Soma Cube - Trivia

Trivia

Similar to Soma cube is the 3D pentomino puzzle, which can fill boxes of 2×3×10, 2×5×6 and 3×4×5 units.

Piet Hein authorized a finely crafted rosewood version of the Soma cube manufactured by Theodor Skjøde Knudsen's company Skjøde Skjern (of Denmark). Beginning in about 1967, it was marketed in the U.S. for several years by the game manufacturer Parker Brothers. Plastic Soma cube sets were also commercially produced by Parker Brothers in two colors (blue and red) during the 1970s.

Solving the soma cube has been used by as a task to measure individuals' performance and effort in a series of psychology experiments. In these experiments, test subjects are asked to solve a soma cube as many times as possible within a set period of time. For example, Edward Deci asked his research subjects to solve a soma cube under conditions with varying incentives in his dissertation work on intrinsic and extrinsic motivation establishing the social psychological theory of crowding out.

In each of the 240 solutions to the cube puzzle, there is only one place that the "T" piece can be placed. Each solved cube can be rotated such that the "T" piece is on the bottom with its long edge along the front and the "tongue" of the "T" in the bottom center cube (this is the normalized position of the large cube). This can be proven as follows: If you consider all the possible ways that the "T" piece can be placed in the large cube (without regard to any of the other pieces), it will be seen that it will always fill either two corners of the large cube or zero corners. There is no way to orient the "T" piece such that it fills only one corner of the large cube. The "L" piece can be oriented such that it fills two corners, or one corner, or zero corners. Each of the other five pieces have no orientation that fills two corners; they can fill either one corner or zero corners. Therefore, if you exclude the "T" piece, the maximum number of corners that can be filled by the remaining six pieces is seven (one corner each for five pieces, plus two corners for the "L" piece). A cube has eight corners. But the "T" piece cannot be oriented to fill just that one remaining corner; orienting it such that it fills zero corners will obviously not make a cube, and orienting it such that it fills two corners will not make a cube. Therefore, the "T" must always fill two corners, and there is only one orientation (discounting rotations) in which it does that. It also follows from this that in all solutions, five of the remaining six pieces will fill their maximum number of corners and one piece will fill one less than its maximum (this is called the deficient piece).