{"schema":"vela.problem-packet.v0.1","problem":963,"statement":"Let $f(n)$ be the maximal $k$ such that in any set $A\\subset \\mathbb{R}$ of size $n$ there is a subset $B\\subseteq A$ of size $\\lvert B\\rvert\\geq k$ which is dissociated that is, the sums $\\sum_{b\\in S}b$ are distinct for all $S\\subseteq B$. Estimate $f(n)$ - in particular, is it true that\\[f(n)\\geq \\lfloor \\log_2 n\\rfloor?\\]","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)"}