# Is Your Husband a Cheat?

A certain town comprises of 100 married couples. Everyone in the town lives by the following rule: If a husband cheats on his wife, the husband is executed as soon as his wife finds out about him. All the women in the town only gossip about the husbands of other women. No woman ever tells another woman if her husband is cheating on her. So every woman in the town knows about all the cheating husbands in the town except her own. It can also be assumed that a husband remains silent about his infidelity. One day, the mayor of the town announces to the whole town that there is at least 1 cheating husband in the town. What do you think happens?

Stumped? Let’s solve this methodically. Say there was only 1 cheating husband in the town. There will be 99 women who know exactly who the cheater is. The 1 remaining woman, who is being cheated on, would have assumed there are no cheaters. But now that the mayor has confirmed that there is at least one cheater, she realizes that her own husband must be cheating on her. So her husband gets executed on the day of the announcement.

Now let’s assume there are 2 cheaters in the town. There will be 98 women in the town who know who the 2 cheaters are. The 2 wives, who are being cheated on, would think that there is only 1 cheater in the town. Since neither of these 2 women know that their husbands are cheaters, they both do not report their husbands in on the day of the announcement. The next day, when the 2 women see that no husband was executed, they realize that there could only be one explanation – both their husbands are cheaters. Thus, on the second day, 2 husbands are executed.

Through induction, it can be proved that when this logic is applied to **n **cheating husbands, they all die on the **n **th day after the mayor’s announcement.

Can you plz tell how wives will know that their husbands are cheating on them when there are 3 husband cheating. Sorry if I sound silly 😛

If 3 husband are cheating,

97 Women knows about ALL 3 cheater

3 Women knows about other 2’s Cheating husbands- i.e. 3 Women knows that 2 Cheater Husbands are there.

After announcement,

After 2 days when no one will report, It is clear that there are 3 cheater husbands.

So, ALL the women who knows about 2 cheater husbands only will report.

I hope its clear! 🙂

I just have one doubt. Why will they wait N days if there are N cheaters.

Suppose there are 3 cheaters.

97 Women know about ALL 3 cheater

3 Women knows about other 2’s Cheating husbands- i.e. 3 Women knows that 2 Cheater Husbands are there.

Now,

Day of announcement (Day 1): No one reports

Day 2: A wife sees that the other 2 wives who were cheated on didn’t report their husbands. So there are more than 2 cheaters. As she already knows about 99 husbands she realizes that her husband is also a cheater. And she reports it.

This is applicable to all the three women. So, on Day 2 all the three wives report their husbands. I don’t see the reason for waiting for Day 3.

Sorry if I am wrong. This just came to my mind.

I believe, the question was how did Mayor knew about at least 1 cheating husband and also if N=1, then what did the woman whose husband was cheating gossiped about with others?

### Your Answer

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