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 re: No Subject by Math Man)

Agreed, I got hung up on that bit as well.  It's important to remember that the requirements for a quartet are significantly stricter than that for a trio.  With a trio, only three relationships of matching status are needed (confined to three people, of course).  But for a quartet, we have a total of *six* relationships that must match among the four people: 1 to 2, 1 to 3, 1 to 4, 2 to 3, 2 to 4, and 3 to 4.

Posted by Caleb on 2012-08-07 10:58:20