Magic Squares and Cubes
After a chapter on the shapely numbers it seems only logical to consider briefly the age old fascination of assembling the natural numbers 1, 2, 3, 4, … into patterns such that their sum along various symmetry directions is always the same. The most common such pattern is a square and the literature on the so-called magic squares is already enormous without adding to it. Nevertheless the topic does contains unsolved problems so that in this respect it is still ‘alive’ and there is still an opportunity for ‘pushing back the frontiers’. The extension to three dimensions, leading to a search for magic cubes, is of much more recent origin and is, in many respects, still in its infancy. The three dimensional analogue seems to represent a far more difficult problem and, for many years, not a single example of a magic cube was known. Recently, however, a breakthrough has been made and a new area of number fascination has been opened up for all to enjoy.