{"schema":"vela.problem-packet.v0.1","problem":603,"statement":"Let $(A_i)$ be a family of countably infinite sets such that $\\lvert A_i\\cap A_j\\rvert \\neq 2$ for all $i\\neq j$. Find the smallest cardinal $C$ such that $\\cup A_i$ can always be coloured with at most $C$ colours so that no $A_i$ is monochromatic.","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)"}