Question:
139 persons have signed up for an elimination tournament. All players are to be paired up for the first round, but because 139 is an odd number one player gets a bye, which promotes him to the second round, without actually playing in the first round. The pairing continues on the next round, with a bye to any player left over. If the schedule is planned so that a minimum number of matches is required to determine the champion, the number of matches which must be played is
139 persons have signed up for an elimination tournament. All players are to be paired up for the first round, but because 139 is an odd number one player gets a bye, which promotes him to the second round, without actually playing in the first round. The pairing continues on the next round, with a bye to any player left over. If the schedule is planned so that a minimum number of matches is required to determine the champion, the number of matches which must be played is
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In an elimination tournament every match removes exactly one player.
Updated On: Nov 5, 2026
- 136
- 137
- 138
- 139
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The Correct Option is C
Solution and Explanation
Step 1: Players to be eliminated:
To find one champion, \(139 - 1 = 138\) players must be eliminated.
Step 2: Matches:
Each match eliminates exactly one player (a bye eliminates nobody and needs no match). So exactly 138 matches are needed, whatever the pairing.
Final Answer:
The correct option is (3): 138.
To find one champion, \(139 - 1 = 138\) players must be eliminated.
Step 2: Matches:
Each match eliminates exactly one player (a bye eliminates nobody and needs no match). So exactly 138 matches are needed, whatever the pairing.
Final Answer:
The correct option is (3): 138.
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