I've always been fascinated by Rubik's cube. I have developed solutions for it and all the related cubes 2x2, 3x3, 4x4, 5x5. For me the cube it is to group theory (of a partcular type of group) what a slide rule is to real arithmetic. Even "laboratory" might not be too stong a label for it. For example it's immediately obvious how [tex] xy \neq yx [/tex]. If you turn the front of the cube and then the right you get a very different set of faces than the right followed by front. Also, you can discover marvelous "operators" (my terminology) by doing some random series of twists (abc) followed by a particular twist (Z) then undoing the first twists (via cba), that is: abcZcba where the letters stand for some particular oriented twist. What happens is that most of the cube is unperturbed except for some marvelous little permutation like a twisted corner in place or three swapped edges. My solutions then consist of applying these "operators" in sequence by inspection to see which one is "needed" next. Alas however, I am not formally trained in group theory and I would like to know: How would one go about using GT to develop a more effective or efficient solution to something like Rubik's cube? I know it has been done, but my question is very specifically: Can anyone explain to the group theory novice (but Rubik's cube expert) how one would actually go about using GT to devise (more) efficient solutions to such a puzzle?