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.

(In reply to The enemy of my enemy is my friend? by Steve Herman)

The enemy of your enemy could be your friend, your enemy, or even a stranger. It is possible to have 3 mutual enemies.

Posted by Math Man on 2011-07-01 17:21:26