This figure shows a large square cut up into smaller squares, no two of which are the same size.
It's trivial to cut up a square into smaller squares that * are * the same size, but not so
easy if we require the smaller squares to all be different. This example was found in 1978 by A J W Duijvestijn and
is known to use the smallest possible number of squares. A wonderful account of the search for these
dissections can be found in ** Think of a Number, ** by Malcom E Lines.

Is it possible to dissect a cube into smaller cubes no two of which are the same size?