Plus figuring out how to implement the various ways of checking validity was a lot of fun.
Secondly, I don’t see why would want to pick a ‘random’ position that way. If those numbers were correct, it would mean a 1:21 probability that your ‘random’ position was zero moves from the solution.
Edit: I think you simply didn't understand what I was talking about. The distribution of states is not even. If you randomly perform moves on a cube then you're more likely to end up in certain states.
As to the distribution of states, I am not sure what you mean. Insufficient shuffling can introduce bias, but that gets reduced as you continue shuffling. You can trivially shuffle past the point where remaining bias is not detectable. Unless, you want a specific bias, then that’s more easily achieved generating a random number with a specific format.