# One hundred married couples

Question:

In an apartment complex in New York there are one hundred married couples. When one of the husbands cheats on his wife with one of the other wives, his wife has no idea. With the large amount of gossip in the complex, all of the other wives know he is cheating. If a wife finds out that her husband is cheating on her, she kills him the following morning. Someone anonymously sends an email to all of the wives in the building saying that at least 1 man is cheating on his wife in the building.

How many husbands will be killed and how long will it take?

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Solution: All of the men (n) who are cheating will be killed and it will take one less than the number of cheating men nights (n-1) for their wives to discover this.

• If one man was cheating, and that woman hadn’t have heard of any other infidelity she would know it was her husband that was cheating.
• If there were two men cheating, both of their wives would think that since they have only heard of one man cheating he should die the next morning.
• If he doesn’t die, she knows her husband must also be cheating and that’s why the other husband didn’t die.

Following this logic, you can know that all of the men will die after one less night than there are cheating men.