BdMO National Secondary 2011/2

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Moon
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BdMO National Secondary 2011/2

Unread post by Moon » Fri Feb 11, 2011 1:49 pm

Problem 2:
In the first round of a chess tournament, each player plays against every other player exactly once. A player gets $3, 0$ or $-1$ points respectively for winning, drawing or losing a match. After the end of the first round, is it possible that the sum of the scores of all the players is $21$? State your answer with logic.
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FahimFerdous
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Re: BdMO National Secondary 2011/2

Unread post by FahimFerdous » Sun Feb 13, 2011 9:20 pm

After every match, the sum of the points the teams win is even (either 3+(-1)=2 or, 0). So, the sum of everyone's points at the end of the league can't be 21, as it's odd.
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samiul_samin
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Re: BdMO National Secondary 2011/2

Unread post by samiul_samin » Tue Feb 26, 2019 11:15 am

A classical example of INVARIENCE PRINCIPLE.

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