B1. A number of students participated in a test that could be scored up to 100 points. Everyone scored at least 60 points. Exactly five students scored 100 points. The average score of the participating students was 76 points.

How many students participated in this test at a minimum?
B1. 13 There is a solution with thirteen students, because if five students scored 100 points and the remaining eight students scored 61 points, then the average score was indeed $\frac{5 \cdot 100+8 \cdot 61}{13}=\frac{988}{13}=76$ points.

It cannot be that twelve or fewer students participated. Suppose, for instance, that there were $n \leqslant 12$ students. Five of them scored 100 points and the remaining $n-5$ at least 60. Their total score is then at least $500+(n-5) \cdot 60=60 n+200$. Their average score is then at least

$$
\frac{60 n+200}{n}=60+\frac{200}{n} \geqslant 60+\frac{200}{12}=76 \frac{2}{3},
$$

since $n \leqslant 12$. But this contradicts the fact that the average was 76.