A Queen of an island kingdom was concerned about the high level of infidelity among the island's men, so she gathered all the married women of the island and made the following announcement:

"There is at least one unfaithful husband in our kingdom. All the wives know of all the unfaithful husbands, but know nothing about their own husband. You are not allowed to discuss your husband with any of the other women, but if it becomes known to you that your man is unfaithful, you must shoot him at midnight of the following night."

(Assume a shot anywhere on the island is heard at any other point on the island.)

After thirty nine nights of uneasy quiet, on the fortieth night the gunshots echoed across the island. How many men were shot that night, and why? (Assume the wives are all super smart.)

If a wife knew of no unfaithfull-ness, then becuase there was at least one husband, she would know it was hers. The fact that no shots were fired on the first night meant everyone knew of at least one.

On the second night if someone knew of only one, but there was definitely more than one because of what happened the previous night, she would know that her husband was unfaithful. The fact that no gunshots were heard meant that everyone knew of at least two.

This would continue all the way through to the fortieth night. On that night, anyone who knew of 39 unfaithful husbands would know theirs was unfaithful, so I think 40 men were shot.

Posted by Lewis on 2003-08-04 23:16:51