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 45 from each school. Students from any school need to 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: 16.

Solution. Suppose that 46 schools sent 43 students each to the final match, and one school sent 34 students. Since only three groups of 43 students can fit in one row, the number of rows required to accommodate the students from 46 schools should be no less than $\frac{46}{3}=15 \frac{1}{3}$, which means at least 16 rows are needed.

We will show that 16 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 on two sectors. Since any three schools can fit in one sector, four sectors are sufficient for seating the remaining students.