GATE CS 2026 Set 1 — Question 3
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Question
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?
Correct answer
(C) 63
Solution
In a knock-out tournament, every match eliminates exactly one player. To find a single winner from participants, players must be eliminated.Since each game eliminates 1 player:
Total games = Total players to be eliminated = .Alternatively, in each round:
Total games = Total players to be eliminated = .Alternatively, in each round:
- Round 1: 64 players 32 games
- Round 2: 32 players 16 games
- Round 3: 16 players 8 games
- Round 4: 8 players 4 games
- Round 5: 4 players 2 games
- Round 6: 2 players 1 game
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