9. 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?
We have to think who knows what, when, what their actions will be, and what they can infer from other people's actions.
Think what would happen if only one husband were cheating on their wife. This is easy because the wife would know that no other husbands were cheating so when she heard the stranger's announcement she would know it was her husband.
But what if two husbands were cheating, what would happen on the first day? On the second day?
It's a really nice puzzle this. The Question is bit wordy but the root of it is pure logic.
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