Pigeon Hole Principle; 3 know each other, or 3 don't know each other I found another question in my text book, it seems simple, but the hardest part is to prove it. Here the question

There are six persons in a party. Prove that either 3 of them recognize each other or 3 of them don't recognize each other.

I heard the answer use Pigeon Hole Principle, but i have no idea in using it. Could somebody please tell me the way to solve it? Thanks for the attention and sorry for the bad English and my messy post

NOTE: in my answer I assume that the relation "know someone" is symmetric (i.e., A knows B if and only if B knows A). If this relation is not symmetric for you then, I did not really check it but I believe the statement is not true.\\\
Choose a person A at the party. The following two situations are possible:
(CASE 1) A knows at least three people, say B, C and D, at the party;
(CASE 2) A doesn't know at least three people at the party.
In (CASE 1), if at least a pair among {B,C}, {C,D} or {D,B} is formed by people that know each other, then you have three people that know each other. If there is no such pair among these three, then B, C and D are three people that do not know each other.
In (CASE 2) proceed similarly.
