Question

In a chess tournament every participate has to play 1 game with all other. Two players fell ill and left the tournament after having played 3 games each. If the total no. of games played is 84, then the no. of participants is

• A. 15
• B. 20
• C. 16
• D. 18

Answer 1

Answer: (A)

15

Answer 2

$\mathbf{n}\mathbf{-}\mathbf{2}\mathbf{C}_{\mathbf{2}}$ + 6 = 84.

$n - 2C_{2}$ = 78

(n - 2) (n - 3) = 156 = 13 x 12.

n = 15