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Story of a Loyal Village: Group Theory

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Alright, another question related to information sharing in group. Came across this a book am reading:

Consider a village with all young couples. Each woman in the group knows if any-one else's husband is not loyal to that particular woman. But a woman does not know if her own husband is not loyal to her. And there is no way for the women to share this information.

The moment a woman knows that her husband is not loyal to her she will slay him on the same day. But there is no way a woman would know that as information sharing is not allowed.

However, one particular day an oracle visits the village and tells the group that at-least one of the man is not loyal. Now, what happens if 18 men are not loyal. What if 'n' men are not loyal?

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