Damien Porter
Member
Another way of looking at it is a fixed center (occures in odd nxnxn cubes) will multiply the solved state by 4^6/2. That is all 6 centers in any rotation then concider parity.
Also multiply the amount of solved states by (4!)^6 for every set of non fixed centers. That is all posible permutations of same coloured centers on every face. In an even nxnxn cube there are (n-2)^2/4 sets of non fixed edges. In an odd nxnxn cube there are ((n-2)^2-1)/4 non fixed centers.
Edges and corners are always in the correct position.
This creates the formulas
n even
((4!)^6)^((n-2)^2/4)
n odd
4^6/2 × ((4!)^6)^(((n-2)^2-1)/4)
Also multiply the amount of solved states by (4!)^6 for every set of non fixed centers. That is all posible permutations of same coloured centers on every face. In an even nxnxn cube there are (n-2)^2/4 sets of non fixed edges. In an odd nxnxn cube there are ((n-2)^2-1)/4 non fixed centers.
Edges and corners are always in the correct position.
This creates the formulas
n even
((4!)^6)^((n-2)^2/4)
n odd
4^6/2 × ((4!)^6)^(((n-2)^2-1)/4)