace{\\text{\u25cb \u2026 \u25cb}} _ {N-1}\\) \u00d7 \u300d\u3067\u59cb\u307e\u308b\u3068\u304d<br \/>\r\n\u6b8b\u308a \\(N\\) \u304b\u6240\u306e\u3046\u3061 \\(1\\) \u304b\u6240\u304c \u25cb \u3067\u6b8b\u308a\u304c \u00d7 \u3067\u3042\u308b\u5834\u5408\u3067\r\n\\[\r\nN \\ \\text{\u901a\u308a}\r\n\\]<\/li>\r\n<li><p><strong>3*<\/strong>\u3000\u300c \\(\\underbrace{\\text{\u25cb \u2026 \u25cb}} _ {N-2}\\) \u00d7 \u300d\u3067\u59cb\u307e\u308b\u3068\u304d<br \/>\r\n\u6b8b\u308a \\(N+1\\) \u304b\u6240\u306e\u3046\u3061 \\(2\\) \u304b\u6240\u304c \u25cb \u3067\u6b8b\u308a\u304c \u00d7 \u3067\u3042\u308b\u5834\u5408\u3067\r\n\\[\r\n{} _ {N+1} \\text{C}{} _ {2} = \\dfrac{N (N+1)}{2} \\ \\text{\u901a\u308a}\r\n\\]<\/li>\r\n<li><p><strong>4*<\/strong>\u3000\u300c \u25cb \u25cb \u00d7 \u300d\u3067\u59cb\u307e\u308b\u3068\u304d<br \/>\r\n\u6b8b\u308a \\(2N-3\\) \u304b\u6240\u306b \\(\\underbrace{\\text{\u25cb \u2026 \u25cb}} _ {N-2}\\) \u304c \\(1\\) \u3064\u3042\u308b\u5834\u5408\u3067\r\n\\[\r\n(2N-3) -(N-2) +1 = N \\ \\text{\u901a\u308a}\r\n\\]<\/li>\r\n<li><p><strong>5*<\/strong>\u3000\u300c \u25cb \u00d7 \u300d\u3067\u59cb\u307e\u308b\u3068\u304d<br \/>\r\n\u6b8b\u308a \\(2N-2\\) \u7b87\u6240\u306b\u3064\u3044\u3066<\/p>\r\n<ul>\r\n<li>\\(\\underbrace{\\text{\u25cb \u2026 \u25cb}} _ {N-1}\\) \u304c \\(1\\) \u3064\u3042\u308b\u5834\u5408\u3067\r\n\\[\r\n(2N-2) -(N-1) +1 = N \\ \\text{\u901a\u308a}\r\n\\]<\/li>\r\n<li>\\(\\underbrace{\\text{\u25cb \u2026 \u25cb}} _ {N-2}\\) \u304c \\(1\\) \u3064, \u3053\u308c\u3068\u96e2\u308c\u305f \u25cb \u304c \\(1\\) \u3064\u306e\u5834\u5408\u306e\u3046\u3061,<br \/>\r\n\\(\\underbrace{\\text{\u25cb \u2026 \u25cb}} _ {N-2}\\) \u304c\u4e21\u7aef\u306b\u3042\u308b\u5834\u5408\uff08\\(2\\) \u901a\u308a\u3042\u308b\uff09\u306f, \u25cb \u306e\u5834\u6240\u306e\u9078\u3073\u65b9\u306f \\(N-1\\) \u901a\u308a\u3042\u308a,<br \/>\r\n\\(\\underbrace{\\text{\u25cb \u2026 \u25cb}} _ {N-2}\\) \u304c\u4e21\u7aef\u306b\u306a\u3044\u5834\u5408\uff08\\(N-1\\) \u901a\u308a\u3042\u308b\uff09\u306f, \u25cb \u306e\u5834\u6240\u306e\u9078\u3073\u65b9\u306f \\(N-2\\) \u901a\u308a\u3042\u308b\u306e\u3067\r\n\\[\r\n2 (N-1) +(N-1) (N-2) = N (N-1) \\ \\text{\u901a\u308a}\r\n\\]<\/li>\r\n<\/ul><\/li>\r\n<\/ol>\r\n<p>\u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u9078\u3073\u65b9\u306f\r\n\\[\\begin{align}\r\n& 1 +N +\\dfrac{N (N+1)}{2} +N +N +N (N-1) \\\\\r\n& \\qquad = \\dfrac{3}{2} N^2 +\\dfrac{5}{2} N +1 \\\\\r\n& \\qquad = \\underline{\\dfrac{1}{2} (3N+2) (N+1) \\ \\text{\u901a\u308a}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(N\\) \u3092 \\(5\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b. \\(1\\) \u4ee5\u4e0a \\(2N\\) \u4ee5\u4e0b\u306e\u6574\u6570\u304b\u3089, \u76f8\u7570\u306a\u308b \\(N\\) \u500b\u306e\u6574\u6570\u3092\u9078\u3076. \u305f\u3060\u3057 \\(1\\) \u306f\u5fc5\u305a\u9078\u3076\u3053\u3068\u3068\u3059\u308b. \u9078\u3093\u3060\u6570\u306e\u96c6\u5408\u3092 \\(S\\) \u3068\u3057,  &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tkb202102\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/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":[180],"tags":[149,165],"class_list":["post-2043","post","type-post","status-publish","format-standard","hentry","category-tokyo_b_2021","tag-tokyo_b","tag-165"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2043","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=2043"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2043\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=2043"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=2043"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=2043"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}