ASU 173 All Soviet Union MO 1972 1-round hockey tournament, odd points
Source:
July 3, 2019
combinatoricsTournament
Problem Statement
One-round hockey tournament is finished (each plays with each one time, the winner gets points, looser -- , and point for draw). For arbitrary subgroup of teams there exists a team (may be from that subgroup) that has got an odd number of points in the games with the teams of the subgroup. Prove that there was even number of the participants.