{"schema":"vela.problem-packet.v0.1","problem":664,"statement":"Let $c<1$ be some constant and $A_1,\\ldots,A_m\\subseteq \\{1,\\ldots,n\\}$ be such that $\\lvert A_i\\rvert >c\\sqrt{n}$ for all $i$ and $\\lvert A_i\\cap A_j\\rvert\\leq 1$ for all $i\\neq j$.Must there exist some set $B$ such that $B\\cap A_i\\neq \\emptyset$ and $\\lvert B\\cap A_i\\rvert \\ll_c 1$ for all $i$?","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)"}