tag:blogger.com,1999:blog-48110485658142013262024-02-06T20:45:56.184-08:00EnigmatemágicaQuebra-cabeças, problemas de lógica, problemas de estratégia, enigmas, puzzles, problemas com números, chapéus, travessias, prisioneiros.
Enigmatemágica é uma combinação das palavras enigma, matemática e mágica. Afinal, a solução de enigmas envolve raciocínios parecidos com aqueles que usamos na matemática e algumas soluções parecem até mágicas!
Teste seu QI.Unknownnoreply@blogger.comBlogger82125tag:blogger.com,1999:blog-4811048565814201326.post-19374538582860512082019-07-22T19:16:00.000-07:002020-04-16T14:49:28.140-07:00Pesando de um a quarenta<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> No mercado de uma cidade, há um agricultor que vende os
produtos que planta, medindo-os por peso. Para isso ele usa uma balança de
comparação, com dois pratos, como a da figura, tendo 40 pedras, cada uma de um
quilograma, usadas para medir a quantidade de produto desejado. Ele só vende
quantidades que correspondem a valores inteiros de massas entre 1 e 40 kg.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh52hKXxUhRxXWsvBhUXna6YbVSmy3l7JE8ylWNvNiRgj9qYPbksYDomDK7IU-yks75kkcCf7h9QVns8iTy54cNeXeYSy1Ak-JYxhuLj03wuuUxl6z1qqEC4UWrpo_wCnAcpSXln9WTP5wH/s1600/PesandoUmQuarentI.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="145" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh52hKXxUhRxXWsvBhUXna6YbVSmy3l7JE8ylWNvNiRgj9qYPbksYDomDK7IU-yks75kkcCf7h9QVns8iTy54cNeXeYSy1Ak-JYxhuLj03wuuUxl6z1qqEC4UWrpo_wCnAcpSXln9WTP5wH/s320/PesandoUmQuarentI.png" width="320" /></a></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> <o:p></o:p></span><span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;"> </span><span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;">Um dia, entretanto, ele perdeu todas suas pedras e ficou
muito chateado, pois para continuar com seu trabalho – de vender produtos entre
1 kg e 40 kg, no mercado – precisaria encontrar mais 40 pedras de
exatamente um quilograma cada.</span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Mas,
felizmente, quando contou seu problema para um amigo, interessado em
quebra-cabeças numéricos, ouviu dele: “você não precisa de 40 pedras; bastam 4”.<o:p></o:p></span></div>
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> Quanto pesam essas 4 pedras?</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgk1VdR3JD6CUPi0d-cXQiHdaN8_IRCoP1zzPPX1ju9xvDmp-cehDoggHzs0GOmwY2QCMHlnFjQsLraPDdAloc5Ww9KR5wAFbhjEXAqR9Om2pkhgnKSSLGQ6xVQA_juKJ7qVW-P3zaACtd/s1600/capaMatRecr.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="790" data-original-width="532" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgk1VdR3JD6CUPi0d-cXQiHdaN8_IRCoP1zzPPX1ju9xvDmp-cehDoggHzs0GOmwY2QCMHlnFjQsLraPDdAloc5Ww9KR5wAFbhjEXAqR9Om2pkhgnKSSLGQ6xVQA_juKJ7qVW-P3zaACtd/s200/capaMatRecr.jpg" width="134" /></a><b style="font-family: "times new roman", serif; font-size: 14pt;"><a href="https://www.livrariadafisica.com.br/detalhe_produto.aspx?id=146662&titulo=Matem%C3%A1tica+Recreativa">ESTE BLOG VIROU LIVRO. CLIQUE AQUI PARA SITE DA EDITORA</a></b></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> <i>Aqui vai a resposta.
Como é uma balança de dois pratos, ele pode colocar os pesos em ambos os
pratos. Assim, pedras com 1 kg, 3 kg, 9 kg e 27 kg resolvem
o problema. Para pesar um produto de 1 kg, basta colocá‑lo em um dos
pratos da balança e a pedra de 1 kg no outro. Para pesar 2 kg, coloca‑se
o produto em um dos pratos juntamente com a pedra de 1 kg e no outro, a
pedra de 3 kg: os pratos ficarão equilibrados, pois em ambos há 3 kg.
A figura mostra, por exemplo, como ele pesaria um produto de 17 kg.
Examinando com paciência, você verá que é possível pesar qualquer coisa entre 1 kg
e 40 kg com as quatro pedras apenas.<o:p></o:p></i></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdIjsgI71sa3IQq3Ie9Ez12-J11CThKE5trTmGS6IfA7QlFCYiBWqKIQFUjvpC-bYWgb76xI7JZQQLik8fuScv21wWUgzT0hFdXrLfxeQ7nyNy8wDLspq51XPOD8JyOcr5dpdSbuGk-xSo/s1600/PesandoUmQuarentII.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="245" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdIjsgI71sa3IQq3Ie9Ez12-J11CThKE5trTmGS6IfA7QlFCYiBWqKIQFUjvpC-bYWgb76xI7JZQQLik8fuScv21wWUgzT0hFdXrLfxeQ7nyNy8wDLspq51XPOD8JyOcr5dpdSbuGk-xSo/s400/PesandoUmQuarentII.png" width="400" /></a></div>
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<b><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Bases numéricas<o:p></o:p></span></b></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> <i>Uma possibilidade para
se pesar qualquer coisa até 40 kg seria usar pedras na base dois: 1, 2, 4,
8, 16 e 32 kg e apenas um dos pratos da balança, deixando o produto a ser
pesado sozinho no outro prato. (Note que com essas pedras podemos pesar até
63 kg.) Com aquelas pedras podemos balancear qualquer peso. Por exemplo,
37 kg=32 kg+4 kg+1 kg. Por similaridade com a base dois, é
como se escrevêssemos 100101, Ou seja, colocar uma pedra na balança (lembre-se:
estamos usando apenas um prato para as pedras) é como usar o dígito 1 na
posição correspondente àquela pedra; não colocar uma determinada pedra, é como
colocar um dígito 0 na casa correspondente a ela. Mas, nesse caso das pedras 1,
2, 4, 8, 16 e 32, seriam necessárias mais pedras, 6, do que a solução das quatro
pedras com 1, 3, 9 e 27 kg. <o:p></o:p></i></span></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> Epa! Esses valores são potências de 3: 3
elevado a zero, que é um; 3 elevado a um, que é 3; a seguinte é 3×3=9; a
próxima é 3 ao cubo, 3×3×3=27. Será que a solução tem alguma similaridade com a
base 3? Tem. A rigor, na base 3 precisaríamos três algarismos, 0, 1 e 2 para
representar um número. Assim, se tivéssemos duas pedras de 1 kg, duas de
3 kg etc, poderíamos construir qualquer valor usando-as em apenas um dos
pratos e colocando a mercadoria a ser pesada no outro, Mas como só temos duas
possibilidades, colocar ou não uma pedra, usamos um truque, aproveitando o fato
que podemos usar os dois pratos da balança.<o:p></o:p></span></i></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Vamos ver esse truque com um
exemplo. O número 6 na base dez é 20 na base 3. Mas também podemos representar
o número 6 como 100-10 na base 3 (que é igual a 9-3 na base 10). Isso
corresponde a colocar o peso de 9 kg (100) em um dos pratos e o de
3 kg (10) no outro. A diferença será de 6 kg. Ou seja, embora não
tenhamos os três dígitos 0, 1 e 2, temos os dígitos -1, 0 e 1, também três!<o:p></o:p></span></i></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Aproveitando essa possibilidade de
subtração, podemos representar qualquer número de 1 até 40 e, portanto, pesar
qualquer coisa entre 1 kg e 40 kg, <o:p></o:p></span></i></div>
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<b><i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> E
as moedas?<span style="font-variant: small-caps;"><o:p></o:p></span></span></i></b></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> Nós
pagamos coisas com dinheiro. Para isso é necessário que o carreguemos nos
bolsos. Claro que esse dinheiro poderia se resumir a apenas um valor, por
exemplo, moedas de 10 centavos. Assim, sairíamos de casa com centenas delas no
bolso para as despesas diárias. Mas moedas com apenas um valor seria pouco
prático, então, inventamos moedas e cédulas em papel com diferentes valores e
na hora do pagamento, escolhemos as mais adequadas.<o:p></o:p></span></i></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">As moedas (moedas e papel)
brasileiras são divididas de uma forma estranha: 0,10, 0,25, 0,50, 1, 2, 5, 10 ...(tudo
em reais). Esses valores são, aproximadamente, proporcionais a 1, 2, 4, 8 etc.,
quase como na base dois. Ora, comprar coisas é quase como equilibrar coisas em
uma balança de dois pratos. Quando compramos alguma coisa, entregamos ao
vendedor certo valor em dinheiro e ele nos entrega a mercadoria e outra
quantidade de dinheiro. Se os valores das moedas fossem iguais aos valores das
posições na base três, 1, 3, 9, 27, 81 ...,não reduziria a quantidade
necessária de notas de papel e moedas carregadas pelas pessoas, como ocorreu no
caso da balança, no qual pesos na base 3 se mostraram mais eficientes do que na
base dois? (Como temos facilidade para fazer com número redondos, esses valores
poderiam ser 1, 3, 10, 30, 100 ....)</span></i><br />
<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"><br /></span></i>
<span style="font-family: "times new roman" , "serif"; font-size: 14pt; line-height: 115%;"><b><a href="https://www.livrariadafisica.com.br/detalhe_produto.aspx?id=146662&titulo=Matem%C3%A1tica+Recreativa">ESTE BLOG VIROU LIVRO. CLIQUE AQUI PARA SITE DA EDITORA</a></b></span><br />
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Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-4811048565814201326.post-64604204306931510142019-07-10T08:08:00.000-07:002020-04-16T14:48:31.102-07:00Duas luvas para examinar três pacientes<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;">Um
médico, chamado às pressas para um lugar remoto, precisava examinar três
pessoas que poderiam estar com uma doença grave e facilmente transmissível. Por
isso, esse exame deveria ser feito com luvas, que impediriam o médico de se
contaminar e de contaminar as outras pessoas caso alguma delas estivesse
contaminada. Assim, as luvas usadas para examinar uma pessoa não poderiam ser usadas
no exame de outra pessoa, nem o médico poderia tocar nelas com suas mãos
desprotegidas.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;">Mas
havia um problema: o médico dispunha de apenas dois pares de luvas.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;">Como
examinar as três pessoas sem que nenhuma delas, nem o médico, corresse risco?
