1. The problem statement, all variables and given/known data Prove that at any party there are two people who know the same number of people. Assume that if A knows B, then B knows A. Assume also that everyone knows himself or herself. [Hint: Use indirect reasoning.] 2. Relevant equations Proof by contradiction. 3. The attempt at a solution I started by trying to show that if no one knew the same number of people as anyone else, that that would lead to a contradiction. But I'm stuck even at this point. Any suggestions?