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.)

40 unfaithful men were shot.

the reasoning: if only one man was unfaithful, his wife would realise, since she knew of no others, and shoot him on the first night. since no-one was shot on the first night, everyone knew there were at least two unfaithful men. If only two, then the wife of that man would know on the second night, since she knew of only one other, and no-one had been shot the night before. If three, then the wives of those men would shoot on the third night. Likewise for each succeeding night, until the number of proven unfaithful men increased beyond the number known to any one wife.

Unfortunately, if any one wife failed in her duty to shoot her unfaithful husband, then on the next night all innocent men on the island would be shot! (since the remaining wives would each believe that the recalcitrant wife knew of another husband's infidelity of which they were unaware!)

Posted by ubergeek on 2002-12-25 21:46:02