Question 113
Let $\mathcal{G}$ be a $6 \times 6$ grid of unit squares. A rectangle in $\mathcal{G}$ is defined as a set of unit squares whose union forms an axis-aligned rectangle with vertices on grid points. Two such rectangles are said to be disjoint if they share no common point (including boundary and interior). Determine the number of unordered pairs of disjoint rectangles that can be selected in $\mathcal{G}$.