{"id":421929,"date":"2019-09-19T16:30:09","date_gmt":"2019-09-19T19:30:09","guid":{"rendered":"https:\/\/blog-estrategia.mystagingwebsite.com\/blog\/?p=421929"},"modified":"2019-09-19T16:30:11","modified_gmt":"2019-09-19T19:30:11","slug":"permutacoes-caoticas-surpresa-na-fcc","status":"publish","type":"post","link":"https:\/\/www.estrategiaconcursos.com.br\/blog\/permutacoes-caoticas-surpresa-na-fcc\/","title":{"rendered":"Permuta\u00e7\u00f5es Ca\u00f3ticas &#8211; Surpresa na FCC"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Neste artigo, falarei um pouco sobre permuta\u00e7\u00f5es ca\u00f3ticas &#8211; assunto recentemente cobrado em uma prova de Racioc\u00ednio L\u00f3gico da FCC.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Fala, pessoal!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Tudo bem?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Venho comentando que a FCC est\u00e1 cobrando uma enxurrada de\nassuntos implicitamente em seus editais.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Os assuntos mais cobrados em\nRacioc\u00ednio Matem\u00e1tico pela FCC s\u00e3o:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Problemas envolvendo equa\u00e7\u00f5es e sistemas do primeiro grau<\/li><li>Regra de tr\u00eas<\/li><li>Porcentagem<\/li><li>Raz\u00e3o e Propor\u00e7\u00e3o<\/li><li>An\u00e1lise Combinat\u00f3ria<\/li><li>Princ\u00edpio da Casa dos Pombos<\/li><li>Conjuntos Num\u00e9ricos e express\u00f5es num\u00e9ricas<\/li><li>Problemas com fra\u00e7\u00f5es<\/li><li>Problemas com conjuntos<\/li><li>Progress\u00e3o Aritm\u00e9tica<\/li><li>Problemas envolvendo equa\u00e7\u00f5es do segundo grau<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/raciocinio-logico-para-trf-3-raio-x-da-prova\/\">Clique aqui<\/a> para conferir mais detalhes sobre Racioc\u00ednio Matem\u00e1tico na FCC.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Nos \u00faltimos dias, fiz uma profunda pesquisa em provas da FCC\npara tentar mapear tudo que a FCC pode cobrar dentro do tema \u201cRacioc\u00ednio Matem\u00e1tico\u201d.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Analisando as \u00faltimas provas de 2019, fiquei surpreso com a cobran\u00e7a de um <strong>tema avan\u00e7ado de An\u00e1lise Combinat\u00f3ria \u2013 as permuta\u00e7\u00f5es ca\u00f3ticas<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Veja a quest\u00e3o:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>(FCC\n2019\/Prefeitura do Recife \u2013 Assistente de Gest\u00e3o P\u00fablica)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Os quatro\nfuncion\u00e1rios de uma reparti\u00e7\u00e3o trabalham cada um em uma mesa, todos na mesma\nsala. O chefe da reparti\u00e7\u00e3o determinou que os funcion\u00e1rios trocassem de mesa\nentre si. Os funcion\u00e1rios podem ser realocados na sala de modo que nenhum\nfuncion\u00e1rio passe a ocupar a mesa que ocupava antes da realoca\u00e7\u00e3o&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a)&nbsp;de 4\nmaneiras diferentes.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b)&nbsp;de 24\nmaneiras diferentes.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">c)&nbsp;de 9\nmaneiras diferentes.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d)&nbsp;de 6\nmaneiras diferentes.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">e)&nbsp;de 12\nmaneiras diferentes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Aparentemente \u00e9 uma quest\u00e3o bem tranquila. Puro engano!<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">O assunto envolvido\nnessa quest\u00e3o n\u00e3o \u00e9 tratado na esmagadora maioria de livros do Ensino M\u00e9dio. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A quest\u00e3o s\u00f3 \u00e9 fact\u00edvel\nporque o n\u00famero de funcion\u00e1rios \u00e9 bem pequeno, ou seja, o candidato poderia\ndescrever todas as possibilidades e marcar a resposta.