A chess tournament took place between 2 n+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-\sqrt{2 k} and no more than n+\sqrt{2 k} games.