(O médico precisava usar as duas mãos no exame.)<o:p></o:p></span></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;">O médico usaria, no primeiro exame, um dos pares de
luvas. A seguir, retiraria essas luvas, que poderiam ter os lados de fora
contaminados, mas não as descartaria, pois os lados internos não estariam
contaminados. Com o segundo par de luvas, examinaria a segunda pessoa, mas não
tiraria as luvas.<o:p></o:p></span></i></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;">Para examinar a terceira pessoa,
o médico vestiria sobre a luva que usara no segundo exame e cuja parte externa
poderia estar contaminada, o primeiro par de luvas virado no avesso, que
certamente não estava contaminado.<o:p></o:p></span></i><br />
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-32417625528204297242018-12-02T14:12:00.000-08:002019-07-04T10:30:16.279-07:00O problema das doze pérolas<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Um comerciante de pérolas separou 12 delas pensando que todas fossem idênticas e de mesmo peso. Entretanto, por um descuido, incluiu entre elas uma pérola diferente, ou mais pesada ou mais leve do que as demais. Para descobrir qual delas era a pérola diferente e saber se ela é mais pesada ou mais leve do que as demais, ele tinha uma balança de comparação, dessas com dois pratos.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhha0kPe6gfr63yi6Eq8Yv8GHaVzZXEFtiUDnUaDFlMpB5SFgnxN8ChtmzNNdG57TMkN4Rj95nIYyA_GpDmqEeaefBCca-r1lc8ival-8CBNFbcrkK7hFK8hAGBgrFEtTtfMn0dMwwg7X1U/s1600/Sem+t%25C3%25ADtulo.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="270" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhha0kPe6gfr63yi6Eq8Yv8GHaVzZXEFtiUDnUaDFlMpB5SFgnxN8ChtmzNNdG57TMkN4Rj95nIYyA_GpDmqEeaefBCca-r1lc8ival-8CBNFbcrkK7hFK8hAGBgrFEtTtfMn0dMwwg7X1U/s320/Sem+t%25C3%25ADtulo.png" width="320" /></a></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Como, usando apenas três vezes a balança, ele poderia descobrir a pérola mais pesada? (Tudo o que ele tinha eram as pérolas e a balança, nada mais.)<o:p></o:p></span><br />
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<i>Primeira pesagem<o:p></o:p></i></div>
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<i>Em uma primeira pesagem o comerciante deve colocar 4 pérolas em cada um dos pratos da balança. Caso a balança se equilibre, as pesagens seguintes devem seguir o caminho (A); caso se desequilibre, devem seguir o caminho (B).<o:p></o:p></i></div>
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<i>(A) Se a balança se equilibrou, a pérola diferente não está entre as 8 pérolas já pesadas. Na segunda pesagem, nosso amigo deve colocar em um dos pratos uma das pérolas ainda não pesadas com uma das pérolas já pesadas e, portanto, não suspeitas. No outro prato, deve colocar duas das 4 pérolas suspeitas, deixando uma das suspeitas de fora.<o:p></o:p></i></div>
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<i>(A1) Caso o prato da balança com as duas pérolas suspeitas se mostre mais pesado, ela saberá que ou a pérola diferente é mais pesada e está entre as duas do prato mais pesado, ou é mais leve e é aquela que ficou no prato com uma das pérolas “boas”. Na terceira pesagem, o comerciante deve colocar as duas pérolas que ficaram no prato mais pesado, uma em cada um dos pratos da balança: se equilibrar, a pérola diferente é aquela que esteve no prato mais leve, e que ele não usou nessa terceira pesagem, e é mais leve. Caso contrário, é a mais pesada das duas usadas na terceira pesagem. (Evidentemente, caso o prato com as duas pérolas suspeitas se mostre mais leve na segunda pesagem, e não mais pesado, o procedimento é análogo.)<o:p></o:p></i></div>
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<i>(B) Caso a balança se desequilibre na primeira pesagem, a segunda pesagem deve ser feita da forma que segue. Vamos identificar por 1, 2, 3 e 4 as pérolas que estavam no prato mais leve depois da primeira pesagem, e por 5, 6, 7 e 8 as que estavam no prato mais pesado. A segunda pesagem pode ser feita colocando em um dos pratos as pérolas 1, 2 e 5 e no outro, as pérolas 6, 3 e uma das não suspeitas.<o:p></o:p></i></div>
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<i>(B1) Caso os pratos se equilibrem após essa segunda pesagem, a pérola diferente ou é a 4, e mais leve, ou é 7 ou a 8 e mais pesada. Comparando as pérolas 7 e 8 nosso amigo descobrirá a pérola diferente e saberá se ela é mais leve ou mais pesada do que as outras.<o:p></o:p></i></div>
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<i>(B2) Caso os pratos não se equilibrem após a segunda pesagem e o mais pesado na primeira pesagem continue a ser o mais pesado, então ou uma das pérolas entre a 1 e a 2 é mais leve ou a 6 é mais pesada. Uma terceira pesagem com as pérolas 1 e 2, uma em cada prato, resolve o problema. Caso os pratos não se equilibrem, mas o que era mais leve se torna mais pesado, a pérola diferente é uma das que foram trocadas de prato: ou a 3, e é mais leve, ou a 5 é mais pesada. A terceira pesagem resolve o problema.<o:p></o:p></i></div>
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<i>No início do problema, havia 24 possibilidades para os pesos das pérolas: ou uma das 12 era mais pesada, ou era mais leve. Depois da primeira pesagem, ela estava reduzida para 8. Após a segunda pesagem, a quantidade de dúvidas estava reduzida a duas (por acaso) ou a três. Finalmente, após a terceira pesagem não havia mais dúvidas. Aparentemente, a cada pesagem a quantidade de possibilidades é reduzida por um fator três. <span style="color: red;"><b>(Veja o quebra-cabeça "As 27 pérolas".)</b></span> Se isso é verdade, será que é possível descobrir uma pérola diferente, mais pesada ou mais leve, entre 13? Afinal, temos 26 possibilidades de início. Se conseguirmos reduzir por um fator 3 a cada vez...</i><br />
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<span style="color: #0000ee; font-family: "times new roman"; font-weight: 700;"><a href="https://www.livrariadafisica.com.br/detalhe_produto.aspx?id=146662&titulo=Matem%C3%A1tica+Recreativa">😉 ESTE BLOG VIROU LIVRO. CLIQUE AQUI PARA SITE DA EDITORA</a></span></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-31263468481401443812018-07-27T10:01:00.003-07:002020-05-15T17:15:02.935-07:00Este blog virou livro<span style="font-size: large;">Muitos problemas deste blog foram incluídos neste livro</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgt4u10qjAnEUzmaE421WFIN5A5GaMbhDfcmxh9F9fcaVRknDHIT33bif9lpm6jDGvjMZtbM8kWyzmlVIKkPjLOwEW53mUTL_hBa9Di7p8FEuBLSQ8KZ22hPJ3M89F2ei8OjDcUFFOy6Pde/s1600/capaMatRecr.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="790" data-original-width="532" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgt4u10qjAnEUzmaE421WFIN5A5GaMbhDfcmxh9F9fcaVRknDHIT33bif9lpm6jDGvjMZtbM8kWyzmlVIKkPjLOwEW53mUTL_hBa9Di7p8FEuBLSQ8KZ22hPJ3M89F2ei8OjDcUFFOy6Pde/s400/capaMatRecr.jpg" width="268" /></a></div>
