There is no limit to the number of different dimensions that will give
two cubes whose sum shall be exactly seventeen cubic inches. Here is the
answer in the smallest possible numbers. One of the silver cubes must
measure 2-23278/40831 inches along each edge, and the other must measure
11663/40831 inch. If the reader likes to undertake the task of cubing
each number (that is, multiply each number twice by itself), he will find
that when added together the contents exactly equal seventeen cubic
inches. See also No. 20, "The Puzzle of the Doctor of Physic."