SOLVED
This has been resolved in some other way than a proof or disproof.
Let\[H(n)=\min_f \max_{X\subseteq \{1,\ldots,n\}} \left\lvert \sum_{x\neq y\in X} f(x,y)\right\rvert,\]where $f$ ranges over all functions $f:X^2\to \{-1,1\}$. Estimate $H(n)$.
Erdős
[Er63d] proved\[\frac{n}{4}\leq H(n) \ll n^{3/2}.\]Erdős and Spencer
[ErSp71] proved that $H(n)\gg n^{3/2}$.
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T. F. Bloom, Erdős Problem #1028, https://www.erdosproblems.com/1028, accessed 2026-01-16
