Problem 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 $h(n)\to \infty$?
Categories:
Geometry Distances
Progress
It is not even known whether $h(n)\geq 2$ for all large $n$.See also [99].
Source: erdosproblems.com/103 | Last verified: January 13, 2026