Problem
The Problem
At a party with people, each person shakes hands with some subset of the others (possibly none, possibly all). Prove that at any party, the number of people who shook hands with an odd number of people is even.
At a party with people, each person shakes hands with some subset of the others (possibly none, possibly all). Prove that at any party, the number of people who shook hands with an odd number of people is even.