Equal numbers of members
Source: Swiss Math Olympiad 2010 - final round, problem 8
March 16, 2010
floor functioncombinatorics proposedcombinatorics
Problem Statement
In a village with at least one inhabitant, there are several associations. Each inhabitant is a member of at least associations, and any two associations have at most one common member.
Prove that at least associations have the same number of members.