Problem 103

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Statement. 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 $h(n)\to \infty$?

Status. Open.

Source. erdosproblems.com/103, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #103, https://www.erdosproblems.com/103.

Formalization. Statement in formal-conjectures.

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