Background
Rummaging through the stuff of your childhood you find an old toy which you identify as the famous Rubik's Cube. While playing around with it you have to acknowledge that throughout the years your ability to solve the puzzle has not improved a bit. But because you always wanted to understand the thing and the only other thing you could do right now is to prepare for an exam, you decide to give it a try. Luckily the brother of your girlfriend is an expert and able to fix the cube no matter how messed-up it is. The problem is that he stays with his girlfriend in the Netherlands most of the time, so you need a solution for long-distance learning. You decide to implement a program which is able to document the state of the cube and the turns to be made.
Problem
A Rubik's Cube is covered with 54 square areas called facelets, 9 facelets on each of its six sides. Each facelet has a certain color. Usually when the cube is in its starting state, all facelets belonging to one side have the same color. For the original cube these are red, yellow, green, blue, white and orange.
The positions of the facelets can be changed by turning the sides of the cube. This moves nine "little cubes" together with their attached facelets into a new position (see Fig. 1).
The problem is to determine how the facelets of the entire cube are colored after turning different sides in different directions.