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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
10 months, 3 weeks 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 · 10 months, 2 weeks ago

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