Problem 99

Erdős Problem #99: declared status 'open'. Formalized: yes. Let $A\subseteq\mathbb{R}^2$ be a set of $n$ points with minimum distance equal to 1, chosen to minimise the diameter of $A$. If $n$ is sufficiently large then must there be three points in $A$ which form an equilateral triangle of size 1? Prize: $100. Tags: distances, geometry.