Are there any Rubik's cubers who can solve a cube to an arbitrary position?

Question

By "solve to an arbitrary position" I mean something like I give you two scrambled cubes and you make one cube match the other.

This question and its answers confirms that it's possible, but are there any well-known human cubers who can do this repeatedly or quickly?

Note: based on feedback in the comments, I've edited the question to clarify that I'm asking about humans who can solve cubes this way

Answer 1

My comment wanted to be turned into an answer, so here it is.

First, as a cuber myself, I think it is quite possible to change a cube state from scrambled (lets call this 1) to another scrambled state (lets call this 2). All it takes is for the solver to get used to 1, (the state where you start the transformation into 2), and imagine 1 to be solved.

As found from this youtube video, it is clear that it is possible to go from a solved position into a scrambled position. There is no cuber that I can find that has attempted the challenge, but I have done so myself just then I completed the challenge.

Answer 2

Not the most efficient method but works well: solve cube 1 as usual. Solve cube 2 as usual remembering (or write down) the moves. Apply reversed moves on cube 1.

Answer 3

I used to do this sometimes, just for fun. I would mix up 1 cube and then try to match it. It doesn't matter if the second cube is starting from solved or some other random position, it's equally as difficult. I don't know if I ever timed myself, but I would estimate it took me about 10-15 minutes to solve to a random position. For reference, I was never that great of a cuber to begin with, with my average time to solve a mixed up cube being about 75 seconds.

Answer 4

It's actually very easy to do this if you use this method of solving the cube, and it can be done reasonably fast (say a few minutes) after some practice. Fundamentally, once you understand commutators it is equally easy to get to the solved state as it is to get to any other reachable state. The only difference is that in getting to a solved state you already know what are the desired pieces and orientations, whereas in getting to a given reachable state you have to keep referring to the desired state unless you have really good memory and visualization skills.

Answer 5

As a new but sort-of-successful blindfolded solver (my fastest time is 8 minutes), I think that for Blindfolded solvers, if they are starting with a solved cube, this would actually only be slightly more difficult than a normal blindfolded solve. Blindfolded solvers reduce a cube state to a sequence of somewhere around 20 letters in order to memorize what to do and in what order. It would be only one more step to then reverse that letter sequence and apply it to a solved cube.

But in your case, you're talking about going from a scrambled cube to another scrambled state. So, for a top blindfolded cuber like Tommy Cherry, it would probably be fastest to solve it the ordinary way first. Here's how I think Tommy could do it:

1. During inspection, inspect the target cube first, and memorize the letters then reverse them. Since he would need to remember it a little longer than usual, this would take longer than average. Tommy tends to finish memo in 6-10 seconds, from what I've seen, so let's add 2 seconds to reverse the letters in his mind, and another 2 seconds (25%) to commit them to memory more strongly than usual. This adds up to 10-14 seconds, which fits inside the 15 second inspection time a cuber gets before starting the timer.
2. Next, he would quickly inspect the scrambled cube, then start the timer and solve the cube to a solved state (as in normal competition). The inspection would have to be done in only 1 or 2 seconds for someone as fast at memorization as Tommy (you get 15 seconds of inspection time and I just estimated it would take him 12 to memorize the target cube), so it would probably cost him 3 or 4 seconds off his normal solve time of around 7.5 seconds. So, let's say he solves it in 11 seconds (probably not hard for him even with no inspection time).
3. Last, he'd use the blindfolded method to solve the cube into the target scramble using the memorized sequence from step 1. From what I've seen, Tommy tends to spend about half his time memorizing and half his time solving. Since this part would be exactly like a normal blindfolded solve, he would probably get his usual time for this part, which, based on his recent averages of 16-17 seconds, should be 8.5 more seconds.

So, with an hour or so of practice to get used to the strange order of things, I think Tommy Cherry should be able to solve a cube from one scrambled state to another specific one in less than 20 seconds.

One thing that makes me believe this would be the fastest method is that it takes away the hardest part: the part where you have to put pieces where they don't go. It just messes with your head, like solving on the blue cross for the first time when you've only ever solved on white. Without TONS of practice, one would have to be going back and forth between the two cubes to be constantly comparing them. Memorizing the target cube would be almost required. Then, steps like F2L, OLL and PLL would be so mind-bending as to be almost useless. So, it just makes sense to use the blindfolded methods.

Here's my disclaimer: The biggest assumption I'm making here is that it's simple to reverse the letters and then solve it that way. I know it would work for the Old Pochmann method which I use, but I'm not 100% sure it would carry over to the three-style method Tommy uses, though I think it will. If not, he'd have to use Old Pochmann, which would probably triple or quadruple his step 3 time.

He's going to be at a competition that I'm going to soon... maybe I'll be able to ask him.