BdMO Online Forum

Problem 2:
In the first round of a chess tournament, each player plays against every other player exactly once. A player gets $3, 0$ or $-1$ points respectively for winning, drawing or losing a match. After the end of the first round, is it possible that the sum of the scores of all the players is $21$? State your answer with logic.

After every match, the sum of the points the teams win is even (either 3+(-1)=2 or, 0). So, the sum of everyone's points at the end of the league can't be 21, as it's odd.

A classical example of INVARIENCE PRINCIPLE.