3.A badminton tournament has 128 participants and needs to produce just one
winner. In each match, only the winner goes to the next round and plays with
one of the other winners. This proceeds till ultimately there is only one winner.
How many matches will a person need to reach the semi-finals?
8
7
6
5
In a single-elimination badminton tournament with 128 participants, a player must win 5 matches to reach the semi-finals. This format eliminates the loser of each match, halving the field per round until one winner emerges, requiring exactly 127 matches total to crown a champion since 127 players must lose once.
Tournament Structure
The bracket progresses through defined rounds in a 128-player field:
-
Round of 128 (1st round): 128 to 64 players (64 matches).
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Round of 64 (2nd round): 64 to 32 players (32 matches).
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Round of 32 (3rd round): 32 to 16 players (16 matches).
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Round of 16 (4th round): 16 to 8 players (8 matches).
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Quarterfinals (5th round): 8 to 4 players (4 matches).
Reaching the semi-finals means advancing to the final four, which occurs after winning the quarterfinal—precisely 5 victories.
Option Analysis
Each option represents potential misconceptions about the path:
| Option | Matches | Explanation | Correct? |
|---|---|---|---|
| 8 | 8 wins | Would advance to final 2 (after semis), reaching the final—not semi-finals. Requires 6 round wins + 2 more. | No |
| 7 | 7 wins | Exceeds semi-final path; only champion or finalist might approach this, but semis need fewer. | No |
| 6 | 6 wins | Gets to final 2 (semifinal win), entering the championship match. | No |
| 5 | 5 wins | Exact wins: Round of 128, 64, 32, 16, quarters → 4 semifinalists. | Yes |
Key Insights for Badminton Players
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Total Tournament Matches: Always n-1 (127 here) in single elimination, regardless of byes.
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Champion’s Path: 7 wins total (5 to semis + semifinal + final).
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Badminton tournaments like BWF events often use this 128-player draw for singles, confirming the structure.
This logic applies to tennis Grand Slams or other racket sports knockouts too.
