OPEN
This is open, and cannot be resolved with a finite computation.
Let $h(n)$ count the number of incongruent sets of $n$ points in $\mathbb{R}^2$ which minimise the diameter subject to the constraint that $d(x,y)\geq 1$ for all points $x\neq y$. Is it true that $h(n)\to \infty$?
It is not even known whether $h(n)\geq 2$ for all large $n$.
See also
[99].
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T. F. Bloom, Erdős Problem #103, https://www.erdosproblems.com/103, accessed 2026-01-16
