Question

A Men Singles Tennis Tournament is being held out at Mumbai. 30 players participated in the tournament. There is a rule that is implemented, the rule states that, if a player loses a match then he is eliminated from the tournament. How many matches have to be played to decide the winner of the tournament?

• A. 30
• B. 15
• C. 29
• D. 10

Answer 1

The Correct Option is C

To determine the number of matches that need to be played in a single-elimination tennis tournament with 30 players, we should understand the structure of such a tournament. In a single-elimination tournament, one player wins the entire event, and every other player loses exactly once and is then eliminated. Thus, the number of matches necessary to decide a winner equals the number of players minus one.

Explanation:

1. Each match results in one player being eliminated.
2. We begin with 30 players, and we need to determine a winner, which means all other players (29) must lose one match each and be eliminated.
3. Therefore, the total number of matches played will be 30 (total players) - 1 (the winner who is not eliminated) = 29 matches.

Thus, the correct answer is 29 matches.

Answer 2

Instead of using the general rule that a knockout tournament always needs one fewer match than the number of players, this can be verified directly by counting the matches round by round, including how byes are handled when the number of players in a round is odd.

Round 1 starts with 30 players, who split into 15 full pairs, giving 15 matches and 15 winners. Round 2 has 15 players; 14 of them form 7 matches while the one player left over gets a bye, giving \( 7+1=8 \) players for round 3. Round 3 has 8 players, giving 4 matches and 4 winners. Round 4 has 4 players, giving 2 matches and 2 winners. The final round has the last 2 players playing 1 match to decide the overall winner.

Adding up the matches from every round: \( 15+7+4+2+1 = 29 \).

1. Option A (30): This equals the total number of players, not the match count, so this is incorrect.
2. Option B (15): This is only the count from the very first round, not the whole tournament, so this is incorrect.
3. Option C (29): This matches the sum of matches counted round by round, so this is correct.
4. Option D (10): This does not match the total from any reasonable count of the rounds, so this is incorrect.

Counting every round's matches and adding them together gives 29 matches in total.

the correct answer is Option C: 29.