<br />
<a href="https://www.livrariadafisica.com.br/detalhe_produto.aspx?id=146662&titulo=Matem%C3%A1tica+Recreativa"><span style="font-size: large;">Clique aqui para acessar sítio da editora</span></a>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-21552175717036577412017-06-01T14:32:00.001-07:002018-08-07T18:34:11.471-07:00Só aquela que nada via podia saber a cor<div class="MsoNormal" style="margin-bottom: 12.0pt; text-indent: 35.4pt;">
<span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;">Os seis bancos de uma praça tinham sido pintados há pouco, três deles
verdes, dois azuis e um branco. Quatro amigas, Arlete, Berenice, Carla e Dora,
foram à praça levar seus cachorros para passear e, enquanto esperavam,
sentaram-se, cada uma em um banco. Prestando atenção ao que seus cachorros
faziam, nenhuma delas notou o banco no qual sentara nem nos bancos que suas
amigas sentaram. <o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;">Quando foram embora, andando em fila com seus cachorros, cruzaram com
uma amiga que avisou-as que as partes traseiras de suas roupas estavam pintadas
das cores dos bancos. Elas olharam frustradas e chateadas para os seis bancos
recém-pintados. Como andavam em fila, levando seus cachorros, Arlete, que
estava atrás de todas e podia ver as roupas manchadas de suas amigas, disse
“não sei de que cor minha roupa foi manchada”. Em seguida, Berenice, que podia
ver a cor das manchas nas costas de Carla e Dora, mas não na sua própria nem na
de Arlete, afirmou “eu também não”. A seguir, Carla, a segunda da fila e que só
via as costas de Dora, também afirmou não saber de que cor sua roupa estaria
manchada.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;">Dora que não podia ver as costas dela mesma nem de suas amigas, disse
“eu sei em que banco sentei”.<o:p></o:p></span></div>
<span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;">Como Dora, que nada via,
podia saber qual era a cor do banco que sujara sua roupa?</span><br />
<span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;"></span><br />
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<div style="text-align: center;">
<span style="color: #0000ee; font-family: "times new roman"; font-weight: 700;">😉 ESTE BLOG VIROU LIVRO. CLIQUE AQUI PARA VER 😉</span></div>
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<i><span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;">Quando Arlete afirmou
que não podia saber de que cor sua roupa estava manchada era porque as três
cores que viam não podiam ser duas azuis e uma branca. Se fosse assim, a sua
seria verde. Portanto, pelo menos uma das cores que via era verde.<o:p></o:p></span></i></div>
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<i><span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;">Sabendo disso, se Berenice não tivesse visto nenhuma verde, saberia que
a cor do banco no qual entara era verde. Portanto, Berenice viu que Carla ou
Dora, ou ambas, tinham a roupa manchada de verde. <o:p></o:p></span></i></div>
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<i><span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;">Se Carla visse em Dora uma cor diferente de verde, saberia que a cor do
banco em que ela própria sentara era verde. <o:p></o:p></span></i></div>
<span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;"><i style="text-indent: 35.4pt;"><span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;">Seguindo esse raciocínio, Dora concluiu que sua roupa estava manchada
pela tinta verde do banca em que sentara.</span></i></span><br />
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-3917083088125946092017-05-29T19:10:00.000-07:002018-08-07T18:34:38.612-07:00Quem é o mentiroso?<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">A<span class="apple-converted-space"><span style="background: white;"> </span></span><span style="background: white;">polícia
de um país no qual habitavam pessoas que sempre diziam a verdade e outras que
sempre mentiam, prendeu quatro suspeitos de um crime e interrogou cada uma
delas separadamente. A primeira disse que entre eles havia apenas um mentiroso;
a segunda disse que havia dois mentirosos e dois que só falavam a verdade; a terceira afirmou que três deles
eram mentirosos e um, não; e a última pessoas disse que todos os quatro eram mentirosos. </span></span><br />
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"><span style="background: white;">Quais deles eram os mentirosos e quais falavam a verdade?</span></span><br />
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"><span style="background: white;"></span></span><br />
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<span style="font-family: inherit; font-size: large;"><i>Impossível apenas um deles ser mentiroso, pois as quatro respostas são incompatíveis. Portanto, a primeira pessoa não está falando a verdade. A segunda pessoa também não está falando a verdade, pois não há duas respostas consistentes. Se o quarto está dizendo a verdade, ele seria mentiroso, o que é um paradoxo. Portanto, está mentindo.</i><i>Apenas o terceiro está dizendo a verdade.</i></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgk1VdR3JD6CUPi0d-cXQiHdaN8_IRCoP1zzPPX1ju9xvDmp-cehDoggHzs0GOmwY2QCMHlnFjQsLraPDdAloc5Ww9KR5wAFbhjEXAqR9Om2pkhgnKSSLGQ6xVQA_juKJ7qVW-P3zaACtd/s1600/capaMatRecr.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="790" data-original-width="532" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgk1VdR3JD6CUPi0d-cXQiHdaN8_IRCoP1zzPPX1ju9xvDmp-cehDoggHzs0GOmwY2QCMHlnFjQsLraPDdAloc5Ww9KR5wAFbhjEXAqR9Om2pkhgnKSSLGQ6xVQA_juKJ7qVW-P3zaACtd/s200/capaMatRecr.jpg" width="134" /></a></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-31020022761334851122017-05-28T21:09:00.000-07:002019-07-04T10:26:15.496-07:00Casais ciumentos<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Duas jovens e belas noivas
e seus respectivos e atraentes noivos precisavam atravessar um rio. Entretanto,
eles dispunham de um barco que não poderia levar mais do que duas pessoas sem
afundar. Para evitar cenas de ciúmes ou constrangimentos, uma noiva não poderia
ficar com um homem, em uma das margens do rio, se o seu noivo não estivesse
junto.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> Qual a
estratégia para atravessar o rio sem criar nenhum mal estar entre os casais? E
se fossem três os casais?<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> <i>Dois casais</i>.
