{"id":66176,"date":"2016-09-01T18:30:19","date_gmt":"2016-09-01T21:30:19","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=66176"},"modified":"2023-05-11T23:02:27","modified_gmt":"2023-05-12T02:02:27","slug":"desafio-grupo-de-dois","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/desafio-grupo-de-dois\/","title":{"rendered":".Desafio: Grupo de dois"},"content":{"rendered":"<p style=\"margin:20px\">\n<div class=\"g1n\">\n<p class=\"tit\" style=\"line-height:25px;margin:10px\">Problema<br \/>\n<span style=\"font-size:12px;color:#800000\"> (Indicado a partir do 7\u00ba ano do E. F.)<\/span><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\nPara resolver este problema voc\u00ea ter\u00e1 que jogar um joguinho.<\/p>\n<p style=\"margin:20px\">\n<div class=\"g1n cb36\">\n<p class=\"tit c3\" style=\"line-height:25px;margin:10px\">Jogo<\/p>\n<ul>\n<li>Dez palitos de f\u00f3sforo est\u00e3o alinhados.<\/li>\n<li>Voc\u00ea pode formar pares movendo um palito, de modo que ele pule dois outros e seja colocado sobre o terceiro, respeitando sempre a disposi\u00e7\u00e3o dos palitos no momento da movimenta\u00e7\u00e3o.<\/li>\n<li>Depois de formado um par, esse permanece na fileira e n\u00e3o poder\u00e1 ser desfeito!<\/li>\n<li>O objetivo do jogo \u00e9 formar cinco pares, utilizando-se todos os palitos. <\/li>\n<\/ul>\n<p style=\"margin:20px\">\n<p>Clique no bot\u00e3o a seguir para comprovar que o jogo tem solu\u00e7\u00e3o.<\/p>\n<p style=\"margin:20px\">\n<div style=\"text-align:center;\"><input class=\"bo1 c3 cb33 bg3\" value=\"Uma solu\u00e7\u00e3o\" title=\"Clique aqui\" type=\"button\" onclick=    \"if(this.parentNode.getElementsByTagName('div')[0].style.display != ''){this.parentNode.getElementsByTagName('div')[0].style.display = '';this.value = 'Ocultar';} else{this.parentNode.getElementsByTagName('div')[0].style.display = 'none'; this.value = 'Uma solu\u00e7\u00e3o';}\" \/>    <\/p>\n<div  style=\"display: none;\">\n<table  style=\" text-align:justify; margin-left: auto; margin-right: auto; width: 100%; font-size:12px;\">\n<tr>\n<td style=\"border: 1px solid #FFFFFF\">\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/07\/fosf1.png\" alt=\"fosf1\" width=\"430\" height=\"380\" class=\"aligncenter size-full wp-image-64669\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/07\/fosf1.png 644w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/07\/fosf1-300x265.png 300w\" sizes=\"auto, (max-width: 430px) 100vw, 430px\" \/><\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n<div style=\"text-align:justify;\">Para indicar cada passo do jogo, voc\u00ea pode usar a seguinte nota\u00e7\u00e3o:<\/p>\n<ul>\n<li><strong>Passo 1:<\/strong> <strong>1-4<\/strong> 2 3 5 6 7 8 9 10 <\/li>\n<li><strong>Passo 2:<\/strong> 1-4 2 <strong>3-7<\/strong> 5 6 8 9 10<\/li>\n<li><strong>Passo 3:<\/strong> 1-4 2 3-7 6 8 <strong>9-5<\/strong> 10<\/li>\n<li><strong>Passo 4:<\/strong> 1-4 3-7 <strong>6-2<\/strong> 8 9-5 10<\/li>\n<li><strong>Passo 5:<\/strong> 1-4 3-7 6-2 9-5 <strong>10-8<\/strong>.<\/li>\n<\/ul>\n<\/div>\n<\/td>\n<\/tr>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p style=\"margin:40px\">\n<p class=\"ti3\">Encontre todas as solu\u00e7\u00f5es para esse problema e descreva os respectivos passos. <\/p>\n<p style=\"margin:40px\">\n<p><u><strong>Observa\u00e7\u00e3o<\/strong><\/u>: Solu\u00e7\u00f5es com movimenta\u00e7\u00f5es diferentes dos palitos s\u00e3o consideradas solu\u00e7\u00f5es diferentes; mesmo que conduzam aos mesmos pares finais.<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 30px; margin-bottom: 8px;border: 0 none\"\/>\n<hr style=\"height:6px; width:100%;background-color:#800000; margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 8px; margin-bottom: 40px;border: 0 none\"\/>\n<p><strong>Voc\u00ea pode utilizar um  APPLET para ajudar na solu\u00e7\u00e3o do problema. \u00c9 s\u00f3 clicar no bot\u00e3o abaixo!<\/strong><\/p>\n<p style=\"margin:40px\">\n<div style=\"text-align:center;\"><input class=\"bo1 c3 cb33 bg3\" value=\"APPLET\" title=\"Clique aqui\" type=\"button\" onclick=  \"if(this.parentNode.getElementsByTagName('div')[0].style.display != ''){this.parentNode.getElementsByTagName('div')[0].style.display = '';this.value = 'Ocultar';} else{this.parentNode.getElementsByTagName('div')[0].style.display = 'none'; this.value = 'APPLET';}\" \/>    <\/p>\n<div  style=\"display: none;\">\n<p style=\"margin:30px;\">\n<div class=\"gris c3\">\n<p style=\"margin:20px;\">\n<p style=\"text-align: justify;padding-left: 15px;padding-right: 15px; border-style: dotted; border-color :#800000; border-width :thin;\"><span style=\"font-family: Georgia, Times, 'Times New Roman', serif; font-size: 16px; text-align: justify; color: #616161; line-height: 25px;\"><strong>Instru\u00e7\u00f5es:<\/strong><br \/>\n1) Clique <a href=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/r3xa2MTN\/width\/692\/height\/284\/border\/ffffff\/rc\/false\/ai\/false\/sdz\/false\/smb\/false\/stb\/false\/stbh\/true\/ld\/false\/sri\/true\/at\/auto\" target=\"ap1\"><span style=\"color: #800000;\"><strong>AQUI<\/strong><\/span><\/a> e espere o aplicativo carregar completamente.<br \/>\n2) Para mover um palito horizontalmente, clique sobre sua extremidade inferior ( <span style=\"color: #1E90FF; font-size: 18px;\">&diams;<\/span> ) e arraste-o.<br \/>\n3) Para girar um palito (e produzir um <span style=\"font-family:Verdana, serif; font-size: 16px;\"> <strong>X<\/strong> <\/span> quando um par for formado), clique sobre sua extremidade superior ( <span style=\"color: #FF0000; font-size: 18px;\">&#9679;<\/span> ) e gire-o.<br \/>\n4) Para reiniciar a constru\u00e7\u00e3o, clique sobre as setinhas que aparecem no canto superior direito do <em>applet<\/em>.<br \/>\n5) Para modificar o tamanho dos palitos, mova verticalmente o ponto <span style=\"font-family:Verdana, serif; font-size: 16px;  color: #00BF00;\"> <strong>A<\/strong> <\/span> ( <span style=\"color: #00BF00; font-size: 18px;\">&#9679;<\/span> ).