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This is a long chess tournament

100 players take part in a chess tournament where each player plays every other player exactly once. Each win is worth 1 point, each draw \(\frac {1}{2}\) point and each loss 0 point. At the conclusion of the tournament, each player who scores at least 80 points is given a medal.

What is the maximum number of medals that can be awarded? Give proof.

Bonus: Generalise this for \(k\) people who have to score at least \(n\) points, where \(k\) and \(n\) are positive integers such that \(k \geq n\).

Note by Sharky Kesa
1 year, 2 months ago

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No. of total points=No. of matches=4950... Max. no. of people wining the medal=[4950/80]=61 This can be generalized to k people scoring atleast n points... Sarthak Behera · 1 year, 2 months ago

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