Question 25
A square of size $n \times n$ is given. Some of its $1 \times 1$ cells are marked (by their centers). It turned out that there is no convex quadrilateral with vertices at these marked points. For each natural number $n \ge 3$, find the largest value of $m$ (the number of marked cells) for which this is possible.
A quadrilateral is called convex if both of its diagonals lie inside the quadrilateral.
Figure 6
A quadrilateral is called convex if both of its diagonals lie inside the quadrilateral.
Figure 6