{"schema":"vela.problem-packet.v0.1","problem":553,"statement":"Let $R(3,3,n)$ denote the smallest integer $m$ such that if we $3$-colour the edges of $K_m$ then there is either a monochromatic triangle in one of the first two colours or a monochromatic $K_n$ in the third colour. Define $R(3,n)$ similarly but with two colours. Show that\\[\\frac{R(3,3,n)}{R(3,n)}\\to \\infty\\]as $n\\to \\infty$.","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A000791","name":"Ramsey numbers R(3,n).","terms":"1,3,6,9,14,18,23,28,36","url":"https://oeis.org/A000791"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}