In a round-robin chess tournament, 9 boys and 3 girls are participating (each plays against each other once, a win is 1 point; a draw is 0.5; a loss is 0). Can it happen that the total points scored by all the boys will be equal to the total points scored by all the girls?
This one wants a proof. Work it on paper, read the official solution, then mark
yourself honestly — the ladder only means something if the record is true.
Official solution
Boys will only accumulate 9⋅8:2=36 points in their matches against each other, which is more than half of the points played for in the tournament.
## Answer
It is not possible.
Source: NuminaMath-1.5,
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