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 $k \geq n$ .

#Combinatorics #Sharky

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

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 - 5 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$