[iliis]

That might very well be, but is it obviously so? What if there was a position that takes 19 moves to solve in the fastest way possible but the next-best solution takes 21 moves? Is there always a solution that takes an even number of steps?

[Someone]

Yes, there is. If the last turn is a quarter turn, replace it by a half turn and a quarter turn in the other direction. If it is a half turn, replace it by two quarter turns.

[iliis]

Well, okay. Technically you're right ;) But what if you count any movements that are followed by another movement of the same face as a single step?