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: 12^{3} + 1^{3} = 1729 = 10^{3} +
9^{3}.

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.