A chess tournament took place between 2n+1 players. Every player played every other player once, with no draws. In addition, each player had a numerical rating before the tournament began, with no two players having equal ratings. It turns out there were exactly k games in which the lower-rated player beat the higher-rated player. Prove that there is some player who won no less than n−2k and no more than n+2k games. TournamentgamescombinatoricsHi