- Nov 19, 2001
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In the town of X there are N families. All the husbands in town are wise men, and they spend their mornings thinking. Every afternoon they implement their decisions. All of the wives in this town are unfaithful. There is a rule in town that if a husband should learn that his wife is unfaithful, he kills her that day. But while each husband knows about the unfaithfulness of all the other wives, he believes his own wife is an exception.
One day a traveler arrives, looks around, and announces "there is an unfaithful wife in this town". Although the traveler imparts no new information, in exactly N days all N wives are killed by their husbands. Explain why.
Answer:
N = 2, which means there are only 2 wise men.
On the morning of the 2nd day, each one reasons as follows: If my neighbor knows there is only one unfaithful wife, and he didn't kill his own wife, then he assumes that my wife, not his, is unfaithful. He and I are the only ones in this town, so my wife obviously betrayed me with him. This proof works for any N with the help of mathematical induction.
One day a traveler arrives, looks around, and announces "there is an unfaithful wife in this town". Although the traveler imparts no new information, in exactly N days all N wives are killed by their husbands. Explain why.
Answer:
N = 2, which means there are only 2 wise men.
On the morning of the 2nd day, each one reasons as follows: If my neighbor knows there is only one unfaithful wife, and he didn't kill his own wife, then he assumes that my wife, not his, is unfaithful. He and I are the only ones in this town, so my wife obviously betrayed me with him. This proof works for any N with the help of mathematical induction.
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