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 Post subject: Universal Solution?
PostPosted: Wed Oct 25, 2006 7:52 pm 
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I heard somewhere that there is a universal solution to the rubik's cube. Like 80 moves or something, no matter how jumbled up, you do this super algorithim on the cube and it will be solved, NOTE: you may only have to do lets say, 77 moves out of the 80 to solve it, like you dont need to do all of the moves. You know what I am saying?


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PostPosted: Wed Oct 25, 2006 7:54 pm 
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are you serious?

no there are many algorithms... search the forums. there's tons of info, tons of solutions, tons of moves.

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PostPosted: Thu Oct 26, 2006 7:19 am 
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Rumor.

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PostPosted: Thu Oct 26, 2006 2:08 pm 
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not true. Just think about it, the cube is always permuted differently, so there cannot be 1 algorithm to solve it.

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PostPosted: Thu Oct 26, 2006 2:16 pm 
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Rumour indeed :)

And a wrong one. It is however proven that with 2 sequences (algorithms) one can generate the whole group. And no i don't mean that setup moves are allowed in addition. Just those 2 sequences, and nothing more. Im also quite sure that not every center orientation is possible with these 2 sequences. Maybe someone else can shed more light on this?

How many sequences are necessary for the nxnxn cube? And how would we "construct" the sequences??

-Per

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 Post subject:
PostPosted: Thu Oct 26, 2006 4:42 pm 
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You guys are way too fixated on one possible interpretation (and not a very common one outside cubing) of the word algorithm.


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 Post subject:
PostPosted: Thu Oct 26, 2006 5:12 pm 
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Hi :-)

My interpretation of some central terms:

Algorithm : a sequence of turns

Case : a desired effect, a case may be satisfied by many different algorithms ... edge 2-flip for instance can be done in many ways, by many different algoritms

Method : an overall solving strategy for a puzzle

Step : a part of a method, a method consists of a number of steps from fully scrambled to solved

In the old days algorithm could mean a method, a solving strategy. It's still called Twistlethwaite's Algorithm for instance. Though it should be called Twistlethwaite's Method.

Happy cubing,

-Per :solved:

PS! Yes, in computer or mathematics terminology an algorithm normally means a collection of steps towards solving a specific problem. An algorithm may be say a way to find a specific item within some data structure in working memory or external memory ...

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 Post subject: Re: Universal Solution?
PostPosted: Thu Oct 26, 2006 6:00 pm 
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cuben00b wrote:
I heard somewhere that there is a universal solution to the rubik's cube. Like 80 moves or something, no matter how jumbled up, you do this super algorithim on the cube and it will be solved, NOTE: you may only have to do lets say, 77 moves out of the 80 to solve it, like you dont need to do all of the moves. You know what I am saying?


Hi cube n00b,

I know what you're saying.

Although the term "algorithm" is used in speedcubing to mean a sequence of moves, a method is also an algorithm. My method can solve any position with fewer than 60 moves, as can several other methods.

I average somewhere between 33 and 56 moves, mostly in the 40's.

David J

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 Post subject:
PostPosted: Thu Oct 26, 2006 6:09 pm 
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using petrus I use way too many moves. like 55 or so on average. but I'm sure when I'm solving I use more.

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 Post subject:
PostPosted: Thu Oct 26, 2006 7:32 pm 
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perfredlund wrote:
In the old days algorithm could mean a method, a solving strategy. It's still called Twistlethwaite's Algorithm for instance. Though it should be called Twistlethwaite's Method.


In the old days only? Btw, whether you want to call it algorithm or method, you should still call it Thistlethwaite.

Quote:
Yes, in computer or mathematics terminology an algorithm normally means a collection of steps towards solving a specific problem.


More importantly, an algorithm usually gets and reacts on input. And has conditional instructions. Not just a sequence of blindly executed actions like what cubers usually call an algorithm.


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 Post subject:
PostPosted: Fri Oct 27, 2006 11:04 am 
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Ok :)

Sorry about the misspelling :roll: I sincerely hope that most cubers apply their algorithms not blindly but according to the current state of the cube. That's the *input* for cubing.

My main nag however is that some cubers have a wrong conception of what a CASE is. A case is like a problem. It's not a solution. To flip just UF and UR is a case, a problem. This problem has many distinct solutions, or algorithms. Here's 2 solutions to that that i know by heart:

[R' e' R2 e2 R',U'] - 16 turns, counting inner slice turns as 2 turns

F' U F2 U' R' F' U' R2 U R' F2 R2 F2 R2 - 14 turns, 3G solution

Happy cubing!

-Per

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 Post subject:
PostPosted: Fri Oct 27, 2006 12:01 pm 
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I know this has been kind of a heated topic before but heres my view.

