In Mutually friendly, we proved that if any two people are either friends or strangers, then any group of six people either contains 3 mutual friends or 3 mutual strangers, or both. Now, they can also be enemies.

Suppose that any two people are either friends, enemies, or strangers. Prove that any group of 17 people either contains 3 mutual friends, 3 mutual enemies, or 3 mutual strangers.

If it is true that the enemy of my enemy is my friend, then it is not possible to have 3 mutual enemies.  So, I guess it is not true, at least not if there is a group of 17 or more people. 

Posted by Steve Herman on 2011-07-01 14:43:25