<\/p>\n<p style=\"margin:30px;\">\n<div style=\"text-align:center;\">\n<iframe    name=\"ap1\"   width=\"692\" height=\"284\" style=\"border: 1px solid #800000;\"> <\/iframe><\/p>\n<p style=\"text-align: center;\"><span style=\"font-size: 14px;\">OBMEP_ srdg, criado com o <a href=\"http:\/\/www.geogebra.org\/\" target=\"_blank\">GeoGebra<\/a><\/span><\/p>\n<p style=\"margin:10px;\">\n<\/div>\n<\/div>\n<p style=\"margin:20px;\">\n<\/div>\n<\/div>\n<p style=\"margin:30px\">\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"g1n\">\n<p class=\"tit\" style=\"line-height:30px;margin:10px\">Solu\u00e7\u00e3o <\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\nAntes de iniciarmos, vamos analisar algumas situa\u00e7\u00f5es especiais que podem ocorrer durante o jogo.<\/p>\n<p style=\"margin:20px\">\n<div style=\"text-align:center;\"><input class=\"bo1 c3 cb33 bg3\" value=\"Situa\u00e7\u00e3o 1\" title=\"Clique aqui\" type=\"button\" onclick=    \"if(this.parentNode.getElementsByTagName('div')[0].style.display != ''){this.parentNode.getElementsByTagName('div')[0].style.display = '';this.value = 'Ocultar';} else{this.parentNode.getElementsByTagName('div')[0].style.display = 'none'; this.value = 'Situa\u00e7\u00e3o 1';}\" \/>    <\/p>\n<div  style=\"display: none;\">\n<table class=\"gree\" style=\"border:2px solid #800000;\">\n<tr>\n<td class=\"gree\" style=\"color: #616161; border:2px solid #800000; border-right: 2px solid #800000; width:45%; text-align:justify;\">\n<p style=\"margin:10px\">\n<p><strong>(I) Dois palitos podem ficar isolados em um &#8220;canto&#8221;?<\/strong><\/p>\n<p style=\"margin:30px\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/07\/F001.png\" alt=\"F001\" width=\"394\" height=\"103\" class=\"aligncenter size-full wp-image-65079\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/07\/F001.png 394w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/07\/F001-300x78.png 300w\" sizes=\"auto, (max-width: 394px) 100vw, 394px\" \/><br \/>\nVamos analisar a primeira situa\u00e7\u00e3o. Para a segunda, o racioc\u00ednio ser\u00e1 an\u00e1logo.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F0022.png\" alt=\"F0022\" width=\"150\" height=\"109\" class=\"aligncenter size-full wp-image-65385\" \/>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"gree\" style=\"color: #616161; border:1px solid #d8d8d8;\"><strong>(a)<\/strong> Observe que nessa disposi\u00e7\u00e3o n\u00e3o podemos movimentar o palito azul, pois de um lado dele n\u00e3o existem palitos e do outro lado n\u00e3o existem dois palitos isolados e consecutivos, de modo que ele possa pular &#8220;os dois e ser colocado sobre um terceiro&#8221;. Nenhum outro palito formar\u00e1 par com esse palito (1) nesse momento; pois ele s\u00f3 seria o terceiro de uma sequ\u00eancia de tr\u00eas palitos (dois para serem pulados e ele para receber o seu par), se desmont\u00e1ssemos o <strong>X<\/strong> que ocupa a terceira posi\u00e7\u00e3o (3), o que n\u00e3o \u00e9 permitido pelas regras do jogo.<br \/>\n<strong>(b)<\/strong> Para formarmos um par com o palito rosa, ter\u00edamos, a princ\u00edpio, duas op\u00e7\u00f5es.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F0033.png\" alt=\"F0033\" width=\"390\" height=\"121\" class=\"aligncenter size-full wp-image-65386\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F0033.png 390w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F0033-300x93.png 300w\" sizes=\"auto, (max-width: 390px) 100vw, 390px\" \/>Mas, observe que, depois de executarmos qualquer um dos dois movimentos propostos, n\u00e3o seria poss\u00edvel formarmos um par com o palito azul.\n<\/td>\n<\/tr>\n<tr>\n<td class=\"gree\" style=\"color: #616161; border:2px solid #800000; width:45%; text-align: center; background-color: #D3D3D3; font-size:14px; color:#800000;\">\n<strong>Assim, dois palitos n\u00e3o podem ficar isolados em um &#8220;canto&#8221;. (Proibi\u00e7\u00e3o (I))<\/strong>\n<\/td>\n<\/tr>\n<\/table>\n<\/div>\n<\/div>\n<p style=\"margin:40px\">\n<div style=\"text-align:center;\"><input class=\"bo1 c3 cb33 bg3\" value=\"Situa\u00e7\u00e3o 2\" title=\"Clique aqui\" type=\"button\" onclick=    \"if(this.parentNode.getElementsByTagName('div')[0].style.display != ''){this.parentNode.getElementsByTagName('div')[0].style.display = '';this.value = 'Ocultar';} else{this.parentNode.getElementsByTagName('div')[0].style.display = 'none'; this.value = 'Situa\u00e7\u00e3o 2';}\" \/>    <\/p>\n<div  style=\"display: none;\">\n<table class=\"gree\" style=\"border:2px solid #800000;\">\n<tr>\n<td class=\"gree\" style=\"color: #616161; border:2px solid #800000;  width:45%; text-align:justify;\">\n<p style=\"margin:10px\">\n<p><strong>(II) Tr\u00eas palitos podem ficar isolados em um &#8220;canto&#8221;?<\/strong><\/p>\n<p style=\"margin:30px\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F004.png\" alt=\"F004\" width=\"436\" height=\"96\" class=\"aligncenter size-full wp-image-65376\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F004.png 436w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F004-300x66.png 300w\" sizes=\"auto, (max-width: 436px) 100vw, 436px\" \/><br \/>\nVamos analisar a primeira situa\u00e7\u00e3o. Para a segunda, novamente o racioc\u00ednio ser\u00e1 an\u00e1logo.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F005.png\" alt=\"F005\" width=\"173\" height=\"108\" class=\"aligncenter size-full wp-image-65454\" \/>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"gree\" style=\"color: #616161; border:2px solid #800000;\"><strong>(a)<\/strong> Observe que nessa disposi\u00e7\u00e3o n\u00e3o podemos movimentar nenhum dos palitos azuis, segundo a regra do jogo.<br \/>\nCom efeito, do lado esquerdo do palito (1) n\u00e3o existem outros palitos e, do lado direito, ao pular os dois palitos consecutivos, n\u00e3o existe um terceiro palito isolado para que o palito (1) possa ser colocado sobre ele e formar um par.<br \/>\nCom rela\u00e7\u00e3o ao palito (2), tanto do seu lado esquerdo como do direito, s\u00f3 existe um palito isolado, logo o palito (2) n\u00e3o pode ser movimentado segundo as regras do jogo.