Volleyball tournament
Source: Kvant Magazine No. 2 2022 M2686
March 8, 2023
Kvantcombinatoricsgraph theory
Problem Statement
At a two-round volleyball tournament participated 99 teams. Each played a match at home and a match away. Each team won exactly half of their home matches and exactly half of their away matches. Prove that one of the teams beat another team twice.Proposed by M. Antipov