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 $d(x,y)\ge 1$ for all points $x\ne y$. Is it true that $h(n)\to \infty$?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

It is an open problem of Erdős (listed as Erdős Problem #103). In fact, even the much weaker statement “for all large $n$, there are **at least two** non-congruent diameter-minimising configurations” is not proved. ([erdosproblems.com][1])

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.