Prove that if any two people are either friends or strangers, then any group of 18 people contains either 4 mutual friends or 4 mutual strangers.

(In reply to "Solution"....but only for a total of 20 people by Caleb)

Let A be one of the 18 people. Then, A either has at least 9 friends or at least 9 strangers. Suppose A has at least 9 friends. Let B be one of the 9 people. Out of the 8 other people, find out how many friends and strangers B must have.

Posted by Math Man on 2012-08-07 09:14:37