Question

10 teams played a round-robin baseball tournament (meaning that every team played exactly 9 games: one game against each of the other teams; there are no ties in baseball). No two teams won exactly the same number of games. Prove that there is a team that won exactly 6 games.

Answer 1

Every team play 9 games, no two team won exactly the same number of games, so
Team 1- 9 wins
Team 2- 8 wins
And so on,
last team (team 9) wins 0
So one team must won 6 times. (Because no two team won exactly the same number )