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 Post subject: General solving method
PostPosted: Mon Oct 18, 2010 7:46 pm 
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I'm not sure if this has been done before or not, and I'm pretty new to the forum. Just looking through, there's a lot to learn!

But seriously, I bought a teraminx a while back, and scrambled it. Without ever having solved a 4x4, 5x5, 6x6, 7x7, gigaminx, I attempted a solve.

Lo and behold, it took me a great deal of time <cough>six and a half hours</cough> but I got the job done :)

And from the resulting solve arose a NON-ALGORITHMIC method which has probably been thought of long ago, and discussed much, but nevertheless is, in my opinion, worth posting in case it hasn't.


From scramble to solve, my method will work with any face-turning cube or mod of one, as well as all regular dodecahedral X by X puzzles.

Before I delve into a detailed description of the solution, I was wondering if anyone:

1. Has mentioned something like this before
2. If anybody really cares LOL. my method is ridiculously slow, but fully intuitive and gets the job done.

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 Post subject: Re: General solving method
PostPosted: Mon Oct 18, 2010 8:46 pm 
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I'm impressed by the fact that your first high-order puzzle is teraminx instead of 4x4x4. I am interested in your method. But how exactly do you define a NON-ALGORITHMIC method? My understanding is that an algorithm is nothing but a method that is used again and again. Algorithms could be intuitive and flexible. The algorithms based on commutators of short sequences can be intuitive and flexible. Maybe you can take 3x3x3 as an example to illustrate your approach.


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 Post subject: Re: General solving method
PostPosted: Mon Oct 18, 2010 8:51 pm 
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Well technically, yes, it is algorithmic.
But take the Heise method; it's supposed to be non-algorithmic too.

So yes, I could write them as algorithms, but when I solve puzzles I prefer not to use algorithms.

My definition of non-algorithmic? Not solved using algorithms/solvable without algorithms, and only a general methodological guide.

What would you define it as?

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 Post subject: Re: General solving method
PostPosted: Mon Oct 18, 2010 9:10 pm 
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NType3 wrote:
Well technically, yes, it is algorithmic.
But take the Heise method; it's supposed to be non-algorithmic too.

So yes, I could write them as algorithms, but when I solve puzzles I prefer not to use algorithms.

My definition of non-algorithmic? Not solved using algorithms/solvable without algorithms, and only a general methodological guide.

What would you define it as?
Hmm so I think what you are looking for is a method for developing a method. That is, you don't want to have a pre-set sequence of moves before you start a puzzle.

Put another way, you have the puzzle in some state S1 and you want to transition to state S2 without a preset sequence of moves.

The Heise method is 4 steps where the first three seem to be intuition and trial and error and the last step is "use a commutator".

Since you aren't memorizing anything for each of the steps and in the 4th step you have to develop a commutator to fit the situation, you aren't really memorizing any move sequences. What you have memorized though is the four steps you have to perform in order. Hence you have a method (algorithm) for developing a method.

If you accept this definition as what you're looking for then it sounds like you want to learn is the basics of commutation, conjugation, block building, and reduction. A decent place to start is Jaap's "Useful Mathematics"/"Theory" page.

If you need puzzles to practice on then Gelatinbrain's Virtual Magic Polyhedra page is a clearing house for puzzle awesomeness.

And if you want to discuss solving Gelatinbrain's puzzles or read about how others have done it there is discussion thread about them here.

And when it comes to developing a working method for solving a new puzzle Schuma is clearly the best, even though he rarely shares his "secrets" :( .

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 Post subject: Re: General solving method
PostPosted: Mon Oct 18, 2010 9:41 pm 
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Ah. Thanks guys!

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 Post subject: Re: General solving method
PostPosted: Tue Oct 19, 2010 1:25 am 
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The fact the matter is that 99% of people cubing with whatever puzzle will use algorithms, written in stone or not. For example, without any form of a tutorial, or any planned algorithms, I developed my own method for solving any face turning puzzle layer by layer. Does this mean I didn't use planned algorithms, but when solving the puzzle I definately used algorithms.

I will still congratulate you for solving a Teraminx without any prior knowledge on the sort. But once you know how to solve a 3x3x3, your mind is open to logical ideas, which will give someone a better chance at solving a 24 Cube with only knowing how to solve a 3x3x3 than without.

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 Post subject: Re: General solving method
PostPosted: Fri Oct 22, 2010 9:34 am 
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NType3 wrote:
2. If anybody really cares LOL. my method is ridiculously slow, but fully intuitive and gets the job done.
I would really like to know your steps. I've solved almost 60 puzzles on Gelatinbrain's page now, mentioned earlier in this thread, and my methods are also quite slow and inefficient. Still, my way of solving a puzzles has worked fine for me. I strongly recommend that you take a look at Gelatinbrain's applet and see if you can't solve a few. It's fun :D


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 Post subject: Re: General solving method
PostPosted: Sat Oct 23, 2010 11:46 am 
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I can't say my method is "non-algorithmic", but it's based on two commutators: ABA'B' and ABCB'A'BC'B', and I've successfully solved just about every puzzle just by using suitable adaptations of it. (The only exceptions are parity swaps on even-order cubes, which I developed a homegrown algo for.) I first learned this method from Phillip Marshall's "Ultimate Solution to the Rubik's Cube", which teaches you to solve the 3x3x3 using this method. After mastering the method, I realized that, suitably modified, it can be applied to the megaminx too. Then later on, I realized that the two commutator patterns are generally applicable; you can substitute just about anything you want for A, B, and C, and it will still work. Which means that, suitably adapted, it works for every permutation puzzle.

So yeah, I can't say my method is "non-algorithmic", but so far I've only ever needed 2 algos to solve any permutation puzzle you throw at me. Even non-twisty puzzles like Rubik's Shells can be solved this way.


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 Post subject: Re: General solving method
PostPosted: Sat Oct 23, 2010 11:59 am 
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Well now i'm interested in your method... :lol:

Seems someone got to it first


How does your method work?

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I don't know half of you half as well as I should like and I like less than half of you half as well as you deserve.


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 Post subject: Re: General solving method
PostPosted: Sat Oct 23, 2010 1:01 pm 
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NType3 wrote:
Well now i'm interested in your method... :lol:

Seems someone got to it first


How does your method work?

Well, maybe Phillip Marshall himself explains it best:

http://helm.lu/cube/MarshallPhilipp/

The most important thing about this is what he calls the two series, which is essentially the two commutators I mentioned earlier. The specifics of how each one is applied is applicable really only to the 3x3x3, but the key here is to realize that, for example, the "corner-piece series" doesn't have to use only face-turns. If you substitute the left face turn with, say, the middle slice, you get something the permutes 3 edge pieces instead of 3 corners. The way they are permuted resembles the way the corner pieces are permuted (it's hard to describe, you have to try it out yourself to see). On a higher-order cube, substituting both left and right face turns with middle slice turns transforms the series into something that cycles 3 face centers -- so just by this, you see that you can already solve all NxNxN cubes.

Then on non-cubic puzzles, you can do the same thing... for example, on the Skewb Ultimate, the corner piece series translates literally: you get a series that cycles 3 corners without touching the face centers.

Just this week, I managed to solve the Rex cube twice: using an adaptation of the "edge piece series" to solve the edges, then a suitably adapted version of it to cycle 3 crescent slices, and an adaptation of the "corner piece series" to cycle 3 half-crescent+face center pairs. I haven't perfected the method yet, but you can see how using what really amounts to 2 commutator patterns, you can just about solve anything. Of course, like my Rex Cube solution, it takes a while to perfect the method, but you can pretty much solve everything the first time, even if only inefficiently.


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