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, and the tournament ends with exactly one player left undefeated.

Answer 1

The Correct Option is C

Step 1: Understand the elimination rule.
This is a knock-out tournament, so every single game played has exactly one loser, and that loser is eliminated right away. No player can return once she loses.

Step 2: Link games played to players eliminated.
Since each game removes exactly one player from the tournament, the number of games played always equals the number of players eliminated so far.

Step 3: Count how many players must be eliminated.
The tournament starts with 64 players and ends when only 1 player, the winner, remains undefeated. So the number of players who must be eliminated is
\[ 64-1=63 \]

Step 4: Match eliminations to games.
Because one game produces exactly one elimination, 63 eliminations require exactly 63 games.

Step 5: Check the other options.
127 does not fit a simple knock-out structure at all. 64 wrongly assumes the winner also plays one extra unnecessary game after already winning the tournament. 32 is only the number of games in the very first round, when 64 players are paired into 32 matches, not the total across every round.

Final Answer:
The tournament needs 63 games in total to leave exactly one undefeated winner. \[ \boxed{63} \]