{"schema":"vela.problem-packet.v0.1","problem":1025,"statement":"Let $f$ be a function from all pairs of elements in $\\{1,\\ldots,n\\}$ to $\\{1,\\ldots,n\\}$ such that $f(x,y)\\neq x$ and $\\neq y$ for all $x,y$. We call $X\\subseteq \\{1,\\ldots,n\\}$ independent if whenever $x,y\\in X$ we have $f(x,y)\\not\\in X$.Let $g(n)$ be such that, in every function $f$, there is an independent set of size at least $g(n)$. Estimate $g(n)$.","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)"}