Rubik's Cube Proof Cut To 25 Moves 386
KentuckyFC writes "A scrambled Rubik's cube can be solved in just 25 moves, regardless of the starting configuration. Tomas Rokicki, a Stanfordtrained mathematician, has proven the new limit (down from 26 which was proved last year) using a neat piece of computer science. Rather than study individual moves, he's used the symmetry of the cube to study its transformations in sets. This allows him to separate the 'cube space' into 2 billion sets each containing 20 billion elements. He then shows that a large number of these sets are essentially equivalent to other sets and so can be ignored. Even then, to crunch through the remaining sets, he needed a workstation with 8GB of memory and around 1500 hours of time on a Q6600 CPU running at 1.6GHz. Next up, 24 moves."
Which 25 moves? (Score:5, Funny)
Re:Which 25 moves? (Score:5, Funny)
Left, right, right, down, down, left, up, right, up, up, left, down, down, right, up, down, left, right, up, left, down, down, right, up, left.
Just a guess ;)
Wow, it really works (Score:5, Funny)
Re:Wow, it really works (Score:5, Funny)
Re:Wow, it really works (Score:4, Insightful)
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Amateurs! (Score:3, Funny)
Re:Wow, it really works (Score:5, Insightful)
Re:Wow, it really works (Score:5, Interesting)
There are at least two subtypes of interesting:
 Interesting to someone with joint degrees in math and computer science
 Interesting to someone who has smoked two joints
Any thread involving Rubik's cube is going to pull both, sorry.
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Re:Wow, it really works (Score:5, Funny)
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No intuition. My numbers are based on a program I wrote a decade ago that generated all possible solutions. It generated static html pages such that you chose to go first or second, and you'd click on the square, and it would load the appropriate next page. 2000 pages to cover every pos
Re:Which 25 moves? (Score:5, Funny)
The old 26 move algorithm was the same except 'select' then 'start'
Re:Which 25 moves? (Score:5, Funny)
Those sound familiar, but I can't be sure  don't have anyone's thighs wrapped around my head at the moment...
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Re:Which 25 moves? (Score:4, Funny)
Re:Which 25 moves? (Score:4, Funny)
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Re:Which 25 moves? (Score:5, Funny)
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http://en.wikipedia.org/wiki/Konami_Code [wikipedia.org]
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Re:Which 25 moves? (Score:5, Insightful)
In other words, they are left as an exercise to the reader.
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Re:Which 25 moves? (Score:5, Funny)
No, what he proved is the upper limit (Score:4, Informative)
An optimal solution would probably look like a bell curve going from "zero moves required" (ie. already solved) all the way up to "25 moves required" (which we now know is the upper limit...)
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as someone (Dik Winter) has already written a program that does just that.
Source: http://mathworld.wolfram.com/RubiksCube.html [wolfram.com]
Re:Which 25 moves? (Score:5, Informative)
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Re:Which 25 moves? (Score:5, Funny)
Re:Which 25 moves? (Score:5, Funny)
"may be nonintuitive" (Score:3, Interesting)
I actually solved the cube all by myself back in the 80's. I'm amazed that so much effort is still being put into it and some of the methods used by the record breakers need an awful lot of dedication to learn.
Re:Which 25 moves? (Score:5, Insightful)
Yup  that's a bizarre thing to say. Surely after the first move in solving a configuration that can be optimally solved in 22 moves you obtain a configuration that can be optimally solved in 21 moves, by definition?
You only need one (Score:4, Funny)
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*./ no ecnerefer kreT ratS rehtona s'ti
Re:You only need one (Score:5, Interesting)
Fun trick: Take a solved cube, and on one of the inner edge pieces (the ones with two stickers), and swap the colors. Mix it up, and give it to someone to solve. Or take a corner piece and rotate it.
Hint: It's unsolvable. The Rubik's Cube, if taken apart and put back together randomly, will more often than not end up being unsolvable.
A great way to frustrate that showoff cuber at the office. Especially if they appreciate it when someone scrambles the cube and they'll have it solved in front of everyone. Just go and put it back together randomly, or do one of those devious swaps, and you'll have fun watching him try to solve it.
Re:You only need one (Score:4, Insightful)
Re:You only need one (Score:5, Funny)
Re:You only need one (Score:4, Funny)
Re:You only need one (Score:5, Funny)
The answer is that it takes three licks to get to the center of a standard Rubik's cube.
1.6ghz? (Score:4, Insightful)
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Then again, it could just be an error in the article.
Re:1.6ghz? (Score:4, Informative)
Re:1.6ghz? (Score:5, Funny)
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Re:1.6ghz? (Score:4, Funny)
Re:1.6ghz? (Score:5, Funny)
Re:1.6ghz? (Score:5, Funny)

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The stock heat sink isn't good at all. And their thermal compound, even after repeated heat cycling, only covers a small fraction of the CPUheatsink interface. Just throw i
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Anyway... if anyone is looking for a rep
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Re:1.6ghz? (Score:5, Interesting)
In benchmarks, AMD CPUs tend to beat Intel CPUs on memory bound tasks, even though Intel CPUs win at CPU intensive tasks because the AMD CPUs integrate a faster memory controller ondie instead of relying on a slower FSB. Intel's weakness is less noticeable when the CPU is running at a clock speed closer to the FSB, and given that increases in CPU clock speed increase the power and heat usage geometrically, it wouldn't make sense to run the CPU at full clock for a task of this nature.
