Prove that any group of six people contains either 3 mutual friends or 3 mutual strangers.

(For the purpose of this problem any pair of people must be either friends or strangers.)

(In reply to by Dulanjana)

I don't think it's a question from an IQ test since the answer is a little more involved than what you posted.

If your reasoning were true, it whould work as well for a group of, say, five people, but as TomM has shown, that group can easily have neither 3 mutual friends nor 3 mutual strangers.

As I recall I have gotten this problem from some list online, and I think it came from rec.puzzle before that.

Posted by levik on 2002-07-02 02:11:03