Question 71
Let $m, n$ be natural numbers. Consider a square lattice of $(2m+1) \times (2n+1)$ points in the plane. A set of rectangles is called good if the following holds:
a. For each of the rectangles the four vertices lie on lattice points and the sides are parallel to the lattice lines.
b. No two of the rectangles have a common vertex.
Determine the greatest possible value of the sum of the areas of all rectangles in a good set.
a. For each of the rectangles the four vertices lie on lattice points and the sides are parallel to the lattice lines.
b. No two of the rectangles have a common vertex.
Determine the greatest possible value of the sum of the areas of all rectangles in a good set.