Move sequence to hit every cube state?

[nickvu2]

I'm curious if there is a sequence of 3x3 turns that, if repeated, would land on every state in cube space? Give the some 43 quadrillion states, there's no chance of brute forcing a solution. Surely mathematics would get you there, but I don't even know where to start, lol! Anyone want to take a stab at it, or at least offer some direction?

 

[Lucas Garron]

I can trivially define a sequence that reaches every cube state. I can even define it so that I can give you turn #N for any N you ask. It's not very exciting.

Now, a 43,252,003,274,489,856,000-turn Devil's alg would be exciting, but I don' think there's been an good work on that.

 

[Erdos]

^Not exactly sure if that's even possible (too lazy to prove or disprove), but it was, then it certainly wouldn't be a unique moveset (mirror, inverse, rotation, etc.). Just sayin'.

 

[Erzz]

I wonder what the shortest turn sequence is that reaches every cube state if repeated. Or which has the least repetitions/total moves.

 

[qqwref]

There is almost certainly an optimal sequence (number of moves = number of states minus one) that does this, but finding and writing out one of them is a truly monumental task.

 

[tx789]

Only for the cases without a flipped edge or twisted corner and two piece swaps

 

[luke1984]

There is almost certainly an optimal sequence (number of moves = number of states minus one) that does this, but finding and writing out one of them is a truly monumental task.

And, executing it would take hundreds of millions of years, even at reasonable tps.