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May be this could be an easy problem but somehow cannot arrive to any conclusive result to this indecisiveness problem

For a certain number of teams ($n$) playing a series of matches ($m$), and given the total score for each team, is it possible to determine the number of matches that ended with draw? Considering the score is calculated by the usual convention. Winner receives 3 points If its Draw, both team receives 1 Loser receives 0 points

An example could be as below The Total score for each team is mentioned next to the Team,

$$ \begin{array}{l|r} \text{Team 1} &9\\\ \text{Team 2} &13\\\ \text{Team 3} &11\\\ \text{Team 4} &7\\\ \text{Team 5} &13\\\ \text{Team 6} &13\\\ \text{Team 7} &9\\\ \text{Team 8} &11\\\ \text{Team 9} &9\\\ \text{Team 10} &12 \end{array} $$

The Total draw for the above calculation was 47.

Given the above data, can we arrive somehow to this number 47 i.e. no of matches that ended as draw?

Please note, it may also be possible that all matches may not have yet been played and we need to calculate the result at the middle of the tournament knowing the number of matches that was played till far.

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1 Answer 1

up vote 1 down vote accepted

Each match that ends in a draw awards $2$ points. Each match that doesn't end in a draw awards $3$ points. Thus the total number of points is $p=2d+3(n-d)=3n-d$, where $n$ is the number of matches played and $d$ is the number of draws. Solving for $d$ yields $d=3n-p$.

This doesn't work out for your example; solving for the number $n$ of matches yields $n=(p+d)/3=(107+47)/3=154/3$, which isn't an integer. Are you sure you got the data right?

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Thank you a lot. I was surely dumb when I looked into the data. And yes, looking into the sequence of data again, it is evident they may not be correct. –  Abhijit Mar 30 '12 at 11:55

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