Annoying my older brother (Score:2, Funny)
Re:Annoying my older brother (Score:4, Funny)
Re:Annoying my older brother (Score:5, Funny)
Re:Annoying my older brother (Score:5, Funny)
Re:Annoying my older brother (Score:4, Funny)
One day I decided to look up the algorithm to beat it, and you can imagine how I felt when I realized that the stickers had been removed and there was no solution. I nearly pulled a Ballmer, but I happened to be sitting in the only chair in the room. Not that it stopped me from trying to throw it.
The next big thing in GREEN TECH (Score:4, Funny)
I still beat him! (Score:2, Interesting)
Theory versus practice (Score:5, Insightful)
This could make a good case study for business schools
Re:Theory versus practice (Score:5, Insightful)
Instead, it makes a great case for doing the research on the front end to eliminate lengthy repetition of useless iterations to shorten the overall time.
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The study would simply say that business majors aren't good at anything except pimping mathematicians.
Not funny..... true.
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Zero moves.... (Score:5, Funny)
Where can I sign up (Score:2)
Computational proofs (Score:3, Interesting)
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Imagine trying to crack a password by proof. Not showing how to crack passwords, but cracking *one* specific password.
Re:Computational proofs (Score:5, Interesting)
I would guess that it is more common in fields like graph theory and other discrete math just because obviously the discrete lends itself well to computers, and many times it's not hard to whittle it down to a finite number of cases to check. The objects of study also tend to admit matrix representations and other things computers are good at working with. Even before computers you'd cut things into lots of cases that you needed to verify but now it's easier to handle proofs that need larger number of cases.
I've actually seen some really interesting proofs using computers to check things over continuous domains. The basic idea lots of times is if you can check things over a fine enough "net" of cases in some space and you can prove that the variance between each of these points is small enough, then you can cover your entire space by just checking a finite number of cases.
Given all this people still have a healthy amount of skepticism for computer aided proofs and would rather not if possible in most cases, especially when you're talking about billions of cases. Then again what is the potential for errors in a computer checking billions of cases based on a relatively small amount of code versus some of these enormous humancreated decadeslong behemoth [wikipedia.org] proofs?
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Distributed computing (Score:3, Interesting)
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next project: getting a date! (Score:4, Funny)
However I've noticed a problem: if I introduce a parameter to model a female's response to this research, the spaces collapse to zero, i.e., a null set.
I find this quite puzzling. Simply by examining my chances of getting laid, I reduce my chances to zero.
Did I mention I can solve the Rubik's cube in 25 moves?
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Apparently, this video [youtube.com] explains how to do it in 5 steps, much simpler even than solving the Rubik's cube.
Suboptimal Nonsolution (Score:5, Funny)
The original paper (Score:4, Informative)
Yeah...24 moves.. (Score:2, Funny)
pffffft (Score:3, Funny)
pfffft... Java
"God's Algorithm" (Score:5, Interesting)
One, and only one vertex in this graph corresponds to the solved configuration of the cube.
Note that this graph represents all possible moves and positionsany scrambled cube is a vertex somewhere in the graph, and solving that cube is equivalent to traversing a path in this graph to the "solved" vertex. In general, many paths to the solution exist, some of which will be shorter than others.
The question of interest is this: Which vertex/vertices of this graph is/are farthest away (i.e., requiring the most edge traversals) from the solved vertex, and how far is it? As of this latest discovery, this maximum distance is 25. It means that every possible scrambled configuration of the cube can be solved in 25 moves or less.
Wikipedia notes that we know that at least 20 moves are required to solve the cube for every configurationthat is to say, we know that this maximum distance is at least 20 (there exists some vertex that is at least 20 steps away from the solved vertex). It is believed that the true "least upper bound" is closer to 20 than it is to 25.
Finally, we should clarify that a "single move" can either mean a rotation of a face by either a quarter or halfturn, or it could mean a quarterturn only. These different metrics of what constitutes a "move" leads to different answers.
Re:"God's Algorithm" (Score:5, Interesting)
So the comic was right!! (Score:3, Interesting)
Solve This! (Score:3, Interesting)
Math and the Rubik's Cube (Score:3, Informative)
If you are interested in playing around with the symmetry group associated to the Rubik's cube, Sage (http://www.sagemath.org) has good support for it; the documentation can be found at http://www.sagemath.org/doc/html/ref/modulesage.groups.permgps.cubegroup.html [sagemath.org] . Sage also includes a number of efficient solvers for the Rubik's cube.
Tomas who? (Score:3, Informative)
And of course! He's the author of dvips [radicaleye.com]! So we have him to thank not only for this cuttingedge breakthrough in mathematical solutions to Rubik's Cube, but also for turning our notoverlyportable DVI files into beautiful, beautiful Postscript.
brush with greatness (Score:4, Funny)
Nice guy and all, but it took me half an hour to finish shaking his hand.
Persons without Asperger Syndrome Support Group (Score:3, Funny)
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I suggest that you only need SIX moves to solve the cube, regardless of starting position. Each move consists of plastering an array of nine colored squares onto a side.
Re:Damn. (Score:5, Funny)
Re:Damn. (Score:4, Funny)
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But if you take it apart carefully, the worst evidence you'll leave is a pair of scratches from the screwdriver you used to pry off the first piece.
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21 is the absolute minimum (Score:2)
You'll never get to single digits on a truly scrambled cube.
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A *human* can solve a cube in seconds  it's not impressive for a computer to do it.
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