<br \/>\nTamb\u00e9m, nenhum outro palito formar\u00e1 par com os palitos (1) e (2), j\u00e1 que eles s\u00f3 seriam o quarto de uma sequ\u00eancia de quatro palitos (um a ser movimentado, dois para serem pulados e cada um deles para receber o seu respectivo par) se desmont\u00e1ssemos o <strong>X<\/strong> que ocupa a quarta posi\u00e7\u00e3o, o que n\u00e3o \u00e9 permitido.<br \/>\n<strong>(b)<\/strong> O palito rosa pode ser movimentado e tamb\u00e9m \u00e9 o terceiro de uma sequ\u00eancia de tr\u00eas palitos. Assim, ter\u00edamos as pr\u00f3ximas op\u00e7\u00f5es de movimento.<br \/>\n <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F007.png\" alt=\"F007\" width=\"407\" height=\"112\" class=\"aligncenter size-full wp-image-65456\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F007.png 407w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F007-300x83.png 300w\" sizes=\"auto, (max-width: 407px) 100vw, 407px\" \/>Mas depois de executarmos qualquer um desses movimentos, n\u00e3o seria poss\u00edvel formarmos pares com os palitos azuis nos demais movimentos.\n<\/td>\n<\/tr>\n<tr>\n<td class=\"gree\" style=\"color: #616161; border:2px solid #800000; width:45%; text-align: center; background-color: #D3D3D3; font-size:14px; color:#800000;\">\n<strong>Assim, tr\u00eas palitos n\u00e3o podem ficar isolados em um &#8220;canto&#8221;. (Proibi\u00e7\u00e3o (II))<\/strong>\n<\/td>\n<\/tr>\n<\/table>\n<\/div>\n<\/div>\n<p style=\"margin:40px\">\n<div style=\"text-align:center;\"><input class=\"bo1 c3 cb33 bg3\" value=\"Situa\u00e7\u00e3o 3\" title=\"Clique aqui\" type=\"button\" onclick=    \"if(this.parentNode.getElementsByTagName('div')[0].style.display != ''){this.parentNode.getElementsByTagName('div')[0].style.display = '';this.value = 'Ocultar';} else{this.parentNode.getElementsByTagName('div')[0].style.display = 'none'; this.value = 'Situa\u00e7\u00e3o 3';}\" \/>    <\/p>\n<div  style=\"display: none;\">\n<table class=\"gree\" style=\"border:2px solid #800000;\">\n<tr>\n<td class=\"gree\" style=\"color: #616161; border:2px solid #800000; border-right: 2px solid #800000; width:45%; text-align:justify;\">\n<p style=\"margin:10px\">\n<p><strong>(III) Quatro palitos podem ficar isolados em um &#8220;canto&#8221; ou entre &#8220;dois X&#8221;?<\/strong><\/p>\n<p style=\"margin:30px\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F011_1.png\" alt=\"F011_1\" width=\"519\" height=\"112\" class=\"aligncenter size-full wp-image-65749\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F011_1.png 519w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F011_1-300x65.png 300w\" sizes=\"auto, (max-width: 519px) 100vw, 519px\" \/>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"gree\" style=\"color: #616161; border:1px solid #d8d8d8;\">\n<ul>\n<li> <\/strong>A an\u00e1lise nas situa\u00e7\u00f5es <strong>A<\/strong> e <strong>B<\/strong> s\u00e3o an\u00e1logas:<br \/>\n&#9632;\t o \u00fanico movimento poss\u00edvel com o primeiro palito em <strong>A<\/strong> ou o \u00faltimo palito em <strong>B<\/strong> deixaria &#8220;dois palitos isolados em um canto&#8221; (<strong>Proibi\u00e7\u00e3o (I)<\/strong>);<br \/>\n&#9632;\t n\u00e3o existem movimentos poss\u00edveis para o segundo e o terceiro palitos em <strong>A<\/strong> e nem para o pen\u00faltimo e o antepen\u00faltimo palitos em <strong>B<\/strong>;<br \/>\n&#9632;\t para o quarto palito em <strong>A<\/strong> existem, no m\u00e1ximo, duas possibilidades de movimento:<\/li>\n<\/ul>\n<p style=\"margin:5px 5px 5px 80px;\">&#8211; se for poss\u00edvel ele pular o <strong>X<\/strong>, ficam &#8220;tr\u00eas palitos isolados no canto&#8221; esquerdo (<strong>Proibi\u00e7\u00e3o (II)<\/strong>);<br \/>\n&#8211; se ele formar par com o primeiro palito, como um par n\u00e3o pode ser desfeito, a configura\u00e7\u00e3o depois do movimento seria an\u00e1loga \u00e0 da<strong> Proibi\u00e7\u00e3o (I)<\/strong>: dois palitos isolados em um canto.<\/p>\n<p style=\"margin-left: 37px;\">&#9632; para o palito imediatamente ap\u00f3s o <strong>X<\/strong> em <strong>B<\/strong>, a discuss\u00e3o \u00e9 an\u00e1loga ao caso do quarto palito em <strong>A<\/strong>.<\/p>\n<ul>\n<li>Analisemos a situa\u00e7\u00e3o <strong>C<\/strong>.<br \/>\n&#9632;\t para o primeiro palito temos duas possibilidades de movimento:<\/li>\n<\/ul>\n<p style=\"margin:5px 5px 5px 80px;\">&#8211; se ele formar par com o quarto palito da sequ\u00eancia, como um par n\u00e3o pode ser desfeito, a configura\u00e7\u00e3o depois do movimento seria an\u00e1loga \u00e0 da<strong> Proibi\u00e7\u00e3o (I)<\/strong>: &#8220;dois palitos isolados no canto&#8221; esquerdo.<br \/>\n&#8211; se for poss\u00edvel ele pular o <strong>X<\/strong>, ficaria an\u00e1logo ao caso dos \u201ctr\u00eas palitos isolados no canto\u201d(<strong>Proibi\u00e7\u00e3o (II)<\/strong>);<\/p>\n<p style=\"margin:5px 5px 5px 10px;\">&#9632; n\u00e3o existem movimentos poss\u00edveis para o segundo e o terceiro palitos;<br \/>\n&#9632;\t para o quarto palito, a discuss\u00e3o \u00e9 an\u00e1loga ao caso do primeiro palito.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"gree\" style=\"color: #616161; border:2px solid #800000; width:45%; text-align: center; background-color: #D3D3D3; font-size:14px; color:#800000;\">\n<strong>Assim, quatro palitos n\u00e3o podem ficar isolados em um &#8220;canto&#8221; ou entre &#8220;dois X&#8221;. (Proibi\u00e7\u00e3o (III))<\/strong>\n<\/td>\n<\/tr>\n<\/table>\n<\/div>\n<\/div>\n<p style=\"margin:40px\">\n<div style=\"text-align:center;\"><input class=\"bo1 c3 cb33 bg3\" value=\"Situa\u00e7\u00e3o 4\" title=\"Clique aqui\" type=\"button\" onclick=    \"if(this.parentNode.getElementsByTagName('div')[0].style.display != ''){this.parentNode.getElementsByTagName('div')[0].style.display = '';this.value = 'Ocultar';} else{this.parentNode.getElementsByTagName('div')[0].style.display = 'none'; this.value = 'Situa\u00e7\u00e3o 4';}\" \/>    <\/p>\n<div  style=\"display: none;\">\n<table class=\"gree\" style=\"border:2px solid #800000;\">\n<tr>\n<td class=\"gree\" style=\"color: #616161; border:2px solid #800000; border-right: 2px solid #800000; width:45%; text-align:justify;\">\n<p style=\"margin:10px\">\n<p><strong>(IV) Seis palitos podem ficar isolados ?