<i>Em uma primeira viagem, vão as duas
noivas e volta uma delas. Na segunda viagem, vão os dois noivos e volta a noiva
que havia ficado do outro lado do rio. Finalmente, vão as duas noivas.<o:p></o:p></i></span><br />
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"><i><br /></i></span></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">No
caso de três casais, para facilitar a descrição, vamos chama-los de Ari e Ana,
Beto e Beth e Caio e Cora.</span></i></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Na
primeira travessia, vão Beth e Cora e Cora volta. A seguir, Ana e Cora vão e Cora
volta. Na próxima vez, vão Ari e Beto; Ari e Ana voltam. A seguir, vão Caio e Ari
e Beth volta. Na próxima travessia, vão Beth e Ana vão e Beth volta. Finalmente,
vão Cora e Beth.<o:p></o:p></span></i></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">A tabela abaixo mostra esse situação descrita.</span></i></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"><br /></span></i></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-43535178630250552472017-05-27T10:48:00.000-07:002018-08-07T18:35:30.245-07:00Os monges de olhos verdes<!--[if gte mso 9]><xml>
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<![endif]--> Em uma distante e alta montanha há um monastério com 100 monges que jamais falam uns com os outros, pois isso seria considerado uma falta totalmente inaceitável. Mas essa não é a única coisa estranha nesse mosteiro: os monges acreditam piamente que aqueles que têm olhos verdes são amaldiçoados, devendo abandonar o monastério durante a noite, para preservar a sacralidade do local. E essa sagrada regra jamais seria desobedecida pelos monges desta história.<br />
Como os monges se recolhem para dormir ao cair da noite, em quartos separados e isolados, caso alguém abandonasse o mosteiro, isso só seria sabido na manhã seguinte, quando todos os monges se reunissem para o café da manhã em uma grande mesa.<br />
Além de jamais dizerem uma única palavra, nesse monastério não há espelhos ou qualquer outra coisa que possa refletir a imagem de uma pessoa, pois ver o próprio rosto é considerado uma violação gravíssima de um preceito sagrado. Portanto, impedidos de trocar sequer uma única palavra, alguém que tenha olhos verdes não tem como saber disso (pense que eles foram para o monastério ainda quando eram crianças muito pequenas, que sequer sabiam ver cores...). Assim, os monges viviam em paz, apesar de haver entre eles 10 com olhos verdes, que, claro, não sabiam disso.<br />
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Mas um dia um montanhista aventureiro passou em frente à mesa onde os 100 monges tomavam o café da manhã. Inadvertidamente, comentou em voz alta “puxa, não sabia que pessoas com olhos verdes poderiam ser monges”. Fez esse comentário e continuou seu caminho, sem dizer quantos eram os monges de olhos verdes. Todos ouviram esse comentário, mas mantiveram o sagrado silêncio absoluto. <br />
Na primeira noite, nenhum monge deixou o monastério e, na manhã seguinte, todos os cem monges se encontraram no café da manhã. Nada aconteceu também na segunda noite: ninguém abandonou o monastério. Os dias foram se passando até que no décimo primeiro dia apenas os 90 monges que não tinham olhos verdes se encontraram para o café da manhã. Os outros dez companheiros haviam abandonado o monastério durante a noite.<br />
Como isso aconteceu?<br />
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<i> Suponha que houvesse um único monge de olhos verdes. Como ele conhecia a cor dos olhos de todos os seus companheiros, saberia que nenhum deles tem olhos verdes. Ouvindo o indiscreto comentário de montanhista, de que havia pelo menos um monge com olhos verdes, concluiria que este só poderia ser ele. Assim, ele abandonaria o mosteiro na primeira noite e não apareceria no dia seguinte para tomar café com seus silenciosos amigos.<br /> Caso houvesse dois monges com olhos verdes, cada um deles conheceria apenas um outro com esse estigma, ficando na dúvida se havia apenas um – o outro – ou se seriam dois, sendo ele mesmo o segundo. Ora, se houvesse apenas um, este teria ido embora na primeira noite. Como na primeira noite ninguém foi embora, cada um dos dois monges de olhos verdes ficaria sabendo que não havia apenas um com esse terrível estigma, sendo ele o segundo. Assim, ambos abandonariam o mosteiro na segunda noite.<br />Continuando com esse raciocínio, se houvesse três com olhos verdes, estes abandonariam o mosteiro na terceira noite e assim por diante. Portanto, na décima noite os dez monges com olhos verdes foram embora.<br />Há várias versões desse problema, com chapéus – cada um pode ver a cor do chapéu dos outros, mas não a cor do seu próprio chapéu –, com placas nas costas e com algumas outras coisas ou características que todos sabem menos a própria pessoa. </i><br />
<i>Mas há uma curiosidade: claro que antes do viajante fazer seu comentário, todos sabiam que havia pessoas com olhos, pois umas olhavam para as outras. Por que, então, o comentário do viajante criou uma nova situação? Eu não sei a resposta!</i><br />
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<a href="https://enigmatemagica.blogspot.com/2018/07/este-blog-virou-livro.html">ESTE BLOG VIROU LIVRO. CLIQUE AQUI PARA VER</a></div>
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Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-4811048565814201326.post-27704611802915487892017-05-26T18:40:00.000-07:002018-08-07T18:35:53.767-07:00Fios embaralhados<div class="MsoNormal" style="text-indent: 35.4pt;">
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tubo com 36 fios isolados uns dos outros foi enterrado ao longo de um trecho de
vinte quilômetros. Depois de completado o serviço, verificou-se que os extremos
de um mesmo fio não foram previamente marcados e todos eram idênticos. Isso,
evidentemente, criou um enorme problema. Depois de muita discussão, um dos
técnicos, bastante experiente, disse que resolveria o problema.</span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">“Eu
resolvo esse problema e marco os dois extremos de cada um dos fios apenas com
uma ida e volta até o outro extremo do tubo. Para isso, preciso apenas uma fonte de tensão
(uma bateria ou uma pilha, por exemplo) e uma lâmpada, para testar
continuidade, e etiquetas e caneta para marcar os fios”.</span><br />
<span style="font-family: "times new roman" , serif;"><span style="font-size: 18.6667px;">Como isso foi feito?</span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYKizYzHFOP1aUryLl_mPiXWDPAmeqeC0vGLb9W7QKuOnS7gG2G51KNP0rDqzrqkoZXbuy02kjSDIvEp1oXICuYuOCf0DiFt7Jk6GgDMTduo1BV7GPpmTNnT0mdD5nh-Do61Zmio7ohDpZ/s1600/FiosEmbaralhados.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="217" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYKizYzHFOP1aUryLl_mPiXWDPAmeqeC0vGLb9W7QKuOnS7gG2G51KNP0rDqzrqkoZXbuy02kjSDIvEp1oXICuYuOCf0DiFt7Jk6GgDMTduo1BV7GPpmTNnT0mdD5nh-Do61Zmio7ohDpZ/s400/FiosEmbaralhados.jpg" width="400" /></a></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> <i>O técnico, trabalhando
em uma das saídas da tubulação, deixou um dos extremos de um dos fios solto e
marcou-o com a letra A, juntou dois outros fios, marcando cada um com uma
etiqueta com a letra B. Em seguida, juntou três outros extremos de fios e
marcou cada um deles com a letra C. A seguir, juntou depois quatro fios e fez o
mesmo, até juntar os extremos de oito fios, marcando dada um deles com a letra
H. Ao todo, trabalhou com 1+2+3+...+8=36 fios. Em seguida, foi ao outro lado e
usando a lâmpada e a fonte de tensão não teve dificuldade em descobrir quais
eram os outros extremos dos fios marcados com A, B, C etc. Assim, colocou em
cada fio uma etiqueta com a letra correspondente.<o:p></o:p></i></span></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">A seguir, juntou
o fio A com um dos fios etiquetados com B, colocando a etiqueta A8 em um deles
e B8 no outro, uniu-os a um dos fios C, no qual colocou a etiqueta C8, e com um
dos fios D, que etiquetou com D8 etc., até um dos fios H, que recebeu a
etiqueta H8. A seguir, pegou um segundo fio B, etiquetando-o como B7, e
juntou-o a um dos fios C ainda soltos, que ganhou a etiqueta C7, depois juntou-os
a um dos fios D ainda não usado, que recebeu
a identificação D7, etc., até um fio que recebeu a etiqueta H7. Em
seguida, fez o mesmo com o terceiro fio C, ainda não usado,</span></i><span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;"> </span><i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">chamando-o
de C6 e continuou até um dos fios H, que foi nomeado H7. Continuou com esse
procedimento até que, ao final, cada um tinha uma etiqueta com um número, sendo
que fios com mesmos números estavam ligados uns aos outros.</span></i><span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;"><o:p></o:p></span></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Finalmente, voltou ao primeiro
extremo do longo cabo, separou os fios que tinha unido e, usando a lâmpada e a
bateria, pode identificar quais estavam ligados entre si no outro extremo do
tubo e, portanto, os respectivos números, que colocou nas etiquetas,
completando o serviço.<o:p></o:p></span></i></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Um aspecto interessante neste
problema é que basta uma ida até o outro extremo, independentemente da
quantidade de fios.</span></i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"><o:p></o:p></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgk1VdR3JD6CUPi0d-cXQiHdaN8_IRCoP1zzPPX1ju9xvDmp-cehDoggHzs0GOmwY2QCMHlnFjQsLraPDdAloc5Ww9KR5wAFbhjEXAqR9Om2pkhgnKSSLGQ6xVQA_juKJ7qVW-P3zaACtd/s1600/capaMatRecr.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="790" data-original-width="532" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgk1VdR3JD6CUPi0d-cXQiHdaN8_IRCoP1zzPPX1ju9xvDmp-cehDoggHzs0GOmwY2QCMHlnFjQsLraPDdAloc5Ww9KR5wAFbhjEXAqR9Om2pkhgnKSSLGQ6xVQA_juKJ7qVW-P3zaACtd/s200/capaMatRecr.jpg" width="134" /></a></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-13651285038292089822017-05-14T18:39:00.005-07:002018-08-07T18:36:45.716-07:00Repartindo o chocolate<span style="background: white; font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> Uma barra de chocolate tem m×n pequenos
retângulos. Quantas vezes você precisaria quebrar essa barra para separar todos
eles?</span><span style="background: white; font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"><br /></span>
<span style="background: white; font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"></span><br />
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<i><span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;">Note que a cada vez que você quebra uma barra de chocolate ou uma parte
dela, o número de pedaços aumenta de uma unidade. Como no final haverá m×n
pedaços, você precisa quebrar m×n-1 vezes.<o:p></o:p></span></i></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-58198755587057266792017-05-07T18:24:00.003-07:002018-08-07T18:37:07.847-07:00Um truelo (se é que essa palavra existe)<div style="text-align: left;">
<span style="font-weight: normal;"> <span style="font-family: "times new roman" , serif; font-size: 14pt;">Três pessoas, A, B e C, participavam de um desafio mortal,
um truelo, uma espécie de duelo a três. Nesse desafio, cada um deles deveria
escolher um dos dois outros para dar um tiro. O participante A não era muito
bom de pontaria e tinha uma chance de 30% de sucesso. O participante B, por sua
vez, tinha uma chance de sucesso e 60% e C não errava um tiro: em cem por cento
dos casos, acertava fatalmente o alvo. (Considere que as únicas hipóteses são
acertar fatalmente ou errar o alvo.)</span></span><br />
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<div class="MsoNormal" style="margin-bottom: 12.0pt; text-indent: 35.4pt;">
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> O
combinado era que inicialmente atiraria A, em seguida, B e, finalmente, C,
depois A novamente, seguido de B, de C etc. ... evidentemente, caso estivessem
vivos. Cada um deles, repetindo, podia escolher seu alvo livremente. Como deve
ser o primeiro tiro de A?</span><span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;"><o:p></o:p></span></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> O
melhor que A deve fazer é atirar para cima, sem tentar acertar ninguém.
