{"schema":"vela.problem-packet.v0.1","problem":362,"statement":"Let $A\\subseteq \\mathbb{N}$ be a finite set of size $N$. Is it true that, for any fixed $t$, there are\\[\\ll \\frac{2^N}{N^{3/2}}\\]many $S\\subseteq A$ such that $\\sum_{n\\in S}n=t$?If we further ask that $\\lvert S\\rvert=l$ (for any fixed $l$) then is the number of solutions\\[\\ll \\frac{2^N}{N^2},\\]with the implied constant independent of $l$ and $t$?","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)"}