<\/strong><\/p>\n<p style=\"margin:30px\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/f021.png\" alt=\"f021\" width=\"599\" height=\"94\" class=\"aligncenter size-full wp-image-65856\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/f021.png 599w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/f021-300x47.png 300w\" sizes=\"auto, (max-width: 599px) 100vw, 599px\" \/>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"gree\" style=\"color: #616161; border:1px solid #d8d8d8;\"><\/strong>Como pares n\u00e3o podem ser desfeitos, qualquer uma das tr\u00eas situa\u00e7\u00f5es equivaleria a jogar o jogo com seis palitos e, nesse caso, o pr\u00f3ximo movimento nos levaria necessariamente a uma das pr\u00f3ximas configura\u00e7\u00f5es.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F018.png\" alt=\"F018\" width=\"718\" height=\"109\" class=\"aligncenter size-full wp-image-65859\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F018.png 718w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F018-300x46.png 300w\" sizes=\"auto, (max-width: 718px) 100vw, 718px\" \/><\/p>\n<ul>\n<li> Na primeira e segunda configura\u00e7\u00f5es ter\u00edamos a Proibi\u00e7\u00e3o (III): quatro palitos isolados em um \u201ccanto\u201d.\n<\/li>\n<li> Nas terceira e quarta configura\u00e7\u00f5es ter\u00edamos a Proibi\u00e7\u00e3o (II): tr\u00eas palitos isolados em um \u201ccanto\u201d.<\/li>\n<li> Nas duas \u00faltimas configura\u00e7\u00f5es ter\u00edamos a Proibi\u00e7\u00e3o (I): dois palitos isolados em um \u201ccanto\u201d.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"gree\" style=\"color: #616161; border:2px solid #800000; width:45%; text-align: center; background-color: #D3D3D3; font-size:14px; color:#800000;\">\n<strong>Assim, seis palitos n\u00e3o podem ficar isolados, ou seja,<br \/>\nn\u00e3o podemos jogar o jogo com seis palitos. (Proibi\u00e7\u00e3o (IV))<\/strong>\n<\/td>\n<\/tr>\n<\/table>\n<\/div>\n<\/div>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 30px; margin-bottom: 8px;border: 0 none\"\/>\n<hr style=\"height:6px; width:100%;background-color:#800000; margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 8px; margin-bottom: 30px;border: 0 none\"\/>\n<p>Tendo em vista as <strong>Proibi\u00e7\u00f5es (I)<\/strong> e <strong>(II)<\/strong>, ap\u00f3s o primeiro passo a sequ\u00eancia dos dez palitos deve ficar em uma das formas abaixo. Vamos analis\u00e1-las uma a uma quanto aos pr\u00f3ximos passos no jogo.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F008.png\" alt=\"F008\" width=\"594\" height=\"205\" class=\"aligncenter size-full wp-image-65462\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F008.png 594w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F008-300x104.png 300w\" sizes=\"auto, (max-width: 594px) 100vw, 594px\" \/><br \/>\n<strong>(a)<\/strong> Observe que, embora produzidas por movimentos iniciais distintos, a posi\u00e7\u00e3o dos palitos nas situa\u00e7\u00f5es <span  style=\"color: #db7613;\"> <strong>E<\/strong><\/span> e <span  style=\"color: #db7613;\"><strong>F<\/strong><\/span> s\u00e3o iguais.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F009.png\" style=\"border:0px;\" alt=\"F009\" width=\"176\" height=\"89\" class=\"aligncenter size-full wp-image-65464\" \/> e tanto \u00e0 esquerda quanto \u00e0 direita do <strong>X<\/strong> temos  a <strong>Proibi\u00e7\u00e3o (III)<\/strong>: quatro palitos isolados em um &#8220;canto&#8221;.<br \/>\n<strong>Assim, com as situa\u00e7\u00f5es<\/strong> <span  style=\"color: #db7613;\"> <strong>E<\/strong><\/span> <strong>e<\/strong> <span  style=\"color: #db7613;\"><strong>F<\/strong><\/span> <strong>n\u00e3o finalizamos o jogo.<\/strong> <\/p>\n<p style=\"margin:20px\">\n<p><strong>(b)<\/strong> Analisemos, agora os casos <span  style=\"color: #db7613;\"> <strong>A<\/strong><\/span> e <span  style=\"color: #db7613;\"><strong>B<\/strong><\/span>. Neles, podemos, a partir do segundo passo, considerar uma sequ\u00eancia de 8 palitos. Devido \u00e0s <strong>Proibi\u00e7\u00f5es (I)<\/strong> e <strong>(II)<\/strong>, uma sequ\u00eancia de oito palitos, ap\u00f3s o pr\u00f3ximo passo (o segundo passo do jogo), vai ficar em uma das formas mostradas abaixo.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F013.png\" alt=\"F013\" width=\"599\" height=\"79\" class=\"aligncenter size-full wp-image-65740\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F013.png 599w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F013-300x40.png 300w\" sizes=\"auto, (max-width: 599px) 100vw, 599px\" \/><\/p>\n<p style=\"margin:5px 5px 5px 10px;\">&#9632; Para os casos <span  style=\"color: #db7613;\"> <strong>AB<sub>1<\/sub><\/strong><\/span> e <span  style=\"color: #db7613;\"> <strong>AB<sub>4<\/sub><\/strong><\/span>, teremos que nos ater a uma sequ\u00eancia de seis palitos. Mas, de acordo com a <strong>Proibi\u00e7\u00e3o (IV)<\/strong>, n\u00e3o podemos concluir o jogo a partir dessa configura\u00e7\u00e3o. <\/p>\n<p style=\"margin:5px 5px 5px 50px;\">Portanto, nos casos <span  style=\"color: #db7613;\"> <strong>AB<sub>1<\/sub><\/strong><\/span> e <span  style=\"color: #db7613;\"> <strong>AB<sub>4<\/sub><\/strong><\/span> n\u00e3o conseguimos finalizar o jogo.<\/p>\n<p style=\"margin:5px 5px 5px 10px;\">&#9632; Analisemos o caso <span  style=\"color: #db7613;\"> <strong>AB<sub>2<\/sub><\/strong><\/span>. Ap\u00f3s o pr\u00f3ximo passo, obteremos uma das sequ\u00eancias a seguir. <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F017.png\" alt=\"F017\" width=\"761\" height=\"131\" class=\"aligncenter size-full wp-image-65821\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F017.png 761w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/F017-300x52.png 300w\" sizes=\"auto, (max-width: 761px) 100vw, 761px\" \/><\/p>\n<p style=\"margin:5px 5px 5px 40px;\">&#8211;  As sequ\u00eancias <strong>(1)<\/strong>, <strong>(4)<\/strong> e <strong>(5)<\/strong> configuram, respectivamente, as <strong>Proibi\u00e7\u00f5es (III), (II), (I)<\/strong>.