A group of mathematicians - ILL 1990 CZS 4
Source:
September 18, 2010
combinatoricsExtremal combinatoricsExtremal Graph Theorygraph theoryvertex degreeIMO ShortlistIMO Longlist
Problem Statement
In a group of mathematicians, every mathematician has some friends (the relation of friend is reciprocal). Prove that there exists a mathematician, such that the average of the number of friends of all his friends is no less than the average of the number of friends of all these mathematicians.