# Prove the generalization of the Box Principle [closed]

Prove the following generalizations of the box principle:

For any natural number $$m$$ and $$n$$, if more than $$mn$$ objects are put into $$n$$ boxes, then some box must contain more than $$m$$ objects.

What would a proof of this look like? I don't quite understand this part of the Pigeonhole Principle.

## closed as off-topic by Eevee Trainer, The Count, Shogun, Lee David Chung Lin, hardmathJul 16 at 4:37

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• Suppose toward contradiction that every box contains less than or equal to $m$ objects... then how many objects are there in total? Why is that a contradiction? – Jane Doé May 2 at 14:30