2 problems

Monochromatic NTIL asymptotics. The exact monochromatic no-three-in-line maxima satisfy

Let $S_n$ be the set of $n^2$ points in $\mathbb{R}^2$ with integer coordinates $(x,y)$ satisfying $1\leq x,y<n$, and let $f_n$ be the maximum size of a subset of $S_n$ containing…