Exercise 895Combinatorics › Counting principlesL1Added 3 Nov 2026

Scheduling tournaments

#scheduling#bipartite#matchings

Statement

In a chess tournament with $n$ players, each pair plays once. How many games does each player play? Total games?

Hint

Each player plays against every other player: $n-1$ games. Total games: $\binom{n}{2}$ .

Show solutionHide solution

Per player. $n-1$ opponents, so $n-1$ games per player.

Total. Sum over players divided by $2$ : $\frac{n(n-1)}{2}=\binom{n}{2}$ games.

Conclusion. $n-1$ games per player, $\binom{n}{2}$ total.