06/03/2020 (2019: AMC 8, Problem 19)

Q: In a tournament there are six teams that play each other twice. A team earns 3 points for a win, 1 point for a draw, and 0 points for a loss. After all the games have been played it turns out that the top three teams earned the same number of total points. What is the greatest possible number of total points for each of the top three teams?

If the top 3 teams want the greatest amount of points and they tie, they have to win against the lower 3 teams. Because they play each team twice, they get 3 (points per win) * 3 (teams they won against) * 2 (games per team) = 18 points.

They have to play each other, so they have to win 2 matches and lose 2 matches. That means they'll get 2 matches won * 3 points per match won = 6 points.

18 points + 6 points = 24 points, so the answer is C.