The question, which goes back to at least 1955 and may have been pondered by Greek thinkers as early as the third century AD, asks, "How can you express every number between 1 and 100 as the sum of three cubes?" Or, put algebraically, how do you solve x^3 + y^3 + z^3 = k, where k equals any whole number from 1 to 100?

Speaking of sums of cubes ... There are only two integers that cannot be written as the sum of at most eight cubes: 239 and the infamous

**23**.

(Another property of

**23** I haven't seen anywhere is that

**23** is the first odd prime which is not a twin.