Problem 132

Erdős Problem #132: declared status 'open'. Formalized: no. Let $A\subset \mathbb{R}^2$ be a set of $n$ points. Must there be two distances which occur at least once but between at most $n$ pairs of points? Must the number of such distances $\to \infty$ as $n\to \infty$? Current best: Erd\H{o}s [Er84c] believed that for $n\geq 5$ there must always exist at least two such distances. Prize: $100. Tags: distances.