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There is a matriarchal town which believes that a prophetic stranger will tell the wives whether any of the husbands are cheating. The stranger will only say yes if there are any and no if there are none, he does not give any additional information. Suppose the stranger comes and says yes, then the rule is that any wife who, on any day following the announcement, deduces that her husband is unfaithful must kick her husband onto the street the next morning. This way everyone in the town knows he was cheating. Suppose each wife is able to deduce whether any man in the town is cheating, except for her own husband. No wife is willing to reveal this information and we assume cheating husbands will not reveal themselves.

Suppose the stranger comes and announces that there are cheating men. On the tenth day some men are kicked into the street for the first time. How many unfaithful men are on the street?

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marked as duplicate by Joe Z., Community Apr 9 '15 at 2:35

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    $\begingroup$ This is just the blue eyes problem stated in terms of cheating husbands. $\endgroup$ – Joe Z. Apr 9 '15 at 2:35
  • $\begingroup$ This problem is not. With 100% rationality, something else entirely happens. I'll leave it to you to figure out what it is. $\endgroup$ – Joshua Aug 6 '15 at 22:20