Question

128 players start in the men's single at a tennis tournament, where this number reduces to half on every succeeding round. How many matches are played totally in the event?

• A. 63
• B. 48
• C. 127
• D. 144

Answer 1

The Correct Option is C

To determine the total number of matches played in a tennis tournament starting with 128 players, where the number of players halves in each round, we need to consider how the tournament progresses. In each match, one player is eliminated until a winner is determined.

Initially, there are 128 players. To identify the number of matches needed until one champion is left, observe the following logic:

• In the first round, 128 players participate, resulting in 64 matches (as each match has 2 players).
• After the first round, half of the players remain, which equals 64 players.
• Continuing the process, the number of rounds and matches are as follows:

• Round 1: 128 players, 64 matches.
• Round 2: 64 players, 32 matches.
• Round 3: 32 players, 16 matches.
• Round 4: 16 players, 8 matches.
• Round 5: 8 players, 4 matches.
• Round 6: 4 players, 2 matches.
• Round 7: 2 players, 1 match.

The pattern continues until one player remains as the champion. Notice that the total number of matches equals the initial number of players minus one.

Thus, with 128 players, the total number of matches is:

128 - 1 = 127.

So, the total number of matches played in the event is 127.