The original (3) Rubik's Cube has eight corners and twelve edges. There are

8! (40,320) ways to arrange the corner cubes. Seven can be oriented independently, and the orientation of the eighth depends on the preceding seven, giving $\displaystyle 3^7$ (2,187) possibilities. There are 12!/2 (239,500,800) ways to arrange the edges, since an odd permutation of the corners implies an odd permutation of the edges as well. Eleven edges can be flipped independently, with the flip of the twelfth depending on the preceding ones, giving $\displaystyle 2^{11}$ (2,048) possibilities.

[19] Finally, there are exactly

http://upload.wikimedia.org/math/4/6...5d09bae015.png permutations