A puzzle by Emily Cox and Henry Rathvon, from the October 1991 issue of Games magazine:
You’re visiting a familiar island on which each resident either invariably lies or invariably tells the truth. Three residents appear.
Resident 1: We’re all liars.
Resident 2: Just one of us is a truth teller.
The third resident doesn’t speak. Which of the three are telling the truth?
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SelectClick for Answer |
Residents 1 and 3 are liars. Resident 2 is a truth teller.
Resident 1’s statement can’t be true, because that would entail a contradiction. So Resident 1 is a liar, and at least one of the three tells the truth.
Resident 2 can’t be a liar — if she were, then Resident 3 would have to be a truth teller, and Resident 2’s statement would then be true, another contradiction.
So Resident 2 is a truth teller, and by her statement Resident 3 must be a liar.
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