Permutaions&combinations1

Supppose that there were n players originally, then original no. of games that have to be played is:

2[1 + 2 + 3 + ... + (n - 1)] = n(n - 1)

So when a player quitted after playing 4 games, the no. of games will be reduced by 2(n - 1) - 4 = 2n - 6 since he/she originally had to play 2(n - 1) games.

So we have:

n(n - 1) - (2n - 6) = 60

n2 - 3n - 54 = 0

(n - 9)(n + 6) = 0

n = 9 or -6 (rej)