MathDB

173

Part of 1972 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 173 All Soviet Union MO 1972 1-round hockey tournament, odd points

Source:

7/3/2019
One-round hockey tournament is finished (each plays with each one time, the winner gets 22 points, looser -- 00, and 11 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.
combinatoricsTournament