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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.

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

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    $\begingroup$ 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? $\endgroup$ – Jane Doé May 2 at 14:30