The GATE Grind

GATE 2026 CS (CS1) – Question 3

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

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?

  1. 127
  2. 64
  3. 63
  4. 32

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Correct answer: (C) 63

Explanation

In any single-elimination (knockout) tournament with $N$ players, each game results in exactly one player being eliminated, and no ties are permitted. To determine a single winner among $N$ players, exactly $N - 1$ players must be eliminated.

Since there are $N = 64$ players:
$$\text{Total games played} = N - 1 = 64 - 1 = 63$$

Therefore, option (C) is correct.