There is an island inhabited by two tribes. The natives of one tribe always tell the truth and the natives of the other tribe always lie. On a recent trip, a visitor was confronted by three natives, but he couldn't tell which tribe they were from. See if you can tell whether they are liars or truth-tellers from the following statements: "Oh, we're all liars," said the first native. "Just one of us is a truth-teller," claimed the second of the three. The third native did not speak. How quickly can you determine each native's tribe? (Only ONE answer will be accepted for this problem -- no second chances!).

Solution to the Problem: The first native was a liar, the second was a truth-teller, and the third was a liar. If the first native was telling the truth, then there is a problem with his statement, "we are all liars." So, he must be a liar. That means that his statement is false, and there must be at least one person telling the truth. If the second native is a liar, then either there are two people telling the truth or none. But we know that they can't all be liars, and there can't be two truth-tellers since the first one is known to be a liar. Hence, the second native is telling the truth, and that means he is the only truth-teller. So the third native is a liar (even though he didn't speak).

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