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?
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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 classes during it.
So different rooms will be needed.