The word algorithm was maybe used correctly in the early cubing days, but since then it's meaning (in speedcubing) seems to have changed to mean "a sequence of moves to fix a given case".

This is just a separate meaning of the word that isn't in the dictionary, jargon. You can see "flea flickers" in the NFL, and "bicycle kicks" in Futbol, but fleas and bicycles aren't involved in either play. That would be great to see though :lol:

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 Post subject:
PostPosted: Fri Oct 27, 2006 5:28 pm 
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perfredlund wrote:
I sincerely hope that most cubers apply their algorithms not blindly but according to the current state of the cube. That's the *input* for cubing.


So you admit that "algorithm" is more than just the raw move sequence? That it includes recognizing the case, orienting the cube (or AUFing and the like) and choosing the appropriate move sequence?


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 Post subject: algorithm
PostPosted: Fri Oct 27, 2006 6:51 pm 
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Stefan Pochmann wrote:
perfredlund wrote:
I sincerely hope that most cubers apply their algorithms not blindly but according to the current state of the cube. That's the *input* for cubing.


So you admit that "algorithm" is more than just the raw move sequence? That it includes recognizing the case, orienting the cube (or AUFing and the like) and choosing the appropriate move sequence?


A recipe is a type of algorithm.

What is the input?

DJ


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 Post subject:
PostPosted: Fri Oct 27, 2006 8:13 pm 
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Back to the question on hand, I would guess there is an algorithm that goes through all the cases of a cube. However since there are 4.3 * 10^19 or so cases, then the algorithm would need to be at least in the quadrillions of moves.

However I would guess that there is a " Super Algorithm " that when repeated goes through all cases of the cube, and that could possibly be less than 10 digits long.

As far as the centers being oriented correctly, why not just choose a corner? No matter what you do to the cube, that corner would always be solved and everything else would be scrambled in relation to it. That way, the core could be treated as a piece instead of the base.

Lets take the "algorithm" " r U R' U " where " r " denotes the right and center slice turning 90degrees clockwise. (Simple notation would be " L U R' U " and would only have 45 iterations) It has 4 moves that goes through 120 iterations. That makes 480 different cases (excluded thought of symmetry and other type cases) just with a 4 move "algorithm". So it isn't so strange that an 80 move sequence could go through more.

Any thoughts?

-Adam-

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 Post subject: Re: algorithm
PostPosted: Fri Oct 27, 2006 9:08 pm 
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David J wrote:
A recipe is a type of algorithm.

Agreed.

Quote:
What is the input?

None, or the empty input? Or maybe there is some, I don't know.

Anyway, I said an algorithm "usually" gets input and by that I meant "in general". Of course it's not necessary. Or you can always use the empty input. I don't say what most cubers call algorithms aren't algorithms. I just say it's not the only type of algorithm and that the word means a lot more. At least outside of cubing. Btw, the guy asking used the word "solution" twice and "algorithm" only once.

P.S. You're right, instead of "is more" I should've said "can be more". Or I should've made it clearer that I was talking about the general notion of algorithm.


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 Post subject: Re: algorithm
PostPosted: Fri Oct 27, 2006 10:17 pm 
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David J wrote:
A recipe is a type of algorithm.

What is the input?


The ingredients. I can take the same inputs (ingredients) and apply different algorithms (recipes) to get different results (end goods).


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 Post subject:
PostPosted: Sat Oct 28, 2006 12:01 pm 
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Stefan Pochmann wrote:
perfredlund wrote:
I sincerely hope that most cubers apply their algorithms not blindly but according to the current state of the cube. That's the *input* for cubing.


So you admit that "algorithm" is more than just the raw move sequence? That it includes recognizing the case, orienting the cube (or AUFing and the like) and choosing the appropriate move sequence?


No! In my view an algorithm is just the sequence of moves! The algorithm in itself and how to use it (correctly) is not quite the same. A car is made for transportation from A to B. But when used wrongly it won't do that :oops:

-Per

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 Post subject: Re: algorithm
PostPosted: Sat Oct 28, 2006 4:40 pm 
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blogan wrote:
David J wrote:
A recipe is a type of algorithm.

What is the input?


The ingredients. I can take the same inputs (ingredients) and apply different algorithms (recipes) to get different results (end goods).


Right, and you can use the same algorithms (recipes) and apply different inputs (ingredients) to get different results (end goods). Like substituting jack cheese for cheddar, spelt for wheat, mayonaise for butter, etc.
That an algorithm operates on something is granted, but that isn't the only way to look at input. I think input in the case of a recipe is wanting to eat whatever the recipe can produce.
The input for a "sequence of movements" type Rubik's cube algorithm is the case it is solving.

Cheers,

David J


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