<br \/>\n&#8211;  A sequ\u00eancia <strong>(3)<\/strong> \u00e9 an\u00e1loga \u00e0 da<strong> Proibi\u00e7\u00e3o (II)<\/strong>: tr\u00eas palitos isolados em um \u201ccanto\u201d.<br \/>\n&#8211; Para a sequ\u00eancia <strong>(2)<\/strong> h\u00e1 oito possibilidades de conclus\u00e3o do jogo, a partir da configura\u00e7\u00e3o <span  style=\"color: #db7613;\"> <strong>A<\/strong><\/span>: <\/p>\n<table  style=\" text-align:justify; margin-left: auto; margin-right: auto; width: 100%;font-size:12px;\">\n<tr>\n<td style=\"border: 1px solid #FFFFFF;\">\n<strong>1-4<\/strong> 2 3 5 6 7 8 9 10<br \/>\n1-4 2 <strong>3-7<\/strong> 5 6 8 9 10<br \/>\n1-4 2 3-7 6 8 <strong>5-9<\/strong> 10<br \/>\n1-4 3-7  <strong>2-6<\/strong> 8 5-9 10<br \/>\n1-4 3-7 2-6 5-9 <strong>8-10<\/strong>\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n<strong>1-4<\/strong> 2 3 5 6 7 8 9 10<br \/>\n1-4 2 <strong>3-7<\/strong> 5 6 8 9 10<br \/>\n1-4 2 3-7 6 8 <strong>5-9<\/strong> 10<br \/>\n1-4 3-7  <strong>2-6<\/strong> 8 5-9 10<br \/>\n1-4 3-7 2-6 <strong>8-10<\/strong> 5-9\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n<strong>1-4<\/strong> 2 3 5 6 7 8 9 10<br \/>\n1-4 2 <strong>3-7<\/strong> 5 6 8 9 10<br \/>\n1-4 2 3-7 6 8 <strong>5-9<\/strong> 10<br \/>\n1-4 <strong>2-6<\/strong> 3-7 8 5-9 10<br \/>\n1-4 2-6 3-7 5-9 <strong>8-10<\/strong>\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n<strong>1-4<\/strong> 2 3 5 6 7 8 9 10<br \/>\n1-4 2 <strong>3-7<\/strong> 5 6 8 9 10<br \/>\n1-4 2 3-7 6 8 <strong>5-9<\/strong> 10<br \/>\n1-4 <strong>2-6<\/strong> 3-7 8 5-9 10<br \/>\n1-4 2-6 3-7 <strong>8-10<\/strong> 5-9\n<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #FFFFFF\">\n<strong>1-4<\/strong> 2 3 5 6 7 8 9 10<br \/>\n1-4 2 <strong>3-7<\/strong> 5 6 8 9 10<br \/>\n1-4 2 3-7 6 8 <strong>5-9<\/strong> 10<br \/>\n1-4 2 3-7 6 5-9 <strong>8-10<\/strong><br \/>\n1-4 3-7 <strong>2-6<\/strong> 5-9 8-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n<strong>1-4<\/strong> 2 3 5 6 7 8 9 10<br \/>\n1-4 2 <strong>3-7<\/strong> 5 6 8 9 10<br \/>\n1-4 2 3-7 6 8 <strong>5-9<\/strong> 10<br \/>\n1-4 2 3-7 6 5-9 <strong>8-10<\/strong><br \/>\n1-4 <strong> 2-6<\/strong> 3-7 5-9 8-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n<strong>1-4<\/strong> 2 3 5 6 7 8 9 10<br \/>\n1-4 2 <strong>3-7<\/strong> 5 6 8 9 10<br \/>\n1-4 2 3-7 6 8 <strong>5-9<\/strong> 10<br \/>\n1-4 2 3-7 6 <strong>8-10<\/strong> 5-9<br \/>\n1-4 3-7 <strong> 2-6<\/strong> 8-10 5-9\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n<strong>1-4<\/strong> 2 3 5 6 7 8 9 10<br \/>\n1-4 2 <strong>3-7<\/strong> 5 6 8 9 10<br \/>\n1-4 2 3-7 6 8 <strong>5-9<\/strong> 10<br \/>\n1-4 2 3-7 6 <strong>8-10<\/strong> 5-9<br \/>\n1-4 <strong>2-6<\/strong> 3-7 8-10 5-9\n<\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:5px 5px 5px 10px;\"> e oito possibilidades de conclus\u00e3o do jogo, a partir da configura\u00e7\u00e3o <span  style=\"color: #db7613;\"> <strong>B<\/strong><\/span>: <\/p>\n<table  style=\" text-align:justify; margin-left: auto; margin-right: auto; width: 100%; font-size:12px;\">\n<tr>\n<td style=\"border: 1px solid #FFFFFF\">\n1 2 3 4 5 6 8 9 <strong>7-10<\/strong><br \/>\n1 <strong>2-5<\/strong> 3 4 6 8 9 7-10<br \/>\n1 2-5 4 6 <strong>3-8<\/strong> 9 7-10<br \/>\n2-5 <strong>1-4<\/strong> 6 3-8 9 7-10<br \/>\n2-5 1-4 3-8 <strong>6-9<\/strong> 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 2 3 4 5 6 8 9 <strong>7-10<\/strong><br \/>\n1 <strong>2-5<\/strong> 3 4 6 8 9 7-10<br \/>\n1 2-5 4 6 <strong>3-8<\/strong> 9 7-10<br \/>\n2-5 <strong>1-4<\/strong> 6 3-8 9 7-10<br \/>\n2-5 1-4 <strong>6-9<\/strong> 3-8 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 2 3 4 5 6 8 9 <strong>7-10<\/strong><br \/>\n1 <strong>2-5<\/strong> 3 4 6 8 9 7-10<br \/>\n1 2-5 4 6 <strong>3-8<\/strong> 9 7-10<br \/>\n<strong>1-4<\/strong> 2-5 6 3-8 9 7-10<br \/>\n 1-4 2-5 3-8 <strong>6-9<\/strong> 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 2 3 4 5 6 8 9 <strong>7-10<\/strong><br \/>\n1 <strong>2-5<\/strong> 3 4 6 8 9 7-10<br \/>\n1 2-5 4 6 <strong>3-8<\/strong> 9 7-10<br \/>\n<strong>1-4<\/strong> 2-5 6 3-8 9 7-10<br \/>\n1-4 2-5 <strong>6-9<\/strong> 3-8 7-10\n<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #FFFFFF\">\n1 2 3 4 5 6 8 9 <strong>7-10<\/strong><br \/>\n1 <strong>2-5<\/strong> 3 4 6 8 9 7-10<br \/>\n1 2-5 4 6 <strong>3-8<\/strong> 9 7-10<br \/>\n1 2-5 4 3-8 <strong>6-9<\/strong> 7-10<br \/>\n2-5 <strong>1-4<\/strong> 3-8 6-9 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 2 3 4 5 6 8 9 <strong>7-10<\/strong><br \/>\n1 <strong>2-5<\/strong> 3 4 6 8 9 7-10<br \/>\n1 2-5 4 6 <strong>3-8<\/strong> 9 7-10<br \/>\n1 2-5 4 3-8 <strong>6-9<\/strong> 7-10<br \/>\n<strong>1-4<\/strong> 2-5  3-8 6-9 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 2 3 4 5 6 8 9 <strong>7-10<\/strong><br \/>\n1 <strong>2-5<\/strong> 3 4 6 8 9 7-10<br \/>\n1 2-5 4 6 <strong>3-8<\/strong> 9 7-10<br \/>\n1 2-5 4 <strong>6-9<\/strong> 3-8 7-10<br \/>\n2-5 <strong>1-4<\/strong> 6-9 3-8 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 2 3 4 5 6 8 9 <strong>7-10<\/strong><br \/>\n1 <strong>2-5<\/strong> 3 4 6 8 9 7-10<br \/>\n1 2-5 4 6 <strong>3-8<\/strong> 9 7-10<br \/>\n1 2-5 4 <strong>6-9<\/strong> 3-8 7-10<br \/>\n<strong>1-4<\/strong> 2-5  6-9 3-8 7-10\n<\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:5px 5px 5px 10px;\">&#9632; A an\u00e1lise do caso <span  style=\"color: #db7613;\"> <strong>AB<sub>3<\/sub><\/strong><\/span> \u00e9 an\u00e1loga ao caso <span  style=\"color: #db7613;\"> <strong>AB<sub>2<\/sub><\/strong><\/span>. Temos, ent\u00e3o, mais dezesseis solu\u00e7\u00f5es para o jogo.