Can the Rubik's Cube be solved with a specific color pattern?

[wuliheron]

I haven't bothered to read the website, but I'm sure they are talking about THEIR solution and not the ideal solution. Evidently they used a computer to devise an algorithm which provides the best possible solution short of actually calculating how to solve it in 13 moves. However, even with their solution dumb luck still plays a part and it should be possible to solve the thing in 13 moves once in awhile. twice I've just been randomly turning faces on a cube and solved it without trying.

If you are interested the cube was developed to teach group theory permutations, the same mathematics in quantum mechanics. It's a closed system or contextual system or fuzzy logic system or whatever the heck you want to call it and those are the rules that govern its behavior, not some website talking about their particular solution.

 

[BruceW]

no, I think they actually used brute force computation to calculate that the 'most difficult' initial configuration can still be done in a minimum of 20 moves. Which is quite impressive. I guess that the number of different possible configurations of a rubik's cube is not impossibly great. (although it is still going to be a very large number, it will be no-where near as great as the number of configurations of a chess game for example, which cannot be 'completely solved' by brute force with today's computers).

Edit: also, yes it is possible to solve it in 13 moves occasionally. But that depends on the initial configuration. In the most difficult initial configuration, it takes 20 moves to solve. And in the most easy initial configuration, it takes zero moves to solve.

 

[wuliheron]

no, I think they actually used brute force computation to calculate that the 'most difficult' initial configuration can still be done in a minimum of 20 moves. Which is quite impressive. I guess that the number of different possible configurations of a rubik's cube is not impossibly great. (although it is still going to be a very large number, it will be no-where near as great as the number of configurations of a chess game for example, which cannot be 'completely solved' by brute force with today's computers).

Edit: also, yes it is possible to solve it in 13 moves occasionally. But that depends on the initial configuration. In the most difficult initial configuration, it takes 20 moves to solve. And in the most easy initial configuration, it takes zero moves to solve.

It is a closed system! Closed, as in no alternatives whatsoever are possible. If you can't understand what that means then I suggest reading up on group theory permutations because that website is only confusing you in my opinion.

 

[BruceW]

You're right. I don't know what you mean by 'no alternatives whatsoever are possible' please explain. hehe, sorry for being sarcastic, but I would like to know what you mean.

edit: at a guess, I'd say you mean that by making moves, you cannot leave the finite set of possible configurations. But I don't know what that has to do with what I was saying.

 

[Borek]

I'm not sure what is confusing you. Computer programs exist which can solve the cube from the most scrambled state in 13 moves every time.

Yes, they scramble the cube from the solved position, however, the thing to remember is the cube is NEVER, EVER, EVER more than 13 steps from being solved.

Can you give any links/quote any sources for these statements?

 

[wuliheron]

A quick check with Google didn't turn up anything, however, I must point out these website are talking about algorithms which are by definition rules for how to solve something rather than specific solutions and there is nothing that insists an algorithm must provide the most parsimonious solutions.

A merry-go-round is a closed system. Your only option is to go round and round and if you get on it thinking it will go someplace else you are a fool. The cube goes round and round and has a minimum and maximum of number of steps required to solve it at any given time. A quarter turn of one face is the minimum that can be solved, and 13 steps (including 180 degree face turns which count as double steps) is the maximum it can require. Algorithms or rules for trying to solve it will always fall short of providing the ideals solutions in some cases by the very nature of their rules limiting the possibilities.

 

[BruceW]

yeah, they are saying that any algorithm cannot beat a 20-move algorithm, in the worst case scenario. That is any algorithm. So it doesn't matter what rule you want to invent, it is proven that you cannot do quicker than 20 moves, given the most difficult initial configuration. Also, why do you say 13 steps?

 

[wuliheron]

yeah, they are saying that any algorithm cannot beat a 20-move algorithm, in the worst case scenario. That is any algorithm. So it doesn't matter what rule you want to invent, it is proven that you cannot do quicker than 20 moves, given the most difficult initial configuration. Also, why do you say 13 steps?

Algorithms are merely convenient shortcuts you can use that may or may not be shorter than something else depending on the specific circumstances. Some days highway traffic is light, while other days the back roads are faster and exactly how the cube is scrambled decides what is the fastest method for unscrambling it rather than any particular algorithm being better than another for every single instance. For example, if just one face is twisted out of sync your algorithm would still work, but not be the shortest solution.

I wish I could still remember the mathematics, but there are 26 pieces, the six center pieces don't move in any way to affect the pattern on the standard cube and, so there are 8 corner pieces and 12 edges to account for which can each only be moved in units of three at a time with their own counterparts. Corners also have to be twisted to orient them and edge pieces flipped which can be done in two at time or more in units of twos. Anyway, what I can remember is that 13 is the absolute minimum number of moves possible and at no time is the cube more than 13 steps from being solved because it is a closed system and the algorithms merely provide approximations. What these algorithms are doing is providing some alternative moves that combine spinning, flipping, and moving pieces simultaneously in some cases when, in actuality, they can almost always be done simultaneously.

 

[BruceW]

http://en.wikipedia.org/wiki/Rubik's_Cube
the section "optimal solutions". I know wikipedia is not always reliable, but until I see a scientific journal stating 13 is the minimum number of moves for the solution of a Rubik's cube, I'm going to assume it is actually 20. No offense intended.

 

[wuliheron]

http://en.wikipedia.org/wiki/Rubik's_Cube
the section "optimal solutions". I know wikipedia is not always reliable, but until I see a scientific journal stating 13 is the minimum number of moves for the solution of a Rubik's cube, I'm going to assume it is actually 20. No offense intended.

Hey, believe whatever you want. However, "optimal solution" does not necessarily mean the "shortest" solution and I caution against reading too much into such things.