MathDB

n \geq 4

players participated in a tennis tournament. Any two players have played exactly one game, and there was no tie game. We call a company of four players

bad

if one player was defeated by the other three players, and each of these three players won a game and lost another game among themselves. Suppose that there is no bad company in this tournament. Let

w_i

and

l_i

be respectively the number of wins and losses of the

i

-th player. Prove that

\sum^n_{i=1} \left(w_i - l_i\right)^3 \geq 0.

Proposed by Sung Yun Kim, South Korea

Problem Statement