Teams in a Volleyball Tournament
Source: All Russian Olympiad 2015 11.3
December 11, 2015
combinatoricsgraph theory
Problem Statement
teams participate in a volleyball tournament. Every team has played every other team exactly once (there are no ties in volleyball). Turns out that in any set of teams, there is one which has lost to no more than of the remaining teams. Prove that in the entire tournament, there is a team that has lost to no more than of the remaining teams.