Meeting
Source: RMO 2003, Grade 8, Problem 2
October 23, 2008
pigeonhole principle
Problem Statement
In a meeting there are 6 participants. It is known that among them there are seven pairs of friends and in any group of three persons there are at least two friends. Prove that:
(a) there exists a person who has at least three friends;
(b) there exists three persons who are friends with each other.
Valentin Vornicu