Fazendo, isso, o próximo tiro é de B e o melhor que este deve fazer é mirar em
C. Caso acerte, o próximo a atirar é A novamente, o qual terá alguma chance de
acertar B e sair vivo.<o:p></o:p></span></i></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Caso erre, certamente C destinará
seu certeiro tiro em B, pois é a melhor forma de reduzir sua chance de morrer.
A seguir, A tentará matar C, tendo alguma chance de sucesso.<o:p></o:p></span></i></div>
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<div class="MsoNormal" style="margin-bottom: 12.0pt;">
<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> Esse
curioso quebra-cabeça mostra que pode ser interessante deixar nossos adversários
ou inimigos seguirem adiante, pois destruir um deles pode ser uma má escolha.
Será que isso é considerado em algumas disputas esportivas ou políticas?</span></i><span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;"><o:p></o:p></span></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-65397380779908262052017-05-03T18:36:00.002-07:002018-08-07T18:38:31.651-07:00O pote envenenado<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Um
riquíssimo e cruel rei recebeu sua remessa anual de mil potes de geleia de
morango, sua sobremesa favorita. Entretanto, seus espiões descobriram que um
dos potes estava envenenado, com um veneno fatal, mesmo que apenas
uma mínima quantidade fosse ingerida, mas não sabiam dizer qual, pois todos os
potes eram idênticos. Como não queria jogar fora seu estoque anual de geleia, o
rei decidiu convocar seus escravos provadores de alimento para descobrir qual deles
estava envenenado.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Mas
o rei não queria que muitos dos seus provadores morressem, pois ainda que fosse
riquíssimo e tivesse muitos escravos, serviçais, provadores de alimento etc.,
ele nada ganhava com a perda deles em quantidade maior do que a necessária para
descobrir o pote envenenado. Assim, o rei convocou seus cientistas e
consultou-os sobre a melhor forma de descobrir o pote de geleia envenenado perdendo
o menor número de escravos provadores possível. A sugestão implicaria, no máximo, na perda de oito provadores.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgk1VdR3JD6CUPi0d-cXQiHdaN8_IRCoP1zzPPX1ju9xvDmp-cehDoggHzs0GOmwY2QCMHlnFjQsLraPDdAloc5Ww9KR5wAFbhjEXAqR9Om2pkhgnKSSLGQ6xVQA_juKJ7qVW-P3zaACtd/s1600/capaMatRecr.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="790" data-original-width="532" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgk1VdR3JD6CUPi0d-cXQiHdaN8_IRCoP1zzPPX1ju9xvDmp-cehDoggHzs0GOmwY2QCMHlnFjQsLraPDdAloc5Ww9KR5wAFbhjEXAqR9Om2pkhgnKSSLGQ6xVQA_juKJ7qVW-P3zaACtd/s200/capaMatRecr.jpg" width="134" /></a></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">provadores e, possivelmente, uma parte
deles sobreviveria. O rei deveria numerar os mil potes de geleia usando o
sistema binário, assim: 1, 10, 11, 100, 101, 110, ... até 1111101000 (que é mil
na base dez). Um provador deveria comer uma pequeníssima parte de todos os
potes de geleia que tivesses o número 1 na última casa à direta, ou seja, dos
potes 1, 11, 101, 111 etc. Outro provador deveria comer uma amostra de cada
pote que tivesse o digito 1 na segunda posição da direita para a esquerda (10,
11, 110 etc.). O provador seguinte comeria uma amostra de cada pote com 1 na
terceira casa e assim por diante. Observando quais provadores morriam, o rei
saberia quais casas do número do pote envenenado tinham o valor 1 e quais
tinham o valor zero.<o:p></o:p></span></i></div>
<br /></div>
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Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-4811048565814201326.post-9084651878832455352017-01-02T10:51:00.000-08:002018-08-07T18:39:23.948-07:00Quais os times de preferência?<span style="font-family: "times new roman" , serif; font-size: 14.0pt; line-height: 115%;">Três amigos, moradores das cidades A, B e C,
estavam conversando sobre preferências futebolísticas. O morador da cidade A
observou, então, que cada um deles tinha como preferência o time da cidade de
um dos outros dois. O amigo que preferia o time da cidade B respondeu ao
morador da cidade A “de fato, isso é verdade”. Quais as cidades dos times de
preferência de cada um dos três amigos?</span><br />
<span style="font-family: "times new roman" , serif; font-size: 14.0pt; line-height: 115%;"></span><br />
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<br />
<span style="font-family: "times new roman" , serif;"><span style="font-size: 18.6667px;"> .Bom, a resposta não está aqui ...</span></span><br />
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-35867865807112293662016-06-12T17:57:00.003-07:002018-08-07T18:39:56.822-07:00Descubra a respostaImagine que você é um(a) motorista de táxi. Em uma segunda-feira pega três passageiros que fazem uma corrida de quatro quilômetros, até chegar em um hotel cinco estrelas.<br />
Qual o nome do(a) taxista?<br />
<a name='more'></a>Diferente dos demais quebra-cabeças deste blog, este não tem resposta. Cabe a você descobrir!<br />
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<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-43613521169140034252016-05-21T08:16:00.003-07:002018-08-07T18:40:21.928-07:00Problema na cozinha<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;">Um cozinheiro
recebeu uma encomenda: fazer uma torta em uma forma muito estranha, como aquela
da figura. A torta deveria ser constituída de uma camada inferior com uma
espessura exatamente igual às muitas outras tortas que ele fazia. Essa camada,
então, seria coberta com uma deliciosa geleia. Mas como ele era um cozinheiro
muito econômico, queria preparar uma camada de massa exatamente suficiente para
cobrir a área da forma e, para isso, precisaria saber a área da forma. Ele
estava acostumado a fazer tortas em formas circulares e retangulares e nesses
casos, não tinha nenhuma dificuldade em calcular a área, mas essa forma era
muito estranha.<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaSDqzsZvjrjmLFuMDwLDImcXGxCCH_8-huMwBtzj60-WpWOJnRq3Tuuw7vCEj9AQFfjvaGx6UJkxDpXHg_Wptf1dSlB8q9Vn16L_aq92wqD4D_WmC4OXJE9PNmPbYiTI6ZdnB8bdU-OWg/s1600/forma.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="211" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaSDqzsZvjrjmLFuMDwLDImcXGxCCH_8-huMwBtzj60-WpWOJnRq3Tuuw7vCEj9AQFfjvaGx6UJkxDpXHg_Wptf1dSlB8q9Vn16L_aq92wqD4D_WmC4OXJE9PNmPbYiTI6ZdnB8bdU-OWg/s320/forma.png" width="320" /></a></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;"> Na sua cozinha tinha tudo o que deve
ter em uma boa cozinha, a até mesmo, uma régua. Como ele poderia medir a área
da forma?<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;"> <i>Talvez
uma forma prática seja a seguinte. Ele derrama na forma uma determinada
quantidade de água conhecida, por exemplo, um litro. A seguir, mede a espessura
da camada de água. Dividindo o volume – um litro – pela espessura, ele obterá a
área da superfície da forma a ser coberta com sua massa.<o:p></o:p></i></span></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-67446418395050865412016-05-21T08:11:00.001-07:002018-08-07T18:41:07.402-07:00Uma faminta formiga<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> Uma
formiga estava no centro de uma das faces de um cubo de vidro quando percebeu
que havia um delicioso grão de açúcar no meio de uma das arestas de outras
