Problem 661

Erdős Problem #661: declared status 'open'. Formalized: no. 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$$o\left(\frac{n}{\sqrt{\log n}}\right)?$$ Prize: $50. Tags: distances, geometry.