A puzzle of the class of spatial puzzles.

The soma cube is a cube, 3x3x3 units. It is subdivided into several unique pieces, each constructed of multiple 1x1x1 units attached.

The puzzle is to get all those pieces to fit together back into the body of 3x3x3.

Many people go on to use the cube pieces as a sculpture, trying to form minimalist shapes, instead of forming the basic cube. Hundreds or thousands of patterns are named after the animals and things they vaguely resemble.

The tangrams and pentominoes puzzles are somewhat related.

To construct a Soma cube puzzle, begin with 27 small cubes. Using no more than four cubes at a time, construct every non-convex shape that you can by gluing cubes face-to-face. This will use up all 27 cubes, and the shapes produced will look like the diagram below. (A "1" is a single cube, while a "2" represents two cubes stacked on top of each other.)
              1   1     1    11  1    1  1
              11  111  111  11   12  21  21
This is the original Soma puzzle invented in 1936 by Danish author Piet Hein. The puzzle was named after the addictive drug Soma which appears in Aldous Huxley's novel Brave New World. Hein came up with the idea for the puzzle while sitting in a physics lecture given by Heisenberg, and by doodling on paper quickly found that these seven pieces can be used to construct a 3x3x3 cube. In 1962 Conway and Guy established that there are 240 distinct ways in which this cube may be assembled; here is one solution:

Begin with this piece:

1
1
11
and hook this piece over the short arm of the L:
 11
11
so that this configuration is reached:
11
12
12
As above, a "2" in the diagram shows that the figure is two cubes deep at that point. The rest of the solution is shown below; it should be easy to find which piece to add to reach each step in the construction:
11       221       221       221       321       333
12  -->  112  -->  212  -->  212  -->  332  -->  333
12        12       312       333       333       333
An interesting feature of the above solution is that in this configuration the finished cube may be balanced on a support which only touches the middle square of its base.

Various visually pleasing figures can be constructed from a set of Soma cubes, and these are often given as puzzles (the question being how to construct them from the seven original pieces). For example, here is one which, for obvious reasons, is sometimes called "the pyramid":

 111
11211
12321
11211
 111
Other variations on the puzzle include assembling larger figures from two sets of Soma cubes, and constructing a double-size version of the piece containing three cubes (the small "L") using the remaining six pieces.

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