# Rubik's Cube Cracked Down to 26 Moves

August 9, 2007 12:34 AM Subscribe

Rubik's Cube Cracked Down to 26 Moves

*"They think they can use their brute-force search method [PDF] on all of the configurations that require 26 steps to find a quicker way to solve them. Even if they manage this feat, however, it will probably leave room for improvement. Most researchers believe that just 20 steps are enough to solve any Rubik's Cube, but no one has proved it yet."*[Previously. See recent post on checkers.]I was always partial to prying off the pieces and reassembling them.

posted by trondant at 12:51 AM on August 9, 2007

posted by trondant at 12:51 AM on August 9, 2007

How To Solve Rubik's Cube

How To Solve a Virtual 20x20x20 Rubik's Cube

Michael Gondry solves it with his nose.

posted by ZachsMind at 1:38 AM on August 9, 2007 [4 favorites]

How To Solve a Virtual 20x20x20 Rubik's Cube

Michael Gondry solves it with his nose.

posted by ZachsMind at 1:38 AM on August 9, 2007 [4 favorites]

**McLir**:

*"that 20x20x20 is freakin' amazing!"*

*geeking out*

I KNOW! Wasn't that the coolest craziest thing you seen in the past well at least the past ninety minutes or so?? At first I was like "God this is gonna be boring I should turn it off" but it became kinda mesmerizing, and then you start seeing the blue side getting filled in, then the orange... It was both freaky and amazing. =)

I'd hate to know what it looks like in reality though. I mean you can make one of those in the computer space, but I don't think from an engineering standpoint it's physically possible to make a fully functional 20x20x20 Rubik's Cube. Still though. Pretty effin' kewl.

posted by ZachsMind at 2:46 AM on August 9, 2007

I wonder if there are purist mathematicians out there who get all bitter every time a computer aided proof by exhaustion solves another problem like this.

posted by BrotherCaine at 3:18 AM on August 9, 2007

posted by BrotherCaine at 3:18 AM on August 9, 2007

ZachsMind, they've made 4x4 Rubik's Cubes ("Rubik's Revenge"), which don't have the unmovable center pieces that the 3x3 model has, so I suspect that it's possible to make a 20x20 as well.

Not that I could do such a thing, not by a long shot.

posted by JHarris at 3:52 AM on August 9, 2007

Not that I could do such a thing, not by a long shot.

posted by JHarris at 3:52 AM on August 9, 2007

My favorite size of cube to crack is 1x1. And I can crack it with very few moves.

Oh, and about the purist mathematicians: If those proofs are 'by exhaustion,' then the mathematician will consider those proofs to lack elegance. I'll bet that some of the things proved by exhaustion now will later be proved in an elegant manner. Let's just see an AI do elegance!

posted by philomathoholic at 4:22 AM on August 9, 2007 [1 favorite]

Oh, and about the purist mathematicians: If those proofs are 'by exhaustion,' then the mathematician will consider those proofs to lack elegance. I'll bet that some of the things proved by exhaustion now will later be proved in an elegant manner. Let's just see an AI do elegance!

posted by philomathoholic at 4:22 AM on August 9, 2007 [1 favorite]

Okay, granted I havn't so much as throught about the rubiks cube in almost 20 years but it never occured to be there might be /algorithms/ to solving it. It's like i need to hand in my geek badge. :) Thanks ZachsMind, it was.. an epiphany.

Oh... also I just lost the game.

posted by adamt at 4:56 AM on August 9, 2007

Oh... also I just lost the game.

posted by adamt at 4:56 AM on August 9, 2007

The Professor's Cube is for sale, and according to Wiki, a 6x6x6 and a 7x7x7 have been built, so I assume (in principle) that a 20x20x20 could be built. Each level of complexity makes the cube more fragile, so I would bet you couldn't turn a face without it falling apart. I can pop my 4x4x4 if I'm not careful.

