Question 18
For a natural number $n \ge 2$, consider an $n \times n$ board. Let $n^2$ points denote the centers of each of the $1 \times 1$ squares on this board. What is the largest number of these points that can be marked in such a way that no three marked points form the vertices of a right triangle?
*(Mykhailo Shtandenko)*
*(Mykhailo Shtandenko)*