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

28 votes
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Does a function from $\mathbb R^2$ to $\mathbb R$ which sums to 0 on the corners of any unit...

The answer is yes, I learned this from the paper that appeared on arXiv literally yesterday https://arxiv.org/abs/2403.01279, they quote R. Katz, M. Krebs and A. Shaheen, Zero sums on unit square vert …
Aleksei Kulikov's user avatar