In a school, there are $m$ teachers and $n$ students. We assume that each teacher has exactly $k$ students, and that any two students always have exactly $l$ teachers in common. Determine a relation between $m, n, k, l$.
Consider an $m \times n$ table, with one row per teacher and one column per student, a 1 at each intersection between a teacher and a student in their class. By assumption:

- each row contains $k 1$s,
- two different columns have exactly $l 1$s aligned horizontally.

By counting the total number of pairs of 1s aligned horizontally, we get: $m \frac{k(k-1)}{2}=\frac{n(n-1)}{2} l$.