faces.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYp9mUIERWklLahbZn9gRbkHdOoGnTuuei9-iHTwbtEOiMQe1Jewp0S6HD6g5Pywpv6ll9WlwREJDb0pLN6lCqJQFYrv7F7VcHYHgD3rA6kpZnF9Lf7O0joJ3fLLUeK-KwGxnsSxexwHqd/s1600/Formiga1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="245" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYp9mUIERWklLahbZn9gRbkHdOoGnTuuei9-iHTwbtEOiMQe1Jewp0S6HD6g5Pywpv6ll9WlwREJDb0pLN6lCqJQFYrv7F7VcHYHgD3rA6kpZnF9Lf7O0joJ3fLLUeK-KwGxnsSxexwHqd/s320/Formiga1.png" width="320" /></a></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;"> A formiga ficou em dúvida de qual seria
o caminho mais curto até o açúcar. Qual é ele, A ou B?<o:p></o:p></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgk1VdR3JD6CUPi0d-cXQiHdaN8_IRCoP1zzPPX1ju9xvDmp-cehDoggHzs0GOmwY2QCMHlnFjQsLraPDdAloc5Ww9KR5wAFbhjEXAqR9Om2pkhgnKSSLGQ6xVQA_juKJ7qVW-P3zaACtd/s1600/capaMatRecr.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="790" data-original-width="532" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgk1VdR3JD6CUPi0d-cXQiHdaN8_IRCoP1zzPPX1ju9xvDmp-cehDoggHzs0GOmwY2QCMHlnFjQsLraPDdAloc5Ww9KR5wAFbhjEXAqR9Om2pkhgnKSSLGQ6xVQA_juKJ7qVW-P3zaACtd/s200/capaMatRecr.jpg" width="134" /><b style="font-family: "times new roman"; text-align: start;"><span style="font-family: "times new roman" , "serif"; font-size: 14pt;"></span></b></a><b style="font-family: "times new roman"; text-align: start;"><span style="font-family: "times new roman" , "serif"; font-size: 14pt;"><a href="https://enigmatemagica.blogspot.com/2018/07/este-blog-virou-livro.html">ESTE BLOG VIROU LIVRO. CLIQUE AQUI PARA VER</a></span></b></div>
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<a name='more'></a><i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> Com um pouco de geometria
(e ajuda do teorema de Pitágoras), descobrimos que o caminho A é igual a
l×(1/2+1/raiz(2)),</span></i><i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> que é igual a 1,21</span><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">×</span><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">l. Para calcularmos o comprimento
do caminho B um truque é desenharmos duas fazes do cubo “desdobrando” dois de
seus lados, a face central e a face superior, como mostra a figura.</span></i><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjo0EnA05aynEh0sx_UTilPq5IoLg9g4Mngn1bH4t4Ayse2tFmdj_ykcwPAoNqAGjDyUvaHHyeDSriaC5ggdGZ8EAfvhu950QwvFByCiCj4AdJZQk9BS17R-fzByCvLWGd3Ym2e8eSYtdp3/s1600/Formiga2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjo0EnA05aynEh0sx_UTilPq5IoLg9g4Mngn1bH4t4Ayse2tFmdj_ykcwPAoNqAGjDyUvaHHyeDSriaC5ggdGZ8EAfvhu950QwvFByCiCj4AdJZQk9BS17R-fzByCvLWGd3Ym2e8eSYtdp3/s320/Formiga2.png" width="244" /></a></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-90797431030253758212016-05-08T19:03:00.000-07:002018-08-07T18:41:37.331-07:00Problemas de travessia<div class="MsoNormal">
<span style="font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;">Há vários problemas de travessia de rios. Este é um
deles.</span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Um homem e uma mulher, ambos com o mesmo peso, e
duas crianças, cada um pesando a metade do peso de cada adulto, precisam
atravessar um rio. Mas o barco que irão usar só pode carregar o peso
correspondente ao de um adulto (ou de duas crianças, que é igual ao de um
adulto). Todos podem remar. <o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqatoraAObBzqgRuA0SJC80wsFUV56gupBgMh_w1uHojroVoKSxfqjM-ud5n-hcO6usWDynVVUVLdnLhisjS8TCLv5whfFC2Ke_hK5RGtQ-V0L4ye5wLXAvKUS4YR-VDL1Sr074nskc4Du/s1600/Barco.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqatoraAObBzqgRuA0SJC80wsFUV56gupBgMh_w1uHojroVoKSxfqjM-ud5n-hcO6usWDynVVUVLdnLhisjS8TCLv5whfFC2Ke_hK5RGtQ-V0L4ye5wLXAvKUS4YR-VDL1Sr074nskc4Du/s400/Barco.png" width="400" /></a></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Qual a melhor estratégia para atravessar o rio?<o:p></o:p></span></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Vamos
direto à resposta. Inicialmente, vão as duas crianças; em seguida, uma delas,
digamos, a primeira, volta; na próxima viagem, vai o outro adulto; em seguida,
o barco volta, trazido pela segunda criança; novamente, vão as duas crianças;
em seguida, uma delas volta; na próxima viagem, vai o segundo adulto; depois,
volta a criança que estava do outo lado. Finalmente, as duas crianças
atravessam o rio. <o:p></o:p></span></i></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-37273512607309968572016-05-07T19:42:00.002-07:002018-08-07T18:42:08.755-07:00Mais uma travessia<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Três aventureiros
precisam atravessar um rio. Mas eles não sabem nadar e o rio é muito profundo
para atravessar andando. Felizmente, eles encontram dois garotos com um bote
que aceita ajudá-los. Mas o pequeno barco só pode transportar os dois garotos
ou um dos aventureiros, pois cada garoto pesa a metade de um aventureiro. Com a
ajuda dos garotos, os três aventureiros conseguiram atravessar o rio. </span><span lang="EN-US" style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Como isso foi feito?</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLX3_Jt3zT6y-xIQziyMc8nspzRUYXNuBpx2tLRxsriI757w9hG-RO7Y4G_-QVmg2YciVOih0COM4B1ug2D6InQzYt2FL7pa8KmnNrD4WPbAukvVT0eQIZqsbgYrr7aavU7IX949CZ499-/s1600/Barco2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="169" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLX3_Jt3zT6y-xIQziyMc8nspzRUYXNuBpx2tLRxsriI757w9hG-RO7Y4G_-QVmg2YciVOih0COM4B1ug2D6InQzYt2FL7pa8KmnNrD4WPbAukvVT0eQIZqsbgYrr7aavU7IX949CZ499-/s320/Barco2.png" width="320" /></a></div>
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<i><span lang="EN-US" style="font-family: "times new roman" , "serif"; font-size: 14.0pt;"></span></i></div>
<a name='more'></a><br />
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;">Primeiro, os dois garotos atravessam o rio; em
seguida, um deles volta com o barco; na próxima viagem, vai um dos
aventureiros; o barco volta com o outro garoto; depois, vão novamente os dois
garotes; a seguir, um deles volta; na próxima viagem, o outro aventureiro vai
para a outra margem; o garoto que estava lá volta com o barco; em seguida, vão
novamente os dois garotos; depois, um deles volta; então,
o terceiro aventureiro vai. Finalmente, o garoto que estava na outra margem
volta.<o:p></o:p></span></i></div>
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<i><span style="font-family: "times new roman" , serif; font-size: 14pt;">Ao todo, foram onde travessias do rio. Se
fossem apenas dois os aventureiros, quantas travessias seriam necessárias para levá-los
para a outra margem?<o:p></o:p></span></i><br />
<i><span style="font-family: "times new roman" , serif; font-size: 14pt;"><br /></span></i>
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<b><span style="font-family: "times new roman" , "serif"; font-size: 14pt;"><a href="https://enigmatemagica.blogspot.com/2018/07/este-blog-virou-livro.html">ESTE BLOG VIROU LIVRO. CLIQUE AQUI PARA VER</a></span></b></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-49380263132755905432016-04-27T18:37:00.001-07:002018-08-07T18:42:33.764-07:00Destros e canhotos<!--[if gte mso 9]><xml>
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<span style="background: white; font-family: "" serif "" , "serif"; font-size: 14.0pt;">Em um jogo de futebol, o técnico deu instruções claras para os jogadores
quanto à tática a ser seguida. Uma delas era esta.</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt;"></span></div>
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<span style="background: white; font-family: "" serif "" , "serif"; font-size: 14.0pt;">Sempre que o jogador A tiver a bola consigo, deverá passá-la para B.
