In a tournament 14 teams play league matches. If each team plays against every…

Concept

A single round-robin match is determined by an unordered pair of distinct teams. Reversing the two teams does not create a new match, so the number of matches among n teams is C(n, 2) = n(n − 1) / 2.

Equivalently, each successive team contributes one fewer new opponent, giving the sum (n − 1) + (n − 2) + … + 1.

Application

1. Here n = 14.

2. Substitute into the pair-count formula: C(14, 2) = 14 × 13 / 2.

3. Compute the numerator: 14 × 13 = 182.

4. Divide by 2: 182 / 2 = 91.

Cross-check

1. Count only new opponents: the teams contribute 13, 12, 11, …, 1 new match in turn.

2. The arithmetic-series sum is 13 × 14 / 2 = 91, which agrees with the combination count.

Result

Therefore, the league contains 91 matches.