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

Step 1: This is a single-elimination (knock-out) tournament - every game produces exactly one loser, and that loser is immediately removed from the tournament.
Step 2: Play continues until exactly one player remains undefeated; she is declared the winner.
Step 3: To go from 64 players down to a single champion, all the other \(64 - 1 = 63\) players must be eliminated at some point.
Step 4: Since each game eliminates exactly one player, the number of games required equals the number of eliminations needed, which is \(63\).
Final Answer: \(\boxed{63}\)