Q.Write the formula for the number of matches in a knock-out tournament and explain in one line why it is N − 1.
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Start your 14-day free trial to unlock the full solution →In a knock-out tournament with N teams, the total number of matches is N - 1 because every team except the champion must lose exactly once.
The Concept: Elimination Logic
A knock-out (or single-elimination) tournament is structured so that a single loss removes a team from the competition. Each match produces exactly one loser, and that loser is immediately eliminated. The tournament continues until only one team remains undefeated—the champion.
The beauty of the formula lies in thinking about losers, not winners. At the start you have N teams. At the end you have one champion. That means (N - 1) teams must have been eliminated. Since each match eliminates exactly one team, you need exactly (N - 1) matches to eliminate (N - 1) teams.
The formula does not depend on the number of rounds or whether the draw is balanced. Whether N = 8 (a perfect power of 2) or N = 13 (requiring byes), the total matches remain N - 1.
The Formula
Total number of matches = N - 1
where N is the total number of teams entering the tournament.
Why N - 1?
Because every team except the champion must lose exactly once, and each match produces exactly one loser. …
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