Question

During the chess championship, each player played with each other two games. Players who win in a game were awarded 1 point, while those who draws were given a half-point. Losing a game was worth zero points. The three best players scored together 24 points, which is twice less than the sum of points of all other players scored. How many players were participating in the championship?

Answer 1

9

Explanation:

If 24 points is half the number of points all other players scored, then the points scored by all other players total 24·2 = 48.

All points together total ...

24 + 48 = 72

A point is awarded for each game, so there were a total of 72 games.

N players will play a total of (N/2)(N-1) games if they play each opponent once. Here, each opponent is played twice, so the total number of games played by N players is ...

N(N-1) = 72

9·8 = 72 ⇒ N = 9

The number of players in the championship was 9.