MathDB

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-\sqrt{2k}

and no more than

n+\sqrt{2k}

games.

Problem Statement