MathDB

In a chess tournament, every participant played with each other exactly once, receiving

1

point for a win,

1/2

for a draw and

0

for a loss. (a) Is it possible that for every player

P

, the sum of points of the players who were beaten by P is greater than the sum of points of the players who beat

P

? (b) Is it possible that for every player

P

, the first sum is less than the second one?

Problem Statement