4. In the stands of the hockey arena, there are several rows with 168 seats in each row. For the final match, 2016 students from several sports schools were invited as spectators, with no more than 40 from each school. Students from any school must be seated in one row. What is the minimum number of rows that must be in the arena to ensure this can always be done?
Answer: 15.

Solution. Suppose that 57 schools sent 35 students each to the final match, and one school sent 21 students. Since only four groups of 35 students can fit in one row, the number of rows required to accommodate the students from 57 schools should be no less than $\frac{57}{4}=14 \frac{1}{4}$, which means at least 15 rows are needed.

We will show that 15 rows are sufficient. Assume that there is one large row on the stand, divided by aisles into sectors of 168 seats each. We will seat the students on this large row, ignoring the aisles, starting with the students from the first school, then the second, and so on. As a result, 12 sectors will be fully occupied. With this seating arrangement, students from no more than 11 schools can be seated in two sectors. Since any four schools can fit in one sector, it is sufficient to have three sectors for seating the remaining students.