Let $n$ be a positive integer. How to prove that if $5n + 1$ objects are distributed in $n$ boxes then some boxes must contain at least $6$ objects?
I think I have to use the pigeonhole principle but I don't know how to use it.
2026-03-25 07:15:14.1774422914
Pigeonhole principle for boxes
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If by contradiction all boxes contain at most $5$ objects then there would be at most $5n$ objects in total. (This is indeed some "generalized" version of the pigeonhole-principle)