Sempre que B tiver a bola, venha ela de onde vier, deverá passá-la para C</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt;">.</span><span style="font-family: "" serif "" , "serif"; font-size: 14.0pt;"><br />
<span style="background: white;">O jogador A é canhoto, o jogador C é destro e
nada se sabe sobre o jogador B, podendo ser destro ou canhoto.</span></span></div>
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<span style="background: white; font-family: "" serif "" , "serif"; font-size: 14.0pt;">Será que nesse arranjo tático algum jogador canhoto passará a bola a um
jogador destro?</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt;"></span></div>
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<span style="font-family: "" serif "" , "serif"; font-size: 14.0pt;"> <i>Caso B seja
destro, um jogador canhoto (A) passaria a bola para um destro (B). Caso B seja
canhoto, como C é destro, a instrução previa a passagem da bola de um canhoto
para um destro. Portanto, seja B destro ou canhoto, a resposta é “sim”.</i></span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt;"></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"><i><a href="https://enigmatemagica.blogspot.com/2018/07/este-blog-virou-livro.html">ESTE BLOG VIROU LIVRO. CLIQUE AQUI PARA VER</a></i></span>
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<b><span style="font-family: "times new roman" , "serif"; font-size: 14pt;"><br />http://enigmatemagica.blogspot.com.br/</span></b></div>
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<span style="font-size: large;">===========================</span><span style="font-size: large;">======</span><span style="font-size: large;">======</span><span style="font-size: large;">======</span></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-21954816077099210482016-04-27T18:34:00.001-07:002018-08-07T18:42:58.754-07:00Quantos jogos são necessários?<!--[if gte mso 9]><xml>
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<span style="font-family: "" serif "" , "serif"; font-size: 14.0pt;">Em uma competição, em cada partida disputam dois jogadores e o que perder é eliminado. Se há 127 jogadores disputando o campeonato, quantos jogos são
necessários para definir o campeão?</span><br />
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<i>Como cada jogo elimina um jogador e há 127 jogadores, são necessários 126 jogos: em cada um desses jogos, um dos jogadores será eliminado, restando apenas um no final.</i><br />
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-73762743000520685932016-04-23T13:53:00.003-07:002018-08-07T18:44:08.028-07:00Uma cinta no equador<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Um
exótico projeto previa a construção de uma cinta de aço, junto ao chão, em
torno do equador terrestre. Suponha que a linha do equador forme um círculo
perfeito, com exatamente 40 mil quilômetros de extensão, desconsidere a
dilatação térmica e tudo o mais que possa complicar o problema. A tal cinta de
exatos 40.000.000 de metros foi então encomendada. Entretanto, depois de
pronta, decidiu-se que a cinta, em vez de ficar em contato com o solo, deveria
ficar a dois metros do solo, de tal forma que uma pessoa pudesse passar sob ela.<o:p></o:p></span></div>
<br />
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"> Quanto mais longa deveria ser essa cinta?<o:p></o:p></span></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">De fato, a cinta de aço não precisa ser muito mais
longa. Basta ser serca de 12 metros mais longa ou, mais precisamente, 2×π×2 m.<o:p></o:p></span></i></div>
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<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"><br /></span></i></div>
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<span style="font-size: large;">===========================</span><span style="font-size: large;">======</span><span style="font-size: large;">======</span><span style="font-size: large;">======</span></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-51381979427502728282016-04-22T19:24:00.001-07:002018-08-07T18:44:32.724-07:00Quantos pés de meias são necessários?<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;">Em uma gaveta,
há dez meias vermelhas e dez meias azuis. Mas é noite sem lua, o quarto está
escuro, a lâmpada está queimada e você não dispõe de lanterna, fósforos, celular
ou qualquer outra coisa que sirva para iluminar. As meias, a menos da cor, são
idênticas. <o:p></o:p></span></div>
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Qual o menor número
de meias que você deve pegar para ter certeza de ter um par da mesma cor? E
qual o menor número para ter, com certeza, um par de meias vermelhas? Se você quiser
dois pares de meias da mesma cor, qualquer que seja ela, quantas meias você
deve pegar?</span><br />
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<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;">Se
metade das meias azuis e metade das meias vermelhas estiverem furadas – e você
não consegue perceber isso com o tato – , quantas meias você deve pegar para
ter, pelo menos, um par da mesma cor e sem furos?</span></div>
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<div class="MsoNormal">
<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;">Vamos direto às respostas. <o:p></o:p></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;">O menos número de meias que você deve pegar para ter
pelo menos duas da mesma cor, é três. </span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;">Mas se você quiser duas meias vermelhas,
deverá pegar pelo menos doze, pois dez delas podem ser azuis. <o:p></o:p></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;">Para ter dois pares de meias da mesma cor, você
precisa pegar pelo menos cinco meias. Caso você pegue apenas quatro, pode ter
três vermelhas e uma azul; qualquer que seja a cor da quinta meia, você terá
dois pares da mesma cor, sejam ambos azuis, vermelhos ou um par de cada cor.<o:p></o:p></span></i></div>
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</div>
<div class="MsoNormal">
<i><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt;">Mas se metade das meias azuis e metade das meias
vermelhas estiverem furadas, você precisará pegar pelo menos treze meias para ter um par sem furos. Mesmo
que você seja azarado e dez das meias pegas estejam furadas, entre as outras
três haverá pelo menos duas as mesma cor.<o:p></o:p></span></i></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-74636215068053388692016-04-19T15:41:00.003-07:002018-08-07T18:44:57.762-07:00Incêndio na ilha<!--[if gte mso 9]><xml>
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<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"><span style="mso-tab-count: 1;"> </span>Um
homem estava em uma ilha quando um incêndio começou em seu extremo norte. Um
vento muito forte, do norte para o sul, fazia o incêndio se dirigir rapidamente
em sua direção. O homem não tinha nada que permitisse apagar o fogo, não tinha
um barco para sair da ilha e nadar era impossível, pois o mar estava totalmente
infestado de famintos tubarões.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgk1VdR3JD6CUPi0d-cXQiHdaN8_IRCoP1zzPPX1ju9xvDmp-cehDoggHzs0GOmwY2QCMHlnFjQsLraPDdAloc5Ww9KR5wAFbhjEXAqR9Om2pkhgnKSSLGQ6xVQA_juKJ7qVW-P3zaACtd/s1600/capaMatRecr.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="790" data-original-width="532" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgk1VdR3JD6CUPi0d-cXQiHdaN8_IRCoP1zzPPX1ju9xvDmp-cehDoggHzs0GOmwY2QCMHlnFjQsLraPDdAloc5Ww9KR5wAFbhjEXAqR9Om2pkhgnKSSLGQ6xVQA_juKJ7qVW-P3zaACtd/s200/capaMatRecr.jpg" width="134" /></a></div>
<b><br /></b>
<a href="https://enigmatemagica.blogspot.com/2018/07/este-blog-virou-livro.html"><b>ESTE BLOG VIROU LIVRO. CLIQUE AQUI PARA VER</b></a><br />
<br /></div>
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<i style="mso-bidi-font-style: normal;"><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">Uma
solução talvez seja a seguinte. O homem ateia fogo em uma região mais ao sul.
