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Rubik's Cube Algorithm Cut Again, Down to 23 Moves
Bryan writes "The number of moves necessary to solve an arbitrary Rubik's cube configuration has been cut down to 23 moves, according to an update on Tomas Rokicki's homepage (and here). As reported in March, Rokicki developed a very efficient strategy for studying cube solvability, which he used it to show that 25 moves are sufficient to solve any (solvable) Rubik's cube. Since then, he's upgraded from 8GB of memory and a Q6600 CPU, to the supercomputers at Sony Pictures Imageworks (his latest result was produced during idle-time between productions). Combined with some of Rokicki's earlier work, this new result implies that for any arbitrary cube configuration, a solution exists in either 21, 22, or 23 moves. This is in agreement with informal group-theoretic arguments (see Hofstadter 1996, ch. 14) suggesting that the necessary and sufficient number of moves should be in the low 20s. From the producers of Spiderman 3 and Surf's Up, we bring you: 2 steps closer to God's Algorithm!"
Call me when it's down to 10 moves! :)
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And here I used to think my method was faster; but since there's more than 23 stickers on the cube I guess it ain't any more...
in 48 moves or less. Luckily the center sticker is always in the right place so I don't need to move that one.
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"Combined with with some of Rokicki's earlier work, this new result implies that for any arbitrary cube configuration, a solution exists in either 21, 22, or and 23 moves"
Or 1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 or 10 or 11 or 12 or 13 or 14 or 15 or 16 or 17 or 18 or 19 or and 20 moves.
Mathematically, the limit is a hard 18 (by faces): 6^2 / 2. alternatively by squares per face: ((9 * 6) / 3) ^ 2 / (2^2)
The math isn't hard. It's finding those correct 18 moves that is.
The summary says for every solvable cube. What does that mean. Every configuration is a solvable one. If you remove a corner and rotate it, and place it back in the cube, the cube is no longer solvable, but I would argue that it's no longer a rubik's cube either.
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1. Pour paint on Cube
2. Let Dry
3. PROPHET
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There, saved you from another 22 pointless moves.
I actually found one of the solutions (obviously not uniquely) for the Rubiks Cube myself. It ended up to be the "corners first"-type of solution which I think is quite a natural way to reach a solution (it's basically a divide and conquer algorithm). If you can put the corners in their right place you only need to use a 8 move permutation to solve the rest which I call "the cross"-pieces.
So I'm curious if anyone else has experienced this as being the obvious but not perfect solution?
Perhaps slightly off-topic, but the Hofstadter cited (via Metamagical Themas) is the same Douglas Scott Hofstader that wrote Goedel, Escher, Bach -- one of the greatest books ever written.
Call me when it's down to 10 moves!
Step 1: Drop cube in can of paint. Done.
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This result required the use of *many* computers to solve *many* positions (approximately four million billion positions), and each found solution was 20 moves or less.
Yes, in some terms it was brute force, but consider how big a number four million billion is, and how long it takes to solve just a single position in 20 moves or less.
And here I used to think my method was faster; but since there's more than 23 stickers on the cube I guess it ain't any more...
So that would be, um, each face is three by three, um, nine stickers on each face. Then multiply that times the number of sides, so six times nine would be, uh, ...
Forty two.
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When the limit was proved to be no worse than 25, there were lots of comments on Slashdot that misunderstood various aspects of what this means.
Here are clarifications for some common points of confusion:
1. What Tom has shown, that "an arbitrary cube can be solved in 23 moves", it means the nastiest legal cube needs no more than 23 face turns to solve. Obviously many starting configurations can be done in less.
2. This type of research doesn't tell you WHICH 23 moves. Only that it's 100% certain that there exists a 23-moves-or-shorter solution, for any legal cube.
3. It's easy to figure out the total number of permutations of the cube. Given that, it can be determined that 17 face-turns doesn't produce enough different permutations, but 18 does, so there is a definite lower bound of 18 moves, that is, there exists at least some configurations that MUST be 18 moves or more away from solved.
4. Specific configurations have been found that provably need 20 face turns to solve. So the worst-case will never get better than that.
5. It may be possible to narrow the limit further, showing that all cubes can be solved in 22 face turns or less. Maybe 21. Maybe 20. It will never get lower than that.
Put succinctly, as of today, the worst-case number of face-turns to solve a cube is no worse than 23. It's been known for a while that the worst case is no better than 20.
As a kid my best time was 1 min ! Used to just take off all the stickers on all faces and put them back in correct order. Friends were confused though as to why i want to solve it alone in a room and not in front of them.