Soma cube

The pieces of a Soma cube
The same puzzle, assembled into a cube

The Soma cube is a solid dissection puzzle invented by Danish polymath Piet Hein in 1933[1] during a lecture on quantum mechanics conducted by Werner Heisenberg.[2]

Seven different pieces made out of unit cubes must be assembled into a 3×3×3 cube. The pieces can also be used to make a variety of other 3D shapes.

The pieces of the Soma cube consist of all possible combinations of at most four unit cubes, joined at their faces, such that at least one inside corner is formed. There are no combinations of one or two cubes that satisfy this condition, but one combination of three cubes and six combinations of four cubes that do. Thus, 3 + (6 × 4) is 27, which is exactly the number of cells in a 3×3×3 cube. Of these seven combinations, two are mirror images of each other (see Chirality).

The Soma cube was popularized by Martin Gardner in the September 1958 Mathematical Games column in Scientific American. The book Winning Ways for your Mathematical Plays also contains a detailed analysis of the Soma cube problem.

There are 240 distinct solutions of the Soma cube puzzle, excluding rotations and reflections: these are easily generated by a simple recursive backtracking search computer program similar to that used for the eight queens puzzle. John Horton Conway and Michael Guy first identified all 240 possible solutions by hand in 1961.[3]

  1. ^ Ole Poul Pedersen (February 2010). Thorleif Bundgaard (ed.). "The birth of SOMA". Retrieved 2010-12-04.
  2. ^ Cf. Martin Gardner (1961).The 2nd Scientific American Book of Mathematical Puzzles & Diversions. New York: Simon & Schuster. Reprinted in 1987 by University of Chicago Press, ISBN 0-226-28253-8, p. 65 (online)
  3. ^ Cite error: The named reference :0 was invoked but never defined (see the help page).