Question

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?

Answer 1

Assign each class to a time period. Then 677 different classes (pigeons) has to be assigned to 38 pigeonholes.

By the Pigeonhole Principle there exists a time period will have at least $\lceil\dfrac{677}{38}\rceil=18$ classes during it.

So $18$ different rooms will be needed.