{"schema":"vela.problem-packet.v0.1","problem":543,"statement":"Define $f(N)$ be the minimal $k$ such that the following holds: if $G$ is an abelian group of size $N$ and $A\\subseteq G$ is a random set of size $k$ then, with probability $\\geq 1/2$, all elements of $G$ can be written as $\\sum_{x\\in S}x$ for some $S\\subseteq A$. Is\\[f(N) \\leq \\log_2 N+o(\\log\\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)"}