Question by Summer Clouds - Discuss with MathYouLike

Summer Clouds moderators

10/11/2017 at 14:10

In a tennis tournament, each of the 10 competitors plays each other player once. What is the maximum number of players who could end the tournament with a record of 7 or more wins?

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Lê Quốc Trần Anh Coordinator 10/11/2017 at 17:43

There are total: \(10\cdot9:2=45\left(matches\right)\) matches in the tournament so there are 45 wins and 45 loses.

If there are 6 players have 7 or more wins, there are: \(6\cdot7=42\left(wins\right)\) , so there are 42 loses left but there must have 6 more lose (the battles together) so it is unsatisfy

But if there are 5 players then it will satisfy the question.

Hence, the answer is 5 players.
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Phạm Tuấn Đạt 11/11/2017 at 13:21

There are total: 10⋅9:2=45(matches) matches in the tournament so there are 45 wins and 45 loses.

If there are 6 players have 7 or more wins, there are: 6⋅7=42(wins) , so there are 42 loses left but there must have 6 more lose (the battles together) so it is unsatisfy

But if there are 5 players then it will satisfy the question.

Hence, the answer is 5 players.

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