Question

In a chess tournament, each player plays every other player exactly once. If it is known that 105 games were played, how many players were there in the tournament?

Answer 1

Explanation:

Let be the number of players. There was a game for every pair of players, so there must be 105 pairs of players.

(−1)/2=105.

should be easy to solve after that.

Answer 2

15 players played in the chess tournament.

Explanation:

When there are 15 players, the first player plays 14 games and step aside.

remaining 14 player

next player plays 13 games. steps aside

remaining 13 players

next player plays 12 games. steps aside

remaining 12 players

next player plays 11 games. steps aside

remaining 11 players

.

.

.

.

Last player plays 1 game and steps aside

remaining 1 player who will not play against himself.

∴ Sum of all games played

= 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 105 games played