From:

Subject:

All the

real mechanical 3x3x3, 4x4x4, 5x5x5 Cubes that I've seen only have

cubies on the outside, but if you can put back all N^3 cubies in the

one I'm describing then you can certainly do the real ones.(In Dan Hoey's notation, I believe that this means I treat the Cube as

the G+C group, where G is generated by the outer slice rotations, and

C is the rotations of the entire thing....

Actually, the distinction between G and G+C is that in the latter we

draw a distinction between cubes that differ by a whole-cube move as

different.

When we take account of the internal cubies I call it the "Theoretical

Invisible cube", described in my Invisible Revenge article 9 August

1982. A solution method is given in

Eidswick, J. A., "Cubelike Puzzles -- What Are They

and How Do You Solve Them?", 'American Mathematical

Monthly', Vol. 93, #3, March 1986, pp. 157-176.

that is pretty much like yours, I think.

As for counting the positions, I haven't got around to checking the

numbers in "Groups of the larger cubes", 24 Jun 1987. You might want

to see how they compare to yours.

Dan Hoey

Hoey@AIC.NRL.Navy.Mil