2009 Cayley Problem 25

Unit squares are arranged to form a rectangular grid that is m units wide and n units tall, where m and n are positive integers with 2n < m < 3n. The region below one of the diagonals of the rectangle is shaded as shown. For certain pairs m and n, there is a unit square in the grid that is not completely shaded but whose shaded area is greater than 0.999. The smallest possible value of mn for which this is true satisfies

\textbf{(A)}\ 496 \le mn \le 500\quad \textbf{(B)}\ 501 \le mn \le 505\quad \textbf{(C)}\ 506 \le mn \le 510\quad \textbf{(D)}\ 511 \le mn \le 515\quad \textbf{(E)}\ 516 \le mn \le 520

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.