Cheating Husbands

♠ Posted by GeekyFry in , at 9:57 AM

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? Will the wife/wives ever come to know about their husband’s infidelity? Explain !



Possible Solution:

Let us start with cheating husband. So there would be 99 wives knowing that 1 cheater husband. And the wife who has been cheated, knows that there are no cheater husband(s) until the day mayor announces about 1 cheater husband. So upon announcement she would know that the cheater husband is hers. So the husband would be immediately located and executed.
Now let us assume there were 2 cheating husbands. So 98 wives know about the cheating husbands. Rest 2 wives think there are no cheater husbands in the town. On the day mayor announces about atleast one cheater husband’s existence, 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 however, when the 2 women see that no husband was executed, they realize that there could only be one explanation – both their husbands are cheaters. Therefore, on the second day, 2 husbands would be executed.
So carrying the same logic further for n husbands being cheaters, all the n husbands would be executed on the nth day from the day of announcement.

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