When the English mathematician G. H. Hardy visited the Indian mathematician Srinivasa Ramanujan one day, he remarked that 1729, the number of the taxicab he rode in, was a dull number. Ramanujan immediately disagreed, pointing out that 1729 was interesting because it was the smallest positive integer that could be written as the sum of two positive cubes in two essentially different ways: 123 + 13 = 1729 = 103 + 93.
This month's challenge is to dissect a 12×12×12 cube into as few pieces as possible so that it, along with a 1×1×1 cube, can be reassemble to make a 10×10×10 cube and a 9×9×9 cube.