BdMO National Primary 2011/9

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Moon
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BdMO National Primary 2011/9

Unread post by Moon » Fri Feb 11, 2011 12:25 pm

Problem 9:
In the first round of a chess tournament, each player plays against every other player exactly once. A player gets $3, 1$ or $-1$ points respectively for winning, drawing or losing a match. After the end of the first round, it is found that the sum of the scores of all the players is $20$. How many players were there in the tournament?
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samiul_samin
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Re: BdMO National Primary 2011/9

Unread post by samiul_samin » Fri Feb 22, 2019 7:41 am

Answer
$5$
Solution
$1+1= 2,3-1=2$
So,$2$ points will be added to score board after each match.
So,total match =$20×0.5=10$
So,$\dbinom n2=10$
So,$n=5$
There were $5$ players in the tournament.

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