Have you ever seen someone solving the Rubik’s cube within a minute? I did and I was amazed! Afterwards I walked through Lissabon staring at the cube and desperately trying to figure out how to solve it. By now I finally learned how to proceed. You can find an intuitive approach on Lars Petrus’ website. As with many complicated toys a lot of math is involved. In this case a lot of group theory and combinatorics. But actually I am no big fan of sober complicated math. Nevertheless I was eager to tinker with the cube and began by writing a program which had an explicit representation of the cubes’ face colors and operations to arbitrarily rotate the sides. The explicit representation is good if you want to modify the cube. However often it is just necessary to identify a particular cube state. Imagine you want to enumerate all cube states starting from the solution then you can use for example a breadth-first search. As with general graphs you need to remember states which you already encountered. For that purpose you should use a more compact representation of the cube. Suppose there are 
Rubik’s cube states in total, then the minimum number of bits to represent a state is clearly 
. You achieve that goal if you are able to assign a unique number 
to each different possible cube state. This number is also called rank and the conversion from the explicit representation to the rank is referred to as ranking. The reverse is of course unranking.
