"Problems worthy of attack prove their worth by hitting back."
The Soma puzzle was a game marketed by Parker Brothers, Co. around 1970 that was based, in turn, upon an idea attributed to the mathematician Piet Hein. Its basis is the theorem that a solid cube composed of a volume of 27 smaller cubes can be decomposed into a group of 7 dissimilar pieces each composed of 4 (in one case, 3) cubes, each of which is a unique configuration of such cubes.
Reputedly, there exist over a million possible combinations of these pieces which result in the formation of the larger cube. However, the true merit of the puzzle consists of its capacity to model a large number of shapes beyond that of the simple cube. The trick is, then, given some shape formed from 27 cubes, how does one build it from the pieces at hand?
Try your luck with the applet below. A simple mouse drag will move a piece laterally. Hold down the SHIFT key and vertical movement will occur. To rotate a piece, pick the face of the cube through which you want the axis of rotation to penetrate. Hold down the CTRL key and click and the piece will rotate clockwise around the axis. Hold down both the CTRL and SHIFT keys and click and the piece will rotate counter-clockwise. (If it doesn't move, something's in the way.)