Slashdot Mirror
Rubik's Cube Proof Cut To 25 Moves
KentuckyFC writes "A scrambled Rubik's cube can be solved in just 25 moves, regardless of the starting configuration. Tomas Rokicki, a Stanford-trained 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."
What are these magic 25 moves that can solve a rubik's cube regardless of starting position?
Give me Classic Slashdot or give me death!
Why wasn't the Q6600 at 2.4ghz like normal? Anyone know?
This is a good example of where the inefficient method (of about 60 moves iirc) is much faster in terms of time. The 25 move solution is elegant but just not worth it in terms of computations, time etc...
:-)
This could make a good case study for business schools
The more annoying thing was to solve it for real, then transpose two of the stickers, and mix it up again. Let's see 'em solve it now!
Insightful and funny are really the same thing, except one has a punch line.
I consider a Rubik's Cube to be "solved" regardless of its starting position. I subscribe to the Fred Rogers solution: it's fine just the way it is.
--I'm so big, my sig has its own sig.
-- See?
No, just make the rubix cube out of the oled keys of the optimus keyboard. Integrate with bluetooth and "solve" the rubix in a single button press.
Well.. maybe. Or Maybe not. But Definitely not sort of.
And if you put the corner on twisted by a third of a turn, then scramble it up again, you have an insoluble puzzle to leave lying about to drive people nuts. B-)
Bantam Dominique roosters crow a four-note song. Once you've heard it as "Happy BIRTHday" you can't NOT hear it that way
In my research, I've reduced female behavior to a set of 50 million parameters. By partitioning this space into subspaces and finding equivalent sets, I think I might be able to get laid.
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?
I've been doing some interesting work in the other direction. I've managed not to solve a Rubik's cube in what I estimate to be 1.5 million moves. That seems to be the upper limit after which the stickers fall off.
Here's the paper itself, if you want more detail than the very general summary in TFA.
I started with a solved cube and now it looks totally scrambled.
One..Two..Three..CRUNCH...Ouch
The answer is that it takes three licks to get to the center of a standard Rubik's cube.
Fascism trolls keeping me up every night. When I starts a preachin', he HITS ME WITH HIS REICH!
As far as I know the first "big" computational proof (which another poster alluded to) is the Four Color Theorem. It was initially met with some distrust but it's pretty widely accepted now, and there are people that worked after the original proof to cut down the amount of computer verification needed from a couple thousand to a couple hundred I think.
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 human-created decades-long behemoth proofs?
Take every possible unique configuration of the cube (those that are obtainable by legal moves--no rearranging stickers or disassembling allowed). Represent each configuration by a vertex. Now join two vertices by an edge if and only if the configurations represented by those two vertices differ by a single move (we will elaborate on what constitutes a "single move" later). The result is a mathematical object called a graph. A horrendously giant graph.
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 positions--any 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 configuration--that 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 half-turn, or it could mean a quarter-turn only. These different metrics of what constitutes a "move" leads to different answers.
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.
Your comment has just made me run through the list of my close acquaintances checking that none of them might ever refer to themselves are `cubers'... I would have hated having to kill any of them!
Hint: For this prank to work, the stickers should be different colors.
After all, I am strangely colored.
good idea, those cubers are a bunch of squares.
Balderdash!