Soma Cube

A solid Dissection puzzle invented by Piet Hein during a lecture on Quantum Mechanics by Werner Heisenberg. There are seven soma pieces composed of all the irregular face-joined cubes (Polycubes) with $\leq 4$ cubes. The object is to assemble the pieces into a Cube. There are 240 essentially distinct ways of doing so (Beeler et al. 1972, Berlekamp et al. 1982), as first enumerated one rainy afternoon in 1961 by J. H. Conway and Mike Guy.

A commercial version of the cube colors the pieces black, green, orange, white, red, and blue. When the 48 symmetries of the cube, three ways of assembling the black piece, and $2^5$ ways of assembling the green, orange, white, red, and blue pieces are counted, the total number of solutions rises to 1,105,920.

See also Cube Dissection, Polycube

References

Albers, D. J. and Alexanderson, G. L. (Eds.). Mathematical People: Profiles and Interviews. Boston, MA: Birkhäuser, p. 43, 1985.

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 112-113, 1987.

Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Item 112, Feb. 1972.

Berlekamp, E. R.; Conway, J. H.; and Guy, R. K. Ch. 24 in Winning Ways, For Your Mathematical Plays, Vol. 2: Games in Particular. London: Academic Press, 1982.

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 203-205, 1989.

Gardner, M. Ch. 6 in The Second Scientific American Book of Mathematical Puzzles & Diversions: A New Selection. New York: Simon and Schuster, pp. 65-77, 1961.

Steinhaus, H. Mathematical Snapshots, 3rd American ed. New York: Oxford University Press, pp. 168-169, 1983.