Como o vento sopra fortemente do norte para o sul, o fogo que ele acendeu
propaga-se, rapidamente, para o sul. Assim, na medida em que o fogo vindo do
norte propaga em sua direção, o incêndio que ele provocou propaga-se
rapidamente para o sul, deixando uma região de mato queimado, para onde ele
pode ir. Quando o incêndio vindo do norte atingir a área já queimada pelo
incêndio provocado, ele se extinguirá. A ilha estará totalmente devastada pelo
fogo, mas nosso amigo estará salvo.</span></i></div>
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<a href="https://enigmatemagica.blogspot.com/2018/07/este-blog-virou-livro.html"><b>ESTE BLOG VIROU LIVRO. CLIQUE AQUI PARA VER</b></a></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-90349831453701394382016-04-19T11:31:00.001-07:002018-08-07T18:46:10.262-07:00Uma formiga azarada<span id="goog_1915267512"></span><span id="goog_1915267513"></span><!--[if !mso]>
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<span style="font-size: small;"><span style="color: black; font-family: "times new roman" , "serif";">Uma pobre formiga está em um extremo de um elástico de 10 cm de
comprimento. No outro extremo do elástico está um delicioso grão de açúcar A
formiga não teria nenhuma dificuldade para chegar até o grão de açúcar se não
fosse o fato que o elástico é segurado por uma criança que o estica de
10 cm, instantaneamente, a cada vez que a formiga anda um centímetro. O
elástico é esticado por um todo, tanto o pedaço que a formiga já andou como o
trecho que a separa do grão de açúcar. </span></span></div>
<span style="font-size: small;">
</span><br />
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<span style="font-size: small;"><span style="color: black; font-family: "times new roman" , "serif";">Se inicialmente a formiga estava a 10 cm do grão de açúcar, depois
de andar um centímetro, o elástico será esticado até ter 20 cm de
comprimento, de tal forma que o trecho andado passará a ter dois centímetros e
o trecho a andar, 18 cm. Mais um centímetro andado, e a criança estica o
elástico de mais 10 cm, fazendo com que o trecho andado passe a ter
3 cm e o grão de açúcar fique a 17 cm de distância da formiga.</span></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOFgi59Nqet-ht5oR3OR7BCWlQqS63GsQLm7uVj0yknKmcTOapeaE3gu-PPO_7TVGEcOZFNvI9mh0iKCKQ3PGL5d02bjFNpRWUHz0y3uU-TGnHnxc8mMSgfK_5QrDXMyY9Sfo7k1FwzIlY/s1600/formigaazarada.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="196" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOFgi59Nqet-ht5oR3OR7BCWlQqS63GsQLm7uVj0yknKmcTOapeaE3gu-PPO_7TVGEcOZFNvI9mh0iKCKQ3PGL5d02bjFNpRWUHz0y3uU-TGnHnxc8mMSgfK_5QrDXMyY9Sfo7k1FwzIlY/s400/formigaazarada.bmp" width="400" /></a></div>
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<span style="font-size: small;"><span style="color: black; font-family: "times new roman" , "serif";">Como este não é um problema da vida real, imagine que o elástico pode
ser esticado indefinidamente e a formiga não deixará, nunca, de se deslocar em
direção ao açúcar. A formiga conseguirá chegar até o grão de açúcar?</span></span><br />
<span style="font-size: small;"><span style="color: black; font-family: "times new roman" , "serif";"><br /></span></span>
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<div style="margin: 0px;">
<a href="https://enigmatemagica.blogspot.com/2018/07/este-blog-virou-livro.html">ESTE BLOG VIROU LIVRO. CLIQUE AQUI PARA VER</a></div>
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<span style="font-size: small;"><span style="color: black; font-family: "times new roman" , "serif";"></span></span></div>
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<span style="font-size: small;"><i style="mso-bidi-font-style: normal;"><span style="color: black; font-family: "times new roman" , "serif"; font-size: 13.5pt;">Aparentemente, a distância a ser
percorrida até o açúcar aumenta cada vez que o elástico é esticado. Afinal, no
início, a formiga estava a 10 cm do açúcar; depois de andar um centímetro
e o elástico ser esticado para 20 cm, ela estará a 18 cm do açúcar
(lembre-se o elástico se estica totalmente, tanto na parte já percorrida pela
formiga como na parte ainda a percorrer). Mais um centímetro andado, ela ficará
a 17 cm do açúcar. Mas, aí, o elástico é novamente esticado; a distância
percorrida é passa a ter 4,5 cm, mas o grão de açúcar estará a
30 cm-4,5 cm=25,5 cm. Portanto, parece que a formiga jamais
alcançará o precioso grão de açúcar.</span></i></span></div>
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<span style="font-size: small;"><i style="mso-bidi-font-style: normal;"><span style="color: black; font-family: "times new roman" , "serif"; font-size: 13.5pt;"><span style="mso-tab-count: 1;"> </span>Mas
não é bem assim. Vamos voltar aos números harmônicos. No primeiro movimento, a
formiga terá andado 1/10 do total a ser percorrido. No segundo movimento,
quando o elástico tiver 20 cm, ela andará 1/20 do total. No terceiro
movimento, quando o elástico tiver 30 cm, ela andará 1/30 do total. Portanto,
depois de n movimentos, ela terá andado uma fração do total igual a</span></i></span></div>
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<span style="font-size: small;"><i style="mso-bidi-font-style: normal;"><span style="color: black; font-family: "times new roman" , "serif"; font-size: 13.5pt;">1/10+1/20+1/30 +1/10n .</span></i></span></div>
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<br />
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<span style="font-size: small;"><i style="mso-bidi-font-style: normal;"><span style="color: black; font-family: "times new roman" , "serif"; font-size: 13.5pt;">Como essa soma é do mesmo tipo que as
somas que encontramos nos problemas do deserto, ela crescerá sempre que n
crescer. A questão a saber é qual será o valor de n para que a soma seja igual
a um. Pois bem, n será 12.367 e quando a formiga atingir o açúcar, o elástico
terá mais do que 1,2 km de comprimento.</span></i></span>
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<![endif]-->Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4811048565814201326.post-7755540775148681202016-03-05T18:59:00.000-08:002018-08-07T18:46:34.877-07:00Aprovado ou reprovado?<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="background-color: white; font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%; text-indent: 35.4pt;">Naquela escola, as notas finais deveriam ser
arredondadas até uma casa depois da vírgula e a nota mínima para ser aprovado
era 5,0. Um estudante ficou com uma nota média 4,95. Por mais que seu professor
revisse todas as provas e trabalhos e recalculasse a média, o resultado final era
sempre o mesmo, 4,95. Esse professor era muito rigoroso no que diz respeito aos
critérios de correção, de aprovação e de arredondamento. A regra de
arredondamento que criou para si próprio e que seguiu durante toda sua vida de
dedicado, sério e rigoroso professor era a seguinte: considerar a casa decimal
a ser preservada que fosse mais próxima do valor a ser arredondado. No caso do
azarado estudante, 4,9, reprovado, e 5,0, aprovado, são igualmente distantes de
4,95.</span></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="background: white; font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJkPRh1NmXo45CR9RzMLe9f_-dd3DBXXvSs47VaAJRveGguIDWDrnTo_Q_llVxNeGJars3NHwfxWSllK3o_yc89LZ8zzRcXTE7XJUxlncoZr7ibit8-ZeXQWoKZ7oqQUlG-orqSzFU8iuh/s1600/AprovadoReporvado.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJkPRh1NmXo45CR9RzMLe9f_-dd3DBXXvSs47VaAJRveGguIDWDrnTo_Q_llVxNeGJars3NHwfxWSllK3o_yc89LZ8zzRcXTE7XJUxlncoZr7ibit8-ZeXQWoKZ7oqQUlG-orqSzFU8iuh/s400/AprovadoReporvado.png" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="background: white; font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;">Por mais que o professore consultasse sua
consciência, revisse as provas e trabalhos e lesse as regras da escola, não
conseguia decidir. Então o estudante fez uma proposta: em um papel seria
escrito “reprovado” e em outro, “aprovado”. Esses papéis seriam dobrados e
colocados em uma caixa. O estudante, então, tiraria um deles ao acaso e o que
estivesse escrito definiria para que lado a nota seria arredondada. O
professor, então, concordou em deixar que o acaso resolvesse seu dilema.<o:p></o:p></span></div>
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<span style="background: white; font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;">O estudante escreveu em um pedaço de papel
“reprovado”, entregou-o ao professor, que verificou o que estava escrito, o
dobrou e colocou na caixa. Em seguida, escreveu em outro pedaço de papel
“reprovado”, dobrou imediatamente sem que o professor o lesse e colocou na
caixa.<o:p></o:p></span></div>
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<span style="background: white; font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;">O estudante sorteou um papel e foi aprovado. Como
pode ser isso?</span></div>
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<i><span style="background: white; font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;"> O estudante sorteou um papel, enfiou no bolso sem abri-lo,
despediu-se do professor e foi embora. O professor, para saber o que estava
escrito no papel levado pelo estudante abriu o que sobrou na caixa, no qual
estava escrito “reprovado” e concluiu que o estudante havia pegado o que estava
escrito “aprovado” e arredondou a nota para 5,0.<o:p></o:p></span></i><br />
<i><span style="background: white; font-family: "times new roman" , serif; font-size: 14pt; line-height: 115%;"><br /></span></i>
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