ABSTRACT
Twelve different shapes can be formed by combining not more than four cubes, all the same size and joined at their faces. The seven of these shapes, one 3-cube and six 4-cubes, left after eliminating all straight shapes constitute the SOMA puzzle invented by Piet Hein. The challenge of the puzzle is to use the seven pieces to construct any one of a profusion of specified forms. This chapter deals with the application of parity and centemess to the assembling of the seven SOMA pieces into a 3 × 3 × 3 shape, the SOMA cube. The cubes composing each SOMA piece or combination of pieces can be colored alternately black and white so that no two faces in contact have the same color. The parity of the piece or combination of pieces is defined as the number of black cubes minus the number of white cubes.
