Problem 1087

Erdős Problem #1087: declared status 'open'. Formalized: no. Let $f(n)$ be minimal such that every set of $n$ points in $\mathbb{R}^2$ contains at most $f(n)$ many sets of four points which are 'degenerate' in the sense that some pair are the same distance apart. Estimate $f(n)$ - in particular, is it true that $f(n)\leq n^{3+o(1)}$? Prize: no. Tags: distances, geometry.