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Question
There is a mythical land whose residents are either Liars or Truth-tellers. A group of three men was questioned by a stranger looking for directions. The stranger, knowing he was in the land of Liars and Truth-tellers asked the group if they were Liars or Truth-tellers. The first said, “We are all Truth-tellers.” The second said. “Only one of us is Truth-teller.” The third said, “The second person is telling the truth.” Who were Truth-tellers and who were Liars?  

Answer
Pam

Suppose that the first is telling the truth. This would make the second a truth-teller, but his statement is clearly a lie. Therefore the first is a liar.

Suppose that the second is telling the truth. This would make the third a liar, but his statement is clearly true. Therefore the second is a liar.

From the above the third's statement is clearly a lie. Therefore he is a liar.

They are all liars.

Bernard.

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Bernard Hawkes

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Please read my Policy Statement. Puzzles and brainteasers. Ask and I will help! That said, I`m best at pure logic puzzles. E.g. You have twelve apparently identical coins of which one is counterfeit, being either slightly heavy or light. Determine the counterfeit coin, and whether it is heavy or light, in no more than three weighings using a balance scale. Rebuses and riddles I`m less good at, but will generally get the answer given time. Requests for oddball facts (e.g. What was the second most common girl`s name in 1900? [genuine example - answer: Ruth]) I regard as outside my remit. However, you are welcome to ask, but I may not be able to help you.

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Member of Mensa. Solution to "gry" riddle.

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