The Volokh Conspiracy - More on Numbers of Friends:

Prove that in any group of people (no matter how large), there are always two people with exactly the same number of friends within the group. Note that we define friendship to be symmetric, so that if A is friends with B, then B is also friends with A.

UPDATE: Assume the group has at least two people.

	[Puzzleblogger Kevan Choset, September 20, 2005 at 12:16pm] Trackbacks More on Numbers of Friends: Prove that in any group of people (no matter how large), there are always two people with exactly the same number of friends within the group. Note that we define friendship to be symmetric, so that if A is friends with B, then B is also friends with A. UPDATE: Assume the group has at least two people.