{"schema":"vela.problem-packet.v0.1","problem":94,"statement":"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.\\]","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A387858","name":"Sum of squares of the multiplicities of pairwise distances among the vertices of a regular n-gon.","terms":"9,20,50,81,147,208,324,425,605,756,1014,1225,1575,1856,2312,2673,3249,3700,4410,4961,5819,6480,7500,8281,9477,10388,1177","url":"https://oeis.org/A387858"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}