{"schema":"vela.problem-packet.v0.1","problem":1027,"statement":"Let $c>0$, and let $n$ be sufficiently large depending on $c$. Suppose that $\\mathcal{F}$ is a family of at most $c2^n$ many finite sets of size $n$. Let $X=\\cup_{A\\in \\mathcal{F}}A$.Must there exist $\\gg_c 2^{\\lvert X\\rvert}$ many sets $B\\subset X$ which intersect every set in $\\mathcal{F}$, yet contain none of them?","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)"}