How do we place $8n$ objects on a square of size $n\times n$ in a form of grid such that no 4 of them form a rectangle? Each object occupies exactly 1 cell in the grid (given $n\geq 100$). Sides of the rectangle should be parallel to sides of the $n \times n$ square. I am not able to figure out any appropriate approach for this problem. I am trying some random object placing but could not achieve the desired result.