I thought that I should explain the purpose of me posting Mathematica solutions to the New Scientist Enigma problems.
The main purpose is to show how one can quickly get a solution to each problem (usually by brute force attack) using the unique processing abilities of Mathematica. Each posting shows the first line of reasoning that led me to the solution, so my reasoning is usually not elegant and is not intended to be elegant; the goal is to find the correct solution and to do it quickly. Sometimes this means that I deliberately use an unusual sequence of manipulations in order to illustrate a particular style of programming. Occasionally this means that I use a peculiar Mathematica idiom that I just happen to know.
Actually, I do worry about the elegance of solutions, but optimising the elegance of a solution is completely different from simply finding the correct solution to a problem. In the case of the New Scientist Enigma problems I strongly suspect that most of them are constructed in a brute force way (i.e. start with a large set of potential solutions, then impose various perverse constraints, until there is only one member of the set remaining), so there is no guarantee that there are slick and elegant solutions to them.