Problem 982

Erdős Problem #982 [status: falsifiable; formalized: yes]. If $n$ distinct points in $\mathbb{R}^2$ form a convex polygon then some vertex has at least $\lfloor \frac{n}{2}\rfloor$ different distances to other vertices. Current best: The regular polygon shows that $\lfloor n/2\rfloor$ is the best possible here. Prize: no. OEIS: A004526. Tags: convex, distances, geometry.