{"schema":"vela.problem-packet.v0.1","problem":498,"statement":"Let $z_1,\\ldots,z_n\\in\\mathbb{C}$ with $1\\leq \\lvert z_i\\rvert$ for $1\\leq i\\leq n$. Let $D$ be an arbitrary disc of radius $1$. Is it true that the number of sums of the shape\\[\\sum_{i=1}^n\\epsilon_iz_i \\textrm{ for }\\epsilon_i\\in \\{-1,1\\}\\]which lie in $D$ is at most $\\binom{n}{\\lfloor n/2\\rfloor}$?","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)"}