Forty-nine students solve a set of 3 problems. The score for each problem is a whole number of points from 0 to 7. Prove that there exist two students
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
and
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
such that, for each problem,
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
will score at least as many points as
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Forty-nine students solve a set of 3 problems. The score for each problem is a whole number of points from 0 to 7. Prove that there exist two students $A$ and $B$ such that, for each problem, $A$ will score at least as many points as $B.$