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More interestingly, the cube is always 20 moves away from a solution, not matter how much you've mixed it up.
by aidos 8y ago
More interestingly, the cube is always 20 moves away from a solution, not matter how much you've mixed it up.
- rimliu 8y agoNitpick: cube is at most 20 moves away from the solution. There may be cases when less moves a needed :) https://en.wikipedia.org/wiki/God%27s_algorithm https://en.wikipedia.org/wiki/God%27s_algorithm
- aidos 8y agoThat's definitely a legitimate nitpick!
- Someone 8y agoNitpick: aidos is right. The cube is always 20 moves away from a solution (but that solution typically isn’t the fastest possible (the 20 is in face turns, not quarter turns, so you can always add extra turns to the optimal solution to make the solution take 20 turns))
- iliis 8y agoThat 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 8y agoYes, 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 8y agoWell, 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?
- Someone 8y agoThe set of possible configurations would split in an even and an odd set, so there would be configurations that can’t be solved in God’s number of moves. (AFAIK, we don’t know God’s number if we count moves that way. I would guess it’s larger than 20)