A football league has n teams. Each team plays one game with every other team. Each win is awarded 2 points, each tie 1 point, and each loss 0 points.
After the league is over, the following statement is true: for every subset S of teams in the league, there is a team (which may or may not be in S) such that the total points the team obtained by playing all the teams in S is odd.
Prove that n is even. number theoryalgebracombinatorics