There are 17 people in a room. Each pair of people are either friends, enemies, or not acquainted. Prove that there is a group of 3 people that are on equal standing with each other (i.e. all 3 are friends, all 3 are enemies, or all 3 are unacquainted).
I'm unfamiliar with Ramsey's Theory and this question. Any help?
The wikipedia article on Ramsey's theorem may be helpful: http://en.m.wikipedia.org/wiki/Ramsey%27s_theorem. The section about R(3,3,3)=17 contains a sketch of a proof.