There are 38 different time periods during which classes at a university can be scheduled. If there are 677 different classes, how many different rooms will be needed?
There are $677$ pigeons and $38$ holes. By the generalized pigeon hole principle, there is at least $1$ time slot with $[677/38]$ classes scheduled. This means we need $19$ rooms to avoid having $2$ classes being held in the same room.
It seems right, but it's an important question so I need to be sure.