<\/p>\n<table  style=\" text-align:justify; margin-left: auto; margin-right: auto; width: 100%; font-size:12px;\">\n<tr>\n<td style=\"border: 1px solid #FFFFFF\">\n<strong>1-4<\/strong> 2 3 5 6 7 8 9 10<br \/>\n1-4 2 3 5 7 8 <strong>6-9<\/strong> 10<br \/>\n1-4 2 <strong>3-8<\/strong> 5 7 6-9 10<br \/>\n1-4 3-8 <strong>2-5<\/strong> 7 6-9 10<br \/>\n1-4 3-8 2-5 6-9 <strong>7-10 <\/strong>\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n<strong>1-4<\/strong> 2 3 5 6 7 8 9 10<br \/>\n1-4 2 3 5 7 8 <strong>6-9<\/strong> 10<br \/>\n1-4 2 <strong>3-8<\/strong> 5 7 6-9 10<br \/>\n1-4 3-8 <strong>2-5<\/strong> 7 6-9 10<br \/>\n1-4 3-8 2-5 <strong>7-10<\/strong> 6-9\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n<strong>1-4<\/strong> 2 3 5 6 7 8 9 10<br \/>\n1-4 2 3 5 7 8 <strong>6-9<\/strong> 10<br \/>\n1-4 2 <strong>3-8<\/strong> 5 7 6-9 10<br \/>\n1-4 <strong>2-5<\/strong> 3-8 7 6-9 10<br \/>\n1-4 2-5 3-8  6-9 <strong>7-10 <\/strong>\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n<strong>1-4<\/strong> 2 3 5 6 7 8 9 10<br \/>\n1-4 2 3 5 7 8 <strong>6-9<\/strong> 10<br \/>\n1-4 2 <strong>3-8<\/strong> 5 7 6-9 10<br \/>\n1-4 <strong>2-5<\/strong> 3-8 7 6-9 10<br \/>\n1-4 2-5 3-8 <strong>7-10<\/strong> 6-9\n<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #FFFFFF\">\n<strong>1-4<\/strong> 2 3 5 6 7 8 9 10<br \/>\n1-4 2 3 5 7 8 <strong>6-9<\/strong> 10<br \/>\n1-4 2 <strong>3-8<\/strong> 5 7 6-9 10<br \/>\n1-4 2 3-8 5 6-9 <strong>7-10<\/strong><br \/>\n1-4 3-8 <strong>2-5<\/strong> 6-9 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n<strong>1-4<\/strong> 2 3 5 6 7 8 9 10<br \/>\n1-4 2 3 5 7 8 <strong>6-9<\/strong> 10<br \/>\n1-4 2 <strong>3-8<\/strong> 5 7 6-9 10<br \/>\n1-4 2 3-8 5 6-9 <strong>7-10<\/strong><br \/>\n1-4 <strong>2-5<\/strong> 3-8 6-9 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n<strong>1-4<\/strong> 2 3 5 6 7 8 9 10<br \/>\n1-4 2 3 5 7 8 <strong>6-9<\/strong> 10<br \/>\n1-4 2 <strong>3-8<\/strong> 5 7 6-9 10<br \/>\n1-4 2 3-8 5 <strong>7-10<\/strong> 6-9<br \/>\n1-4 3-8 <strong>2-5<\/strong> 7-10 6-9\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n<strong>1-4<\/strong> 2 3 5 6 7 8 9 10<br \/>\n1-4 2 3 5 7 8 <strong>6-9<\/strong> 10<br \/>\n1-4 2 <strong>3-8<\/strong> 5 7 6-9 10<br \/>\n1-4 2 3-8 5 <strong>7-10<\/strong> 6-9<br \/>\n1-4  <strong>2-5<\/strong> 3-8 7-10 6-9\n<\/td>\n<\/table>\n<p style=\"margin:10px\">\n<table  style=\" text-align:justify; margin-left: auto; margin-right: auto; width: 100%;  font-size:12px;\">\n<tr>\n<td style=\"border: 1px solid #FFFFFF\">\n1 2 3 4 5 6 8 9 <strong>7-10<\/strong><br \/>\n1 2 3 5 6 <strong>4-8<\/strong> 9 7-10<br \/>\n1 <strong>2-6<\/strong> 3 5 4-8 9 7-10<br \/>\n2-6 <strong>1-3<\/strong> 5 4-8 9 7-10<br \/>\n2-6 1-3 4-8 <strong>5-9<\/strong> 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 2 3 4 5 6 8 9 <strong>7-10<\/strong><br \/>\n1 2 3 5 6 <strong>4-8<\/strong> 9 7-10<br \/>\n1 <strong>2-6<\/strong> 3 5 4-8 9 7-10<br \/>\n2-6 <strong>1-3<\/strong> 5 4-8 9 7-10<br \/>\n2-6 1-3 <strong>5-9<\/strong> 4-8  7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 2 3 4 5 6 8 9 <strong>7-10<\/strong><br \/>\n1 2 3 5 6 <strong>4-8<\/strong> 9 7-10<br \/>\n1 <strong>2-6<\/strong> 3 5 4-8 9 7-10<br \/>\n<strong>1-3<\/strong> 2-6 5 4-8 9 7-10<br \/>\n1-3 2-6 4-8 <strong>5-9<\/strong> 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 2 3 4 5 6 8 9 <strong>7-10<\/strong><br \/>\n1 2 3 5 6 <strong>4-8<\/strong> 9 7-10<br \/>\n1 <strong>2-6<\/strong> 3 5 4-8 9 7-10<br \/>\n<strong>1-3<\/strong> 2-6 5 4-8 9 7-10<br \/>\n1-3 2-6 <strong>5-9<\/strong> 4-8 7-10\n<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #FFFFFF\">\n1 2 3 4 5 6 8 9 <strong>7-10<\/strong><br \/>\n1 2 3 5 6 <strong>4-8<\/strong> 9 7-10<br \/>\n1 <strong>2-6<\/strong> 3 5 4-8 9 7-10<br \/>\n1 2-6 3 4-8 <strong>5-9<\/strong> 7-10<br \/>\n2-6 <strong>1-3<\/strong> 4-8 5-9 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 2 3 4 5 6 8 9 <strong>7-10<\/strong><br \/>\n1 2 3 5 6 <strong>4-8<\/strong> 9 7-10<br \/>\n1 <strong>2-6<\/strong> 3 5 4-8 9 7-10<br \/>\n1 2-6 3 4-8 <strong>5-9<\/strong> 7-10<br \/>\n<strong>1-3<\/strong> 2-6  4-8 5-9 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 2 3 4 5 6 8 9 <strong>7-10<\/strong><br \/>\n1 2 3 5 6 <strong>4-8<\/strong> 9 7-10<br \/>\n1 <strong>2-6<\/strong> 3 5 4-8 9 7-10<br \/>\n1 2-6 3 <strong>5-9<\/strong> 4-8 7-10<br \/>\n2-6 <strong>1-3<\/strong> 5-9 4-8 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 2 3 4 5 6 8 9 <strong>7-10<\/strong><br \/>\n1 2 3 5 6 <strong>4-8<\/strong> 9 7-10<br \/>\n1 <strong>2-6<\/strong> 3 5 4-8 9 7-10<br \/>\n1 2-6 3 <strong>5-9<\/strong> 4-8 7-10<br \/>\n<strong>1-3<\/strong> 2-6 5-9 4-8 7-10\n<\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:20px\">\n<p><strong>(c)<\/strong> Vamos ao caso <span  style=\"color: #db7613;\"> <strong>C<\/strong><\/span>. Ap\u00f3s o pr\u00f3ximo movimento, ter\u00edamos uma das seguintes configura\u00e7\u00f5es.<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/f023.png\" style=\"border:none;\" alt=\"f023\" width=\"768\" height=\"225\" class=\"aligncenter size-full wp-image-65962\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/f023.png 768w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2016\/08\/f023-300x88.png 300w\" sizes=\"auto, (max-width: 768px) 100vw, 768px\" \/><\/p>\n<p style=\"margin:5px 5px 5px 10px;\">&#9632; Para os casos <span  style=\"color: #A0522D;\"> <strong>(6)<\/strong>, <strong>(7)<\/strong>, <strong>(8)<\/strong><\/span> e <span  style=\"color: #A0522D;\"> <strong>(9)<\/strong><\/span> teremos as <strong>Proibi\u00e7\u00f5es (IV), (II), (I), (III)<\/strong>, respectivamente. Logo n\u00e3o poderemos concluir o jogo a partir dessas configura\u00e7\u00f5es.<br \/>\n&#9632; No caso <span  style=\"color: #A0522D;\"> <strong>(11)<\/strong><\/span>, n\u00e3o \u00e9 poss\u00edvel formar um par com o primeiro palito e, portanto, o jogo n\u00e3o poder\u00e1 ser conclu\u00eddo.<br \/>\n&#9632; A sequ\u00eancia <span style=\"color: #A0522D;\"> <strong>(12)<\/strong><\/span>, apresenta a configura\u00e7\u00e3o da Proibi\u00e7\u00e3o (III). Assim, temos mais uma sequ\u00eancia sem possibilidade para a conclus\u00e3o do jogo.<br \/>\n&#9632; Resta-nos apenas a sequ\u00eancia <span  style=\"color: #A0522D;\"> <strong>(10)<\/strong><\/span> e esta \u00e9 a sequ\u00eancia <span  style=\"color: #db7613;\"> <strong>AB<sub>2<\/sub><\/strong><\/span>, obtida a partir da configura\u00e7\u00e3o <span  style=\"color: #db7613;\"> <strong>B<\/strong><\/span> com o movimento <strong>2-5<\/strong> sendo feito antes do<strong> 7-10<\/strong>. Temos, ent\u00e3o, mais oito solu\u00e7\u00f5es.