# Cheating Husband Puzzle

## Cheating Husband Puzzle

A certain town comprises 100 married couples. The town has a rule that if any of the husbands cheat and the wife finds out and reports him, the husband will get executed. In the town all the women gossip among one another and tell about the husbands of other women, however, no woman tells another woman whether her husband is cheating on her or not. Therefore every woman knows about all the husbands except her own. Now one day the mayor announced that some husbands are cheating, but the number is not known, whether one or more.

Assuming that none of the husbands confess their infidelity and only their wives can report the husbands, do you think the cheating husbands are caught? If they’re caught, then how?

## Cheating Husband Puzzle

A certain town comprises 100 married couples. The town has a rule that if any of the husbands cheat and the wife finds out and reports him, the husband will get executed. In the town all the women gossip among one another and tell about the husbands of other women, however, no woman tells another woman whether her husband is cheating on her or not. Therefore every woman knows about all the husbands except her own. Now one day the mayor announced that some husbands are cheating, but the number is not known, whether one or more.

Assuming that none of the husbands confess their infidelity and only their wives can report the husbands, do you think the cheating husbands are caught? If they’re caught, then how?

## Solution

Yes, they will be caught.

Let us assume that only one husband is cheating. Now all the 99 women know except for the wife. Now the wife knows there is one cheater and she knows that the other 99 husbands are not cheating(because they gossip), thus she will realize that it is her husband who is cheating and report him. He will be executed on the day of the announcement.

If there were 2 cheaters, say, then the 98 women know the cheaters. The 2 wives would think that there is 1 cheater in town(excluding their husbands). Since both, of the wives, are unaware they will not report their husbands on the day of the announcement.

When the next day they will realize that no one was executed, they will conclude their husbands are cheating and report them and they both will get executed on the 2nd day.

Similarly, for 3 cheating husbands, it will take the wives 3 days to realize that their husbands are cheating.

## Get over 200+ course One Subscription

Courses like AI/ML, Cloud Computing, Ethical Hacking, C, C++, Java, Python, DSA (All Languages), Competitive Coding (All Languages), TCS, Infosys, Wipro, Amazon, DBMS, SQL and others