A traveler came to a fork in the road at which he found a bystander. He knew that at the end of one of the forks there was a village inhabited by people who always told the truth. At the end of the other fork was a village inhabited by people who always told lies. He also knew that the bystander lived in one of the villages, but he didn’t know which. How could the traveler find which fork led to the village of the truthtellers by asking the bystander just one question?
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He should ask, Is this the road to the village in which you live? If the answer is no, then the road has to lead to the village of the liars since the answer would be a no whether the bystander were a truthteller or a liar. Conversely, if the answer is a yes, then the road would have to lead to the village of the truthtellers.
The engineering department was arranging for a rather expensive catered lunch to bid farewell to their retiring colleague. They calculated that it would cost each person $30. One good mathematician remarked, "It's lucky that there aren't five fewer of us to split the...