Question 10
Let $n\ge m\ge2$ and consider an $m\times n$ grid of unit squares. Such grids will contain many rectangles whose vertices are points on the grid, and whose edges are lines from the grid. For example, a $2\times2$ rectangular grid contains exactly three non-congruent rectangles as shown below.
Find all $m\times n$ grids that contain exactly $100$ non-congruent rectangles.
Investigation (3 bonus marks). Let $n\ge m\ge2$. Describe the set of positive integers $k$ for which there is an $m\times n$ grid containing $k$ non-congruent rectangles.
Find all $m\times n$ grids that contain exactly $100$ non-congruent rectangles.
Investigation (3 bonus marks). Let $n\ge m\ge2$. Describe the set of positive integers $k$ for which there is an $m\times n$ grid containing $k$ non-congruent rectangles.