Puzzling out the Soma cube
The mathematical writing in Example 3 also uses diagrams but for a very different purpose. It arises from a particular three-dimensional puzzle, sometimes called a Soma cube, pictured below.
There are seven wooden pieces, which can be assembled to form a solid cube. The manufacturer of the puzzle claimed that there are over 16,000 ways of assembling the cube. The writer of Example 3 had found, by trial and error, several different solutions but was beginning to doubt the claim that there were as many as 16,000. The example shows the notes that he made as ideas crossed his mind about how to make sense of the manufacturer's claim.
There were two particular problems faced by the writer. First, what precisely is meant by a ‘solution’: what makes one solution different from another? Second, what is the best way of recording a particular solution: what notation is best to use?