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sejam (a, b, c, d) os funcion\u00e1rios em suas posi\u00e7\u00f5es originais. Queremos realocar os funcion\u00e1rios de modo que nenhum ocupe a sua posi\u00e7\u00e3o original. Dizemos que essa \u00e9 uma <strong>permuta\u00e7\u00e3o ca\u00f3tica (ou desarranjo)<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">As permuta\u00e7\u00f5es ca\u00f3ticas s\u00e3o: <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(b, a, d, c); (c, a, d, b); (d, a, b, c); (c, d, a, b); (d, c, a, b); (b, d, a, c); (b, c, d, a); (c, d, b, a) e (d, c, b, a).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Logo, <strong>h\u00e1 9 maneiras diferentes<\/strong> de realocar os funcion\u00e1rios de modo que nenhum funcion\u00e1rio ocupe a posi\u00e7\u00e3o original.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Veja que com 4 pessoas j\u00e1 \u00e9 bastante complicado descrever todas as permuta\u00e7\u00f5es ca\u00f3ticas.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">E se fossem 5 pessoas ou 8 pessoas? <\/p>\n\n\n\n<h2 class=\"wp-block-heading\">C\u00e1lculo das Permuta\u00e7\u00f5es Ca\u00f3ticas<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Apresento-lhes\nagora a f\u00f3rmula para calcular o n\u00famero de permuta\u00e7\u00f5es ca\u00f3ticas (desarranjos) de\nn objetos:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/wp-content\/uploads\/2019\/09\/Captura-de-Tela-2019-09-19-\u00e0s-15.20.01-1024x204.png\" alt=\"\" class=\"wp-image-421936\" width=\"489\" height=\"97\" \/><figcaption>F\u00f3rmula das Permuta\u00e7\u00f5es Ca\u00f3ticas<\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">O termo <img decoding=\"async\" class=\"wp-image-421938\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2019\/09\/19162107\/Captura-de-Tela-2019-09-19-%C3%A0s-15.20.58.png\" alt=\"\" style=\"width: 40px\" \/> simplesmente indica que os sinais das fra\u00e7\u00f5es v\u00e3o sendo alternados.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por exemplo,\npara n = 4, temos:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/wp-content\/uploads\/2019\/09\/Captura-de-Tela-2019-09-19-\u00e0s-15.21.35-966x1024.png\" alt=\"\" class=\"wp-image-421939\" width=\"340\" height=\"360\" \/><figcaption>Permuta\u00e7\u00f5es Ca\u00f3ticas para n = 4<\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Veja o resultado\npara n = 6.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/wp-content\/uploads\/2019\/09\/Captura-de-Tela-2019-09-19-\u00e0s-15.22.18-1024x716.png\" alt=\"\" class=\"wp-image-421940\" width=\"460\" height=\"321\" \/><figcaption>Permuta\u00e7\u00f5es Ca\u00f3ticas para n = 6<\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u00c9 claro que seria\nimposs\u00edvel voc\u00ea escrever todas as possibilidades \u00e0 m\u00e3o.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Mas, Guilherme,\nessa f\u00f3rmula \u00e9 muito complicada. Corro o risco de ficar nervoso e esquec\u00ea-la!<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Calma, amigo. <strong>Agora\nvem a salva\u00e7\u00e3o<\/strong>. Existe uma maneira bem mais f\u00e1cil e r\u00e1pida de calcular o n\u00famero\nde permuta\u00e7\u00f5es ca\u00f3ticas.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00c9 poss\u00edvel\ndemonstrar que o n\u00famero de permuta\u00e7\u00f5es ca\u00f3ticas \u00e9 o inteiro mais pr\u00f3ximo de<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2019\/09\/19162320\/Captura-de-Tela-2019-09-19-%C3%A0s-15.23.11.png\" alt=\"\" class=\"wp-image-421941\" width=\"53\" height=\"75\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Na express\u00e3o\nacima, <strong>e <\/strong>\u00e9 a constante de Euler: e = 2,718&#8230;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Observe para o caso\nn = 6.