Question

In a chess tournament each of six players will play every other player exactly once. How many matches will be played during the tournament?

• A. 36
• B. 30
• C. 15
• D. 12

Answer 1

Answer: (C)

15

First player can play 5 matches with other five players. Second player can play 4 matches with other four players and proceeding this way, the fifth player will play only one match with sixth player.
$\therefore$ Total number of matches played = 5 +4 + 3 + 2 + 1 = 15.
Short cut : Number of matches played by n players = $\frac{n(n+1)}{2}$