{"schema":"vela.problem-packet.v0.1","problem":776,"statement":"Let $r\\geq 2$ and $A_1,\\ldots,A_m\\subseteq \\{1,\\ldots,n\\}$ be such that $A_i\\not\\subseteq A_j$ for all $i\\neq j$ and for any $t$ if there exists some $i$ with $\\lvert A_i\\rvert=t$ then there must exist at least $r$ sets of that size.How large must $n$ be (as a function of $r$) to ensure that there is such a family which achieves $n-3$ distinct sizes of sets?","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)"}