The 30 members of a club decided to play a badminton singles tournament. Every…
2023
The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner?
Answer: B. 29 — In a single knock-out (single-elimination) tournament with no ties, every match has exactly one loser, and a loser is eliminated from the tournament…
- A.
15
- B.
29
- C.
61
- D.
None
Attempted by 1 students.
Show answer & explanation
Correct answer: B
In a single knock-out (single-elimination) tournament with no ties, every match has exactly one loser, and a loser is eliminated from the tournament immediately. To be left with exactly one champion out of n players, exactly (n - 1) players must be eliminated - so the tournament requires exactly (n - 1) matches, however the rounds or pairings are arranged.
Applying this to the given tournament:
Total members in the club, n = 30.
Every match eliminates exactly one player (no ties; a single loss puts a player out).
To leave exactly 1 winner out of the 30 members, 30 - 1 = 29 players must be eliminated.
Since each match eliminates exactly one player, the number of matches needed equals the number of players eliminated = 29.
Cross-check: this count does not depend on how the matches are scheduled - byes, seeding, or bracket shape can all differ, but each match still eliminates exactly one player, so the total always remains (number of participants) - 1 = 29 matches.
Minimum number of matches required = 29.