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?

• A. 127
• B. 64
• C. 63
• D. 32

Hint:

Each game eliminates exactly one player; going from 64 players to a single champion requires exactly 63 eliminations, i.e., 63 games.

Answer 1

The Correct Option is C

Alternate approach - count games round by round: With 64 players, Round 1 has 32 games (64 players → 32 winners), Round 2 has 16 games, Round 3 has 8 games, Round 4 has 4 games, Round 5 has 2 games, and the Final has 1 game.
Total games = \(32+16+8+4+2+1 = 63\).
This matches the general knock-out rule: for \(n\) players, exactly \(n-1\) games are needed to crown one champion, since every game permanently removes exactly one contestant.
Hence the total number of games played is \(63\).