Consider a knock-out women’s badminton singles tournament where there are no ties. The loser in each game is eliminated from the tournament. Every player plays until she is defeated or remains the last undefeated player. The last undefeated player is declared the winner of the tournament. If there are 64 players in the beginning of the tournament, how many games should be played in total to declare the winner of the tournament?

Question

Prepp Team · Accepted Answer

Analyzing the Knock-out Badminton Tournament

This question concerns a single-elimination, or knock-out, badminton tournament. In such tournaments, each game results in one winner and one loser. The loser is eliminated.

Determining Total Games Played

The core principle of a knock-out tournament is that exactly one player is eliminated per game. To determine a single winner from an initial pool of players, all other players must be eliminated.

Initial number of players, $N = 64$.
Number of players to be eliminated = $N - 1$.
Since each game eliminates exactly one player, the total number of games required is equal to the number of players eliminated.

Calculation:

Total games = Number of players - 1

Total games = $64 - 1 = 63$

Therefore, 63 games must be played in total to declare the winner of the tournament.