>>11693211This could probably be done using group theory.
I will try to find the generators and their relations.
Each action string (accounting for equivalencies) should correspond to a distinct rubix cube pattern.
WLOG we let the white side face towards us.
There are six distinct actions:
: rotate the top piece horizontally to the right
: rotate the middle piece horizontally to the right
: rotate the bottom piece horizontally to the right
: rotate the leftmost piece vertically to the right
: rotate the middle piece vertically to the right
: rotate the rightmost piece vertically to the right
Other actions can be done via some combination of these actions
Relations:
I can't think of any other possible relations (but I might be wrong).
This means we don't need to worry about there being multiple routes to reach end point, but this seems wrong to me.
where a,b,c,d,e,f are elements of {1, 2, 3, 4} and elements can be rearranged.
6! ways to arrange the generators * 4^6 ways to have the generators powered.
6! * 4^6 = 2,949,120 arrangements
So it's definitely either that, or something less than that.
