The Soma Cube
All the irregular shapes (shapes that have a concave corner) that can be
formed with four or less unit cubes are the ones pictured below:
It is a surprising fact, discovered by Piet Hien, that these shapes can be arranged
to form a cube with side length 3. Additionally, the cube can be formed in
240 different ways. This puzzle is called the Soma Cube. The easiest way to make your
own set is to purchase
27 wooden unit cubes (they are inexpensive and available at most craft stores) and
glue them into the configurations pictured above.
Puzzle enthusiasts have also created a number of arrangement puzzles of their own (slightly
more imaginative than a cube), using the soma cube pieces. How many of the following can you assemble?