{"schema":"vela.problem-packet.v0.1","problem":733,"statement":"Call a sequence $1<X_1\\leq\\cdots X_m\\leq n$ line-compatible if there is a set of $n$ points in $\\mathbb{R}^2$ such that there are $m$ lines $\\ell_1,\\ldots,\\ell_m$ containing at least two points, and the number of points on $\\ell_i$ is exactly $X_i$.Prove that there are at most\\[\\exp(O(n^{1/2}))\\]many line-compatible sequences.","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)"}