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Recreational mathematics or puzzles with serious mathematical content. Note that math contest problems are generally considered off-topic.

20 votes
3 answers
3k views

How many unit squares can you pack into a rectangle with nearly integer side lengths?

Earlier today, somebody asked what looks like a homework problem, but admits the following reading which I think is interesting: Suppose $a_1,\dots, a_n$ are positive integers, and $\varepsilon$ i …
30 votes
5 answers
3k views

The ants-on-a-ball problem

Suppose I put an ant in a tiny racecar on every face of a soccer ball. Each ant then drives around the edges of her face counterclockwise. The goal is to prove that two of the ants will eventually col …