Question 11
Let $n$ be a natural number and $G$ the set of points $(x, y)$ in the plane such that $x$ and $y$ are integers with $1 \leq x, y \leq n$. A subset of $G$ is called parallelogram-free if it does not contain four non-collinear points that are the vertices of a parallelogram. What is the largest number of elements a parallelogram-free subset of $G$ can contain?