{"schema":"vela.problem-packet.v0.1","problem":874,"statement":"Let $k(N)$ denote the size of the largest set $A\\subseteq \\{1,\\ldots,N\\}$ such that the sets\\[S_r = \\{ a_1+\\cdots +a_r : a_1<\\cdots<a_r\\in A\\}\\]are disjoint for distinct $r\\geq 1$. Estimate $k(N)$ - in particular, is it true that $k(N)\\sim 2N^{1/2}$?","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)"}