Q.In a knock-out tournament of 19 teams, the total number of matches played is:

A knockout tournament eliminates one team with every match played. Since the tournament must produce exactly one winner, every team except the champion must lose exactly once. That means the number of matches equals the number of teams that must be eliminated.

For N = 19 teams, we need to eliminate 19 - 1 = 18 teams to crown a single winner.

Therefore, the total number of matches is:

Total matches = N - 1 = 19 - 1 = 18

This formula holds regardless of whether the number of teams is a power of two or requires byes. Byes affect the structure of the draw (some teams skip the first round), but they do not change the total count of matches needed to determine a winner.

Why the other options are wrong:

• (b) 19: This would imply every team plays, including the winner losing a match, which contradicts the knockout format. …

Understanding Knockout Tournament Matches

A knockout (or elimination) tournament is structured so that every match eliminates exactly one team. The winner advances, the loser is out. This simple principle leads directly to a beautiful result: if you start with N teams and need to crown one champion, you must eliminate exactly N - 1 teams. Since each match eliminates precisely one team, the total number of matches is always N - 1.

This holds regardless of how the bracket is arranged, how many byes are given, or how many rounds the tournament runs. The logic is ironclad: 19 teams enter, 1 champion emerges, so 18 teams must be eliminated, requiring 18 matches.

where N is the number of teams.

Applying the Formula

For this question, N = 19 teams.

Total matches = 19 - 1 = 18

The tournament will proceed through multiple rounds. Since 19 is not a power of 2, some teams will receive byes in the first round. The next higher power of 2 is 32, so the number of byes is 32 - 19 = 13. This means 13 teams skip the first round, and 19 - 13 = 6 teams play in the first round, producing 3 matches. After the first round, 13 + 3 = 16 teams remain (a power of 2), and the bracket proceeds cleanly: 8 matches in the second round, 4 in the third, 2 in the semi-finals, and 1 final. Summing these: 3 + 8 + 4 + 2 + 1 = 18 matches.