{"schema":"vela.problem-packet.v0.1","problem":178,"statement":"Let $A_1,A_2,\\ldots$ be an infinite collection of infinite sets of integers, say $A_i=\\{a_{i1}<a_{i2}<\\cdots\\}$. Does there exist some $f:\\mathbb{N}\\to\\{-1,1\\}$ such that\\[\\max_{m, 1\\leq i\\leq d} \\left\\lvert \\sum_{1\\leq j\\leq m} f(a_{ij})\\right\\rvert \\ll_d 1\\]for all $d\\geq 1$?","status":"solved","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)"}