`116` people participated in a knockout tennis tournament. The players are paired up in the first round, the winners of the first round are paired up in the second round, and so on till the final is played between two players. If after any round, there is odd number of players, one player is given a by, i.e. he skips that round and plays the next round with the winners. The total number of matches played in the tournment is

Options

A. `115`
B. `53`
C. `232`
D. `116`

Explanation

To find the total number of matches played in a knockout tennis tournament with 116 participants, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Tournament Structure**:
In a knockout tournament, each match eliminates one player. Therefore, to determine the total number of matches, we can note that if there are `n` players, there will be `n - 1` matches played to determine a single winner.

2. **Calculating Matches**:
Since there are 116 players, the total number of matches played will be:
\[ \text{Total Matches} = 116 - 1 = 115 \]

3. **Verification through Rounds**:
- **First Round**:
- Players: 116
- Matches: \( \frac{116}{2} = 58 \)
- Winners: 58
- **Second Round**:
- Players: 58
- Matches: \( \frac{58}{2} = 29 \)
- Winners: 29
- **Third Round**:
- Players: 29 (odd, so one gets a bye)
- Matches: \( \frac{28}{2} = 14 \)
- Winners: 14 + 1 (bye) = 15
- **Fourth Round**:
- Players: 15 (odd, so one gets a bye)
- Matches: \( \frac{14}{2} = 7 \)
- Winners: 7 + 1 (bye) = 8
- **Fifth Round**:
- Players: 8
- Matches: \( \frac{8}{2} = 4 \)
- Winners: 4
- **Sixth Round**:
- Players: 4
- Matches: \( \frac{4}{2} = 2 \)
- Winners: 2
- **Seventh Round (Final)**:
- Players: 2
- Matches: 1
- Winner: 1

4. **Total Matches Calculation**:
Adding all the matches from each round:
\[ 58 + 29 + 14 + 7 + 4 + 2 + 1 = 115 \]

5. **Conclusion**:
The total number of matches played in the tournament is **115**.

### Final Answer:
The total number of matches played in the tournament is **115**.

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