<\/p>\n<table  style=\" text-align:justify; margin-left: auto; margin-right: auto; width: 100%; font-size:12px;\">\n<tr>\n<td style=\"border: 1px solid #FFFFFF\">\n1 <strong>2-5<\/strong> 3 4 6 7 8 9 10<br \/>\n1 2-5 3 4 6 8 9 <strong>7-10<\/strong><br \/>\n1 2-5 4 6 <strong>3-8<\/strong> 9 7-10<br \/>\n2-5 <strong>1-4<\/strong> 6 3-8 9 7-10<br \/>\n2-5 1-4 3-8 <strong>6-9<\/strong> 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 <strong>2-5<\/strong> 3 4 6 7 8 9 10<br \/>\n1 2-5 3 4 6 8 9 <strong>7-10<\/strong><br \/>\n1 2-5 4 6 <strong>3-8<\/strong> 9 7-10<br \/>\n2-5 <strong>1-4<\/strong> 6 3-8 9 7-10<br \/>\n2-5 1-4 <strong>6-9<\/strong> 3-8 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 <strong>2-5<\/strong> 3 4 6 7 8 9 10<br \/>\n1 2-5 3 4 6 8 9 <strong>7-10<\/strong><br \/>\n1 2-5 4 6 <strong>3-8<\/strong> 9 7-10<br \/>\n<strong>1-4<\/strong> 2-5 6 3-8 9 7-10<br \/>\n 1-4 2-5 3-8 <strong>6-9<\/strong> 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 <strong>2-5<\/strong> 3 4 6 7 8 9 10<br \/>\n1 2-5 3 4 6 8 9 <strong>7-10<\/strong><br \/>\n1 2-5 4 6 <strong>3-8<\/strong> 9 7-10<br \/>\n<strong>1-4<\/strong> 2-5 6 3-8 9 7-10<br \/>\n1-4 2-5 <strong>6-9<\/strong> 3-8 7-10\n<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #FFFFFF\">\n1 <strong>2-5<\/strong> 3 4 6 7 8 9 10<br \/>\n1 2-5 3 4 6 8 9 <strong>7-10<\/strong><br \/>\n1 2-5 4 6 <strong>3-8<\/strong> 9 7-10<br \/>\n1 2-5 4 3-8 <strong>6-9<\/strong> 7-10<br \/>\n2-5 <strong>1-4<\/strong> 3-8 6-9 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 <strong>2-5<\/strong> 3 4 6 7 8 9 10<br \/>\n1 2-5 3 4 6 8 9 <strong>7-10<\/strong><br \/>\n1 2-5 4 6 <strong>3-8<\/strong> 9 7-10<br \/>\n1 2-5 4 3-8 <strong>6-9<\/strong> 7-10<br \/>\n<strong>1-4<\/strong> 2-5  3-8 6-9 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 <strong>2-5<\/strong> 3 4 6 7 8 9 10<br \/>\n1 2-5 3 4 6 8 9 <strong>7-10<\/strong><br \/>\n1 2-5 4 6 <strong>3-8<\/strong> 9 7-10<br \/>\n1 2-5 4 <strong>6-9<\/strong> 3-8 7-10<br \/>\n2-5 <strong>1-4<\/strong> 6-9 3-8 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1 <strong>2-5<\/strong> 3 4 6 7 8 9 10<br \/>\n1 2-5 3 4 6 8 9 <strong>7-10<\/strong><br \/>\n1 2-5 4 6 <strong>3-8<\/strong> 9 7-10<br \/>\n1 2-5 4 <strong>6-9<\/strong> 3-8 7-10<br \/>\n<strong>1-4<\/strong> 2-5 6-9 3-8 7-10\n<\/td>\n<\/tr>\n<\/table>\n<p><strong>(d)<\/strong> Resta, apenas, o caso <span  style=\"color: #db7613;\"> <strong>D<\/strong><\/span> e este \u00e9 an\u00e1logo ao caso <span  style=\"color: #db7613;\"> <strong>C<\/strong><\/span>. Temos, ent\u00e3o, mais oito solu\u00e7\u00f5es.<\/p>\n<table  style=\" text-align:justify; margin-left: auto; margin-right: auto; width:100%; font-size:12px;\">\n<tr>\n<td style=\"border: 1px solid #FFFFFF\">\n1-4 2 3 5 7 8 <strong>6-9<\/strong> 10<br \/>\n<strong>1-4<\/strong> 2 3 5 7 8 6-9 10<br \/>\n1-4 2 <strong>3-8<\/strong> 5 7 6-9 10<br \/>\n1-4 3-8 <strong>2-5<\/strong> 7 6-9 10<br \/>\n1-4 3-8 2-5 6-9 <strong>7-10 <\/strong>\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1-4 2 3 5 7 8 <strong>6-9<\/strong> 10<br \/>\n<strong>1-4<\/strong> 2 3 5 7 8 6-9 10<br \/>\n1-4 2 <strong>3-8<\/strong> 5 7 6-9 10<br \/>\n1-4 3-8 <strong>2-5<\/strong> 7 6-9 10<br \/>\n1-4 3-8 2-5 <strong>7-10<\/strong> 6-9\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1-4 2 3 5 7 8 <strong>6-9<\/strong> 10<br \/>\n<strong>1-4<\/strong> 2 3 5 7 8 6-9 10<br \/>\n1-4 2 <strong>3-8<\/strong> 5 7 6-9 10<br \/>\n1-4 <strong>2-5<\/strong> 3-8 7 6-9 10<br \/>\n1-4 2-5 3-8  6-9 <strong>7-10 <\/strong>\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1-4 2 3 5 7 8 <strong>6-9<\/strong> 10<br \/>\n<strong>1-4<\/strong> 2 3 5 7 8 6-9 10<br \/>\n1-4 2 <strong>3-8<\/strong> 5 7 6-9 10<br \/>\n1-4 <strong>2-5<\/strong> 3-8 7 6-9 10<br \/>\n1-4 2-5 3-8 <strong>7-10<\/strong> 6-9\n<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #FFFFFF\">\n1-4 2 3 5 7 8 <strong>6-9<\/strong> 10<br \/>\n<strong>1-4<\/strong> 2 3 5 7 8 6-9 10<br \/>\n1-4 2 <strong>3-8<\/strong> 5 7 6-9 10<br \/>\n1-4 2 3-8 5 6-9 <strong>7-10<\/strong><br \/>\n1-4 3-8 <strong>2-5<\/strong> 6-9 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1-4 2 3 5 7 8 <strong>6-9<\/strong> 10<br \/>\n<strong>1-4<\/strong> 2 3 5 7 8 6-9 10<br \/>\n1-4 2 <strong>3-8<\/strong> 5 7 6-9 10<br \/>\n1-4 2 3-8 5 6-9 <strong>7-10<\/strong><br \/>\n1-4  <strong>2-5<\/strong> 3-8 6-9 7-10\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1-4 2 3 5 7 8 <strong>6-9<\/strong> 10<br \/>\n<strong>1-4<\/strong> 2 3 5 7 8 6-9 10<br \/>\n1-4 2 <strong>3-8<\/strong> 5 7 6-9 10<br \/>\n1-4 2 3-8 5 <strong>7-10<\/strong> 6-9<br \/>\n1-4 3-8 <strong>2-5 <\/strong>7-10 6-9\n<\/td>\n<td style=\"border: 1px solid #FFFFFF\">\n1-4 2 3 5 7 8 <strong>6-9<\/strong> 10<br \/>\n<strong>1-4<\/strong> 2 3 5 7 8 6-9 10<br \/>\n1-4 2 <strong>3-8<\/strong> 5 7 6-9 10<br \/>\n1-4 2 3-8 5 <strong>7-10<\/strong> 6-9<br \/>\n1-4 <strong>2-5 <\/strong> 3-8 7-10 6-9\n<\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:30px\">\n<p class=\"ti2\" style=\"color:#800000\">Finalmente, dentro do esp\u00edrito do que foi definido como solu\u00e7\u00e3o do jogo,<br \/>\ntemos exatamente 48 solu\u00e7\u00f5es<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 15px;border: 0 none\"\/>\n<p class=\"g2\" style=\"line-height:20px;\">Solu\u00e7\u00e3o elaborada pelos <strong>Moderadores do Blog<\/strong>.