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 there was/were x unfaithful husband(s), a wife obedient to the queen would shoot her husband on the x+1^th midnight.

As the shots were fired on the fortieth midnight, thirty-nine of the husbands were discovered or known to be unfaithful.

I believe the solution posted is off by one, as the wife is to shoot her husband the midnight of the following night that it becomes known to her that her husband is unfaithful. If only one husband were unfaithful, he would have been shot on the second night, and so forth. Following, the number of nights to pass quietly is equal to the number of unfaithful husbands. As thirty-nine nights passed quietly, there were thirty-nine unfaithful husbands. 

Posted by Dej Mar on 2010-06-23 10:38:12