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# Liars on the Island

Robinson found himself on an island where some of the people were liars, and others always told the truth. When he met with one of the inhabitant of the island, he asked him: "Are you a liar or not?"

"I'm not a liar", answered the person.

"All right, if it is so, you'll be my companion", Robinson said.

After a while they saw another man.

Robinson pointed to the man and asked his new friend,

"Could you, please, ask him, if he is a liar or not?"

The new friend asked the question to the man, came back and said,

"He said he was not a liar".

"All right, now I'm convinced that you are not a liar!" smiled Robinson. What convinced Robinson?

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Solution:
Regardless of who is interrogated (liar or not), to the question "Are you a liar or not?" the person will answer: "I'm not a liar!". Indeed, if he is not a liar, then he is telling the truth. If he is a liar, then he will say a lie about himself (that is, that he is not a liar).

So, Robinson was just checking the honesty of his companion: if the companion was a liar, then he would lie and tell Robinson that the answer was "I'm a liar!". Since the companion said that the answer was "I'm not a liar!", then the companion must be a truth-teller.