By counting carefully it can be seen that a rectangular grid measuring 3 by 2 contains eighteen rectangles:

Although there exists no rectangular grid that contains exactly two million rectangles, find the area of the grid with the nearest solution.

def rectangles(x, y):
    count = 0
    for i in range(y + 1):
        for j in range(x + 1):
            count += (i * j)
    return count


def run():
    result = []
    # Limit 100 found by trial and error
    for x in range(1, 100):
        for y in range(x, 100):
            tmp = rectangles(x, y)
            # Limit found by trial and error
            if tmp > 1999000 and tmp < 2001000:
                result = [x, y, tmp]

    x, y, tmp = result

    return x * y