<\/p>\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"g1n\">\n<p class=\"tit\" style=\"line-height:30px;margin:10px\">Explorando a solu\u00e7\u00e3o<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\nPodemos observar que algumas disposi\u00e7\u00f5es dos palitos podem ser obtidas por mais de um conjunto de movimentos. Embora sejam 48 modos diferentes de chegarmos \u00e0 finaliza\u00e7\u00e3o do jogo, existem apenas 15 poss\u00edveis disposi\u00e7\u00f5es finais dos palitos:<\/p>\n<p style=\"margin:10px 10px 20px 50px;\">\n[tex]\\bigstar \\,  \\,  \\, [1,3] \\,  [2,6] \\,  [4,8] \\,  [5,9] \\,  [7,10] \\\\<br \/>\n\\bigstar \\,  \\,  \\,  [1,3] \\,  [2,6] \\,  [5,9] \\,  [4,8] \\,  [7,10] \\\\<br \/>\n\\bigstar  \\,  \\,  \\, [1,4]  \\,  [2,5]  \\,  [3,8]  \\,  [6,9]   \\,  [7,10] \\\\<br \/>\n\\bigstar  \\,  \\,  \\, [1,4]  \\,  [2,5]  \\,  [3,8]  \\,  [7,10]  \\,  [6,9] \\\\<br \/>\n\\bigstar  \\,  \\,  \\, [1,4]  \\,  [2,5] \\,  [6,9]  \\, [3,8]  \\, [7,10] \\\\<br \/>\n\\bigstar  \\,  \\,  \\, [1,4]  \\,  [2,6]  \\,  [3,7]  \\,  [5,9]  \\,  [8,10] \\\\<br \/>\n\\bigstar  \\,  \\,  \\, [1,4]  \\,  [2,6]  \\,  [3,7]  \\,  [8,10]  \\,  [5,9] \\\\<br \/>\n\\bigstar \\,  \\,  \\,  [1,4]  \\,  [3,7]  \\,  [2,6]  \\,  [5,9]  \\,  [8,10] \\\\<br \/>\n\\bigstar \\,  \\,  \\,  [1,4]  \\,  [3,7]  \\,  [2,6]  \\,  [8,10]  \\,  [5,9] \\\\<br \/>\n\\bigstar  \\,  \\,  \\, [1,4] \\,  [3,8]  \\, [2,5] \\,  [6,9] \\,  [7,10]\\\\<br \/>\n\\bigstar  \\,  \\,  \\, [1,4] \\,  [3,8] \\,  [2,5] \\,  [7,10] \\,  [6,9] \\\\<br \/>\n\\bigstar  \\,  \\,  \\, [2,5] \\,  [1,4] \\,  [6,9] \\,  [3,8]  \\, [7,10] \\\\<br \/>\n\\bigstar \\,  \\,  \\,  [2,5] \\,  [1,4] \\,  [3,8] \\,  [6,9] \\,  [7,10] \\\\<br \/>\n\\bigstar  \\,  \\,  \\, [2,6] \\,  [1,3] \\,  [4,8]  \\, [5,9] \\,  [7,10] \\\\<br \/>\n\\bigstar \\,  \\,  \\,  [2,6] \\,  [1,3] \\,  [5,9] \\,  [4,8] \\,  [7,10].[\/tex]<\/p>\n<p>A seguir mostramos a frequ\u00eancia dessas configura\u00e7\u00f5es nos 48 movimentos poss\u00edveis:<\/p>\n<p style=\"margin:10px 10px 20px 50px;\">\n[tex]\\bigstar \\,  \\,  \\, [1,3] \\,  [2,6] \\,  [4,8] \\,  [5,9] \\,  [7,10]  \\, (2 \\, conjuntos \\, de \\, movimentos)\\\\<br \/>\n\\bigstar \\,  \\,  \\,  [1,3] \\,  [2,6] \\,  [5,9] \\,  [4,8] \\,  [7,10]  \\, (2 \\, conjuntos \\, de \\, movimentos)\\\\<br \/>\n\\bigstar  \\,  \\,  \\, [1,4]  \\,  [2,5]  \\,  [3,8]  \\,  [6,9]   \\,  [7,10] \\, (8 \\, conjuntos \\, de \\, movimentos) \\\\<br \/>\n\\bigstar  \\,  \\,  \\, [1,4]  \\,  [2,5]  \\,  [3,8]  \\,  [7,10]  \\,  [6,9]  \\, (4 \\, conjuntos \\, de \\, movimentos) \\\\<br \/>\n\\bigstar  \\,  \\,  \\, [1,4]  \\,  [2,5] \\,  [6,9]  \\, [3,8]  \\, [7,10] \\, (4 \\, conjuntos \\, de \\, movimentos) \\\\<br \/>\n\\bigstar  \\,  \\,  \\, [1,4]  \\,  [2,6]  \\,  [3,7]  \\,  [5,9]  \\,  [8,10]  \\, (2 \\, conjuntos \\, de \\, movimentos)\\\\<br \/>\n\\bigstar  \\,  \\,  \\, [1,4]  \\,  [2,6]  \\,  [3,7]  \\,  [8,10]  \\,  [5,9] \\, (2 \\, conjuntos \\, de \\, movimentos)\\\\<br \/>\n\\bigstar \\,  \\,  \\,  [1,4]  \\,  [3,7]  \\,  [2,6]  \\,  [5,9]  \\,  [8,10] \\, (2 \\, conjuntos \\, de \\, movimentos) \\\\<br \/>\n\\bigstar \\,  \\,  \\,  [1,4]  \\,  [3,7]  \\,  [2,6]  \\,  [8,10]  \\,  [5,9] \\, (2 \\, conjuntos \\, de \\, movimentos) \\\\<br \/>\n\\bigstar  \\,  \\,  \\, [1,4] \\,  [3,8]  \\, [2,5] \\,  [6,9] \\,  [7,10] \\, (4 \\, conjuntos \\, de \\, movimentos) \\\\<br \/>\n\\bigstar  \\,  \\,  \\, [1,4] \\,  [3,8] \\,  [2,5] \\,  [7,10] \\,  [6,9] \\, (4 \\, conjuntos \\, de \\, movimentos)  \\\\<br \/>\n\\bigstar  \\,  \\,  \\, [2,5] \\,  [1,4] \\,  [6,9] \\,  [3,8]  \\, [7,10]  \\, (4 \\, conjuntos \\, de \\, movimentos) \\\\<br \/>\n\\bigstar \\,  \\,  \\,  [2,5] \\,  [1,4] \\,  [3,8] \\,  [6,9] \\,  [7,10] \\, (4 \\, conjuntos \\, de \\, movimentos)  \\\\<br \/>\n\\bigstar  \\,  \\,  \\, [2,6] \\,  [1,3] \\,  [4,8]  \\, [5,9] \\,  [7,10]  \\, (2 \\, conjuntos \\, de \\, movimentos)\\\\<br \/>\n\\bigstar \\,  \\,  \\,  [2,6] \\,  [1,3] \\,  [5,9] \\,  [4,8] \\,  [7,10] \\, (2 \\, conjuntos \\, de \\, movimentos).[\/tex]<\/p>\n<p>Observe que determinados pares de palitos podem se apresentar em posi\u00e7\u00f5es  diferentes na configura\u00e7\u00e3o final, gerando solu\u00e7\u00f5es distintas. Por exemplo,  [tex] \\, [1,3] \\,  [2,6] \\,  [4,8] \\,  [5,9] \\,  [7,10]  \\, [\/tex] e [tex] \\,  [1,3] \\,  [2,6] \\,  [5,9] \\,  [4,8] \\,  [7,10]  \\, [\/tex] s\u00e3o disposi\u00e7\u00f5es finais distintas de um mesmo conjunto de pares de palitos.<br \/>\nAssim, se  n\u00e3o levarmos em considera\u00e7\u00e3o a posi\u00e7\u00e3o dos pares na configura\u00e7\u00e3o final temos apenas tr\u00eas conjuntos de pares de cinco palitos nas configura\u00e7\u00f5es poss\u00edveis:<\/p>\n<div style=\"padding-left:10px;font-size:13.5px\">\n<p style=\" border-style: dotted;border-color :#800000; border-width:thin; width:560px;text-align:center\"> Palitos [tex]1[\/tex] e [tex]3[\/tex];  &nbsp;   Palitos [tex]2[\/tex] e [tex]6[\/tex];   &nbsp;  Palitos [tex]4[\/tex] e [tex]8[\/tex];   &nbsp;   Palitos [tex]5[\/tex] e [tex]9[\/tex];    &nbsp;   Palitos [tex]7[\/tex] e [tex]10[\/tex]. <\/p>\n<p style=\" border-style: dotted;border-color :#800000; border-width:thin; width:560px;text-align:center\"> Palitos [tex]1[\/tex] e [tex]4[\/tex];   &nbsp;  Palitos [tex]2[\/tex] e [tex]5[\/tex]; &nbsp;  Palitos [tex]3[\/tex] e [tex]8[\/tex];   &nbsp;  Palitos [tex]6[\/tex] e [tex]9[\/tex];     &nbsp;   Palitos [tex]7[\/tex] e [tex]10[\/tex].<\/p>\n<p style=\" border-style: dotted;border-color :#800000; border-width:thin; width:560px;text-align:center\"> Palitos [tex]1[\/tex] e [tex]4[\/tex];  &nbsp;  Palitos [tex]2[\/tex] e [tex]6[\/tex]; &nbsp;  Palitos [tex]3[\/tex] e [tex]7[\/tex]; &nbsp;   Palitos [tex]5[\/tex] e [tex]9[\/tex];  ;  &nbsp;    Palitos [tex]8[\/tex] e [tex]10[\/tex].<\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Problema (Indicado a partir do 7\u00ba ano do E. F.) Para resolver este problema voc\u00ea ter\u00e1 que jogar um joguinho. Jogo Dez palitos de f\u00f3sforo est\u00e3o alinhados. Voc\u00ea pode formar pares movendo um palito, de modo que ele pule dois outros e seja colocado sobre o terceiro, respeitando sempre a disposi\u00e7\u00e3o dos palitos no momento &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/desafio-grupo-de-dois\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-66176","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/66176","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=66176"}],"version-history":[{"count":24,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/66176\/revisions"}],"predecessor-version":[{"id":67415,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/66176\/revisions\/67415"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=66176"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}