{"schema":"vela.problem-packet.v0.1","problem":653,"statement":"Let $x_1,\\ldots,x_n\\in \\mathbb{R}^2$ and let $R(x_i)=\\#\\{ \\lvert x_j-x_i\\rvert : j\\neq i\\}$, where the points are ordered such that\\[R(x_1)\\leq \\cdots \\leq R(x_n).\\]Let $g(n)$ be the maximum number of distinct values the $R(x_i)$ can take. Is it true that $g(n) \\geq (1-o(1))n$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}