Groups of Students
Source: APMO 2008 problem 2
March 22, 2008
pigeonhole principlecombinatorics proposedcombinatoricsalgorithm
Problem Statement
Students in a class form groups each of which contains exactly three members such that any two distinct groups have at most one member in common. Prove that, when the class size is , there is a set of students in which no group is properly contained.