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/wp-content\/uploads\/2019\/09\/Captura-de-Tela-2019-09-19-\u00e0s-15.23.36-1024x138.png\" alt=\"\" class=\"wp-image-421942\" width=\"506\" height=\"68\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">De fato, para\nn = 6, o n\u00famero de permuta\u00e7\u00f5es ca\u00f3ticas \u00e9 265.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Vamos voltar \u00e0\nquest\u00e3o da FCC.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>(FCC\n2019\/Prefeitura do Recife \u2013 Assistente de Gest\u00e3o P\u00fablica)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Os quatro\nfuncion\u00e1rios de uma reparti\u00e7\u00e3o trabalham cada um em uma mesa, todos na mesma\nsala. O chefe da reparti\u00e7\u00e3o determinou que os funcion\u00e1rios trocassem de mesa\nentre si. Os funcion\u00e1rios podem ser realocados na sala de modo que nenhum\nfuncion\u00e1rio passe a ocupar a mesa que ocupava antes da realoca\u00e7\u00e3o&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a)&nbsp;de 4\nmaneiras diferentes.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b)&nbsp;de 24\nmaneiras diferentes.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">c)&nbsp;de 9\nmaneiras diferentes.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d)&nbsp;de 6\nmaneiras diferentes.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">e)&nbsp;de 12\nmaneiras diferentes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Resolu\u00e7\u00e3o<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A quest\u00e3o pede o n\u00famero de permuta\u00e7\u00f5es ca\u00f3ticas de 4\nelementos. O n\u00famero de permuta\u00e7\u00f5es ca\u00f3ticas \u00e9 o inteiro mais pr\u00f3ximo de<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2019\/09\/19162407\/Captura-de-Tela-2019-09-19-%C3%A0s-15.23.58.png\" alt=\"\" class=\"wp-image-421943\" width=\"189\" height=\"72\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2019\/09\/19162407\/Captura-de-Tela-2019-09-19-%C3%A0s-15.23.58.png 492w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2019\/09\/19162407\/Captura-de-Tela-2019-09-19-%C3%A0s-15.23.58-300x115.png 300w\" sizes=\"auto, (max-width: 189px) 100vw, 189px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">O inteiro mais pr\u00f3ximo \u00e9 9. Logo, h\u00e1 9\nmaneiras para realocar os funcion\u00e1rios de modo que nenhum ocupe a sua posi\u00e7\u00e3o\noriginal.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Gabarito: C<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Espero que tenham gostado! A partir de agora <strong>voc\u00ea vai torcer para cair permuta\u00e7\u00e3o ca\u00f3tica outra vez<\/strong>. Assim, voc\u00ea vai deixar seus concorrentes para tr\u00e1s. :)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Forte abra\u00e7o,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Guilherme Neves<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Neste artigo, falarei um pouco sobre permuta\u00e7\u00f5es ca\u00f3ticas &#8211; assunto recentemente cobrado em uma prova de Racioc\u00ednio L\u00f3gico da FCC. Fala, pessoal! Tudo bem? Venho comentando que a FCC est\u00e1 cobrando uma enxurrada de assuntos implicitamente em seus editais. Os assuntos mais cobrados em Racioc\u00ednio Matem\u00e1tico pela FCC s\u00e3o: Problemas envolvendo equa\u00e7\u00f5es e sistemas do [&hellip;]<\/p>\n","protected":false},"author":739,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"post_tipo":"article","footnotes":""},"categories":[1],"tags":[],"tax_estado":[],"class_list":["post-421929","post","type-post","status-publish","format-standard","hentry","category-cursos-e-concursos"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v28.1 (Yoast SEO v28.1) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Permuta\u00e7\u00f5es Ca\u00f3ticas - Surpresa na FCC<\/title>\n<meta name=\"description\" content=\"Aprenda rapidamente como calcular as permuta\u00e7\u00f5es ca\u00f3ticas. 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