# 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
2 years, 9 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...

- 2 years, 9 months ago