Aqui estão uma moeda de 1 centavo e uma moeda de 25 centavos. Diga uma frase. Se sua frase for verdadeira, então eu vou te dar uma das moedas, sem dizer qual. Mas se sua frase for falsa, então eu não vou te dar nenhuma moeda. O matemático americano Raymond Smullyan diz: 'Há uma frase que você pode dizer tal que eu não teria escolha a não ser te dar a moeda de 25 centavos (assumindo que eu manterei minha palavra)'. Qual frase vai conseguir isso?
(Here are a 1-cent coin and a 25-cent coin. Make a statement. If your statement is true, then I'll give you one of these coins, not saying which. But if your statement is false, then I won’t give you either coin. American mathematician Raymond Smullyan says: 'There is a statement you can make such that I would have no choice but to give you the 25-cent coin (assuming that I will keep my word)'. What statement will accomplish that?)
PCFilho
(pescado no sempre ótimo Futility Closet, que cita o livro 'Logical Labyrinths', de Smullyan, publicado em 2008)
The statement is "You will not give me the 1-cent coin."
ResponderExcluirHere's the explanation as to why this is the sentence:
ExcluirStatement: You will not give me the 1-cent coin.
To make the statement false, you would have to give me the 1-cent coin, which contradicts the assurance that no coins will be given for a false statement. If the statement is true, then you would have to give me a coin, but if it's the 1-cent coin, the statement would become false, leading to another contradiction. Therefore, you would have to give me the 25-cent coin.
That's it. Thank you, Jake!
ExcluirI posted a solution to that mate-in-17 chess problem the other day. Did you see it yet?
ExcluirYes, Jake, I saw it. Perfect, as usual. :)
Excluir