In a parallel universe when Neil Armstrong landed on the moon, he found it to be inhabited by a tribe of humanoids.
He discovered that: a) they were all married, b) the husbands of 10 of the wives were unfaithful, c) Each wife knew whether or not any other wife's husband was a cheater, but did not know whether or not her own husband was a cheater, d) No wife was allowed to tell any other wife that her husband was unfaithful or otherwise. Husbands also did not discuss this but otherwise gossip was gossip…, e) If a wife discovered her husband was unfaithful she had to throw him out of the house and onto the street at precisely 10am the following day, where he would be visible to all others in the tribe.
That's the famous problem related to the concept of the common knowledge, and the solution is well-known though often leads to arguments of people who don't rely upon it. The hint it to solve the problem by induction: suppose that there is only one guy who is cheating and see what happens. Then think of two guys cheating and try reducing it to the previous case, etc.
ReplyDeletewhat happens if thers is only one cheater???
ReplyDeleteIt's difficult to tell based on your description whether or not ALL of the husbands are unfaithful, or only some. For my guess, I'll guess it could be any number, but it should work with all.
ReplyDeleteIf there are X cheating husbands, they will all be kicked out on the Xth day AFTER Neil makes his proclamation (day 0). Let's assume there is 1 cheating husband. Since the wife knows all other husbands are not cheaters and there is at least one, her husband must be unfaithful. If there are two unfaithful husbands, the wives will each know only about the other, and after seeing that there is no husband kicked out on day 1, there must be more than 1 cheaters, so they both know that their husband is also a cheater. This pattern would continue so that if there are 10 unfaithful husbands, the wives will notice that there are more than nine cheaters on the ninth day, and kick their husband out on the tenth.