Catch the Cheating Husband Puzzle
In a certain matriarchal town, the women all believe in an old prophecy that says there will come a time when a stranger will visit the town and announce whether any of the men folks are cheating on their wives. The stranger will simply say “yes” or “no”, without announcing the number of men implicated or their identities. If the stranger arrives and makes his announcement, the women know that they must follow a particular rule: If on any day following the stranger’s announcement a woman deduces that her husband is not faithful to her, she must kick him out into the street at 10 A.M. the next day. This action is immediately observable by every resident in the town. It is well known that each wife is already observant enough to know whether any man (except her own husband) is cheating on his wife. However, no woman can reveal that information to any other. A cheating husband is also assumed to remain silent about his infidelity.
The time comes, and a stranger arrives. He announces that there are cheating men in the town. On the morning of the 10th day following the stranger’s arrival, some unfaithful men are kicked out into the street for the first time.How many of them are there?
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3 comments:
All the men????
The teaser really got me... could you give the answer?
One man. He says "yes." The only way any woman would know for sure that her husband was cheating is if she knows nobody else was cheating. Because the stranger said "yes," she deduces that it can only be her husband.
There are 10 Cheating husbands. From the quest a fact is that every woman knows every other womans situation, i.e. cheating or not, so if there are 50 husbands cheating on their wives, then a woman knows for sure that 50 wives have loyal husbands, and 49 wives have disloyal husbands, obviously she can deduce that the last one wife with a disloyal husband is her.
The last day any husband is thrown out is the final number of husbands that were cheating.
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