MathDB
Teams in a Volleyball Tournament

Source: All Russian Olympiad 2015 11.3

December 11, 2015
combinatoricsgraph theory

Problem Statement

110110 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 5555 teams, there is one which has lost to no more than 44 of the remaining 5454 teams. Prove that in the entire tournament, there is a team that has lost to no more than 44 of the remaining 109109 teams.