{"schema":"vela.problem-packet.v0.1","problem":216,"statement":"Let $g(k)$ be the smallest integer (if any such exists) such that any $g(k)$ points in $\\mathbb{R}^2$ contains an empty convex $k$-gon (i.e. with no point in the interior). Does $g(k)$ exist? If so, estimate $g(k)$.","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A381776","name":"Empty polygon numbers: a(n) is the smallest number of points in the plane (with no three of them collinear) such that an empty convex n-gon cannot be avoided.","terms":"3,5,10,30","url":"https://oeis.org/A381776"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}