Question 11
A rectangular grid is divided by two perpendicular straight lines into four smaller rectangles with integral side lengths. It is possible to remove one among these four rectangles in such a way that the remaining figure can be exactly covered by rectangles of size $2 \times 3$ and $3 \times 2$. Prove that it is possible to exactly cover one among these four smaller rectangles by rectangles of size $2 \times 3$ and $3 \times 2$. (By *exact covering* we mean covering without gaps, overlaps and overflows.)