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