I can't imagine how you could build a 20x20x20, but I couldn't have imagined how to construct a 3x3x3 before I saw it.

posted by MtDewd at 5:00 AM on August 9, 2007

I can't imagine how you could build a 20x20x20, but I couldn't have imagined how to construct a 3x3x3 before I saw it.

posted by MtDewd at 5:00 AM on August 9, 2007

*I wonder if there are purist mathematicians out there who get all bitter every time a computer aided proof by exhaustion solves another problem like this.*

The problem isn't the proof; the problem is the problem. To a mathematician, the question "what is the minimum number of moves necessary to solve a 3x3x3 cube?" is much less interesting (because it is a finite computation) than the question "what is the minimum number of moves necessary to solve an n x n x n cube?" The latter problem

*cannot*be solved by exhaustive search.

I wouldn't say we are bitter, though! Just unsatisfied.

posted by escabeche at 5:28 AM on August 9, 2007 [2 favorites]

*what is the minimum number of moves necessary to solve an n x n x n cube?*

I have discovered a truly remarkable proof which this universe is too small to contain.

posted by eriko at 6:16 AM on August 9, 2007 [2 favorites]

I haven't sat down and worked out all the polarities, but it may be possible to put together a 20x20x20 using the magnetic method.

posted by Partial Law at 6:29 AM on August 9, 2007

posted by Partial Law at 6:29 AM on August 9, 2007

Man, if I were a sadistic despot, I'd give each of my prisoners a 20x20x20 Rubik's cube and tell them they were free to go as soon as they solved it.

posted by Faint of Butt at 7:30 AM on August 9, 2007 [1 favorite]

posted by Faint of Butt at 7:30 AM on August 9, 2007 [1 favorite]

Crap, this is one of those things you have to 'understand math' to appreciate, huh?

The 20x20x20 vid is pretty though.

posted by quin at 10:27 AM on August 9, 2007

The 20x20x20 vid is pretty though.

posted by quin at 10:27 AM on August 9, 2007

Four-dimensional Rubik's cube.

Five-dimensional Rubik's cube.

posted by Wet Spot at 1:57 PM on August 9, 2007

Five-dimensional Rubik's cube.

posted by Wet Spot at 1:57 PM on August 9, 2007

Thinking about hypercubes makes my head hurt, but it's cool at the same time. The 4D and 5D (!) Rubik's cubes give me the same feeling, but exponentially (ironically) more so.

posted by Joakim Ziegler at 5:06 PM on August 9, 2007

posted by Joakim Ziegler at 5:06 PM on August 9, 2007

AdamT:

There is a way to win the game. You don't have to play it the rest of your life. You choose to play, and when you choose to play, you choose to lose.

posted by ZachsMind at 5:54 PM on August 9, 2007

*"Oh... also I just lost the game."*There is a way to win the game. You don't have to play it the rest of your life. You choose to play, and when you choose to play, you choose to lose.

posted by ZachsMind at 5:54 PM on August 9, 2007

**JHarris**:

*"ZachsMind ...I suspect that it's possible to make a 20x20... Not that I could do such a thing, not by a long shot."*

As for the impossibility of a 20x20x20 Rubik's, not to be a picky knit, but I specifically stated "fully functional." I'm sure it's possible to make one that'd fall apart if ya breathe on it, but A 20x20x20 Rubik's cube that one cannot easily manipulate in one's hands without it falling apart is not fully functional.

From an engineering standpoint, the only possible way to make one is virtual. Even if you could keep it from falling apart, you can't make a cube you can wield in your hands that's 20x20x20. In centimeters, that's almost eight inches. The word "cumbersome" doesn't even begin to describe it.

posted by ZachsMind at 6:57 PM on August 9, 2007

*My favorite size of cube to crack is 1x1. And I can crack it with very few moves.*

How many moves exactly? That is, a die is sitting on a table in a random position. How many moves, max, to bring it into a defined position (e.g. 1 on top, 2 facing towards you)

What about a 2x2 cube?

posted by vacapinta at 11:04 PM on August 9, 2007

*How many moves exactly? That is, a die is sitting on a table in a random position.*

Ah, I'm sorry that I didn't state it more clearly. I was thinking of a "rubik's cube" that had exactly one color per side. This cube would not have any moving parts, and it would not require any moves to put it into the "solved" state. Indeed, it would be impossible

*not*to solve it. It is truly the lazy person's preferred size.

posted by philomathoholic at 2:34 PM on August 14, 2007

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posted by amyms at 12:44 AM on August 9, 2007 [1 favorite]