Erdős Problem #661 — Are there, for all large $n$, some points $x_1,\ldots,x_n,y_1,\ldots,y_n\in \mathbb{R}^2$ such that the number of distinct distances $d(x_i,y_j)$ is $o\left(\frac{n}{\sqrt{\log n}}\right)?$

Erdős Problem #661 asks whether, for every sufficiently large $n$, two $n$-point sets in the plane can have fewer than $n/\sqrt{\log n}$ distinct cross-distances in the little-$o$ sense. A current problem ledger marks it verified open; its opening date is unknown, and no retrieved source reports a resolution.

Current status (as of September 2026): The existence of such configurations remains open; no verified proof, counterexample, or exact advance has been recorded.