One “odd” Game in a tournament
Source: Tournament of Towns Spring 2003 - Junior A-Level - Problem 3
June 14, 2011
combinatorics unsolvedcombinatorics
Problem Statement
In a tournament, each of teams played with each other exactly once. Let us call the game “odd” if the total number of games previously played by both competing teams was odd.(a) Prove that there was at least one “odd” game.(b) Could it happen that there was exactly one “odd” game?