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?
Official answer and solution
- Official answer
- C
- From
- Official GATE 2026 answer key
Solution
Use the invariant that each game in a single-elimination tournament eliminates exactly one player.
In a knock-out tournament with no ties, every game produces exactly one loser who is eliminated from the tournament. Starting with players, declaring a single undefeated winner requires eliminating players. Therefore, games must be played in total (equivalently, ).
Option (C)
Answering 64 instead of .
The answer is the one in the official GATE answer key. The solution is this site's own explanation.
Source
- Paper
- GATE 2026 Computer Science and Information Technology - Session 1 (CS1)
- Question
- 3 of 65
- Section
- General Aptitude
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