{"schema":"vela.problem-packet.v0.1","problem":702,"statement":"Let $k\\geq 4$. If $\\mathcal{F}$ is a family of subsets of $\\{1,\\ldots,n\\}$ with $\\lvert A\\rvert=k$ for all $A\\in \\mathcal{F}$ and $\\lvert \\mathcal{F}\\rvert >\\binom{n-2}{k-2}$ then there are $A,B\\in\\mathcal{F}$ such that $\\lvert A\\cap B\\rvert=1$.","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)"}