MathDB

In a chess tournament, each of

2n

players plays every other player once in each of two rounds. A win is worth

1

point, a draw is worth

\frac12

point and a loss is worth nothing. Prove that if for every player, the total score in the first round differs from that in the second round by at least n points, then this difference is exactly n points for every player.
(B Frenkin)

Problem Statement