{"schema":"vela.problem-packet.v0.1","problem":531,"statement":"Let $F(k)$ be the minimal $N$ such that if we two-colour $\\{1,\\ldots,N\\}$ there is a set $A$ of size $k$ such that all subset sums $\\sum_{a\\in S}a$ (for $\\emptyset\\neq S\\subseteq A$) are monochromatic. Estimate $F(k)$.","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)"}