{"schema":"vela.problem-packet.v0.1","problem":771,"statement":"Let $f(n)$ be maximal such that, for every $m\\geq 1$, there exists some $S\\subseteq \\{1,\\ldots,n\\}$ with $\\lvert S\\rvert=f(n)$ such that $m\\neq \\sum_{a\\in A}a$ for all $A\\subseteq S$. Is it true that\\[f(n) = \\left(\\frac{1}{2}+o(1)\\right)\\frac{n}{\\log n}?\\]","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)"}