Question

116 people participated in a singles tennis tournament of knockout format. The players are paired up in the first round, winners of the first round are paired in the second round, and so on till the final is played between two players. If after any round, the number of players is odd, one player is given a bye (he skips that round and plays the next round with the winners). Find the total number of matches played in the tournament.

• A. 115
• B. 53
• C. 232
• D. 116

Hint:

In knockout tournaments, total matches = initial players − 1, regardless of byes.

Answer 1

The Correct Option is A

In a knockout tournament, every match eliminates exactly one player.
Starting with 116 players, to find a single winner, we must eliminate $116 - 1 = 115$ players.
Since each match eliminates exactly one player, the number of matches required equals the number of eliminations, which is 115.
The “bye” condition does not change the total number of eliminations; it only skips a match in a particular round, but the total number of players eliminated over the tournament remains the same. Thus, the total matches = total eliminations = 115.