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 Post subject: Solving Puzzles Using Ultimate Solution
PostPosted: Tue May 17, 2011 2:40 am 
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Hi all

I just wanted to let anyone interested know that I have a blog with tutorials for solving different twisty puzzles using only what's in the original Ultimate Solution method by Philip Marshall.

It's at http://rubiksultimatesolution.blogspot.com/

Those who've remembered any of my (few) posts will know that I talk about the ultimate solution lots. That's because it's the only thing I know. Anyhow, I wanted to make the method (which I think is fantastic, but not easily understandable from the original site) easy to understand for anyone who's interested.

I'm sure that almost everyone on these forums will only be interested as far as novelty value goes, but I also hope that anyone searching for possible solution methods for puzzles might find it useful.

So far I have tutorials for

2x2x2 pocket cube
3x3x3 rubik's cube
4x4x4 rubik's revenge
5x5x5 professor cube
crazy 3x3x3 earth

Obviously there will be puzzles on the blog which are not covered in the original site (eg. crazy earth). I'm hoping to add methods for the crazy 4x4 II, other planet cubes if applicable, megaminx, teraminx and some others.

I'm fully aware that there will be some (many?) puzzles which won't succumb to the method. But there should be quite a few which do. I'm also aware that the ultimate solution is not a speed solving method. I also don't wish to take away from anything by Marshall, rather just to make it more accessible.

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 Post subject: Re: Solving Puzzles Using Ultimate Solution
PostPosted: Tue May 17, 2011 7:57 pm 
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Hi rline, the "Ultimate Solution" for the 3x3x3 is basically 1) simultaneously position and orient the edges with a non-pure [1,1] commutator and then 2) simultaneously position and orient the corners with a pure [[1:1],1] commutated conjugate.

I think the actual details of how the method is applied to the 3x3x3 is not as important as the concept which to me is is roughly 1) identify different types of pieces, 2) find the shortest / easiest pure or non-pure sequences for each piece type, 3) adjust the order you solve the pieces such that the short non-pure sequences are done first and finally 4) finish the puzzle with the necessary pure sequences for the remaining pieces.

If you accept this description as the basic recipe for the "Ultimate Solution" then you can apply the "Ultimate Solution" to any non-bandage and non-jumbling twisty puzzle. You can always solve by piece type and usually it is the easiest method too.

Almost every solution outlined in the Gelatinbrain solving thread is of the solve-by-piece-type variety.

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 Post subject: Re: Solving Puzzles Using Ultimate Solution
PostPosted: Tue May 17, 2011 8:07 pm 
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Hi bmenrigh,

I was using the Ultimate Solution to mean the method that Philip Marshall published. The point of my post was to let people know that there was a site which explained that particular method (the one on Marshall's site) better (I hope) than on the original site.

Thanks

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 Post subject: Re: Solving Puzzles Using Ultimate Solution
PostPosted: Wed May 18, 2011 1:06 am 
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Having very laboriously worked through the Ultimate Solution at Georges' site some years back, and having been through rline's blog, I can say that rline has done an excellent job of simplifying the presentation of the Ultimate Solution.

I think I know what you are saying bmenrigh, but the terminology you use is not familiar. I think you are saying that the Ultimate Solution is solving edges with a commutator that also moves corners, then solving corners with a commutator that does not move the edges.

Then you are saying that most puzzles can be solved using this basic strategy. Right?

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 Post subject: Re: Solving Puzzles Using Ultimate Solution
PostPosted: Wed May 18, 2011 5:17 am 
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Hi rline, in your Step3 Case 4 description you write
Quote:
In this case, carry out an edge piece series using the 4th top edge currently in the center, the middle top edge, and either of the other top edges. Make sure you finish with three top edges facing the top. When you're done, you will have two of the top three correct relative to each other, and can go to Case 2 or 3.
I have not seen an explanation for "middle top edge". In the video you say "any two top edges". If I really use "any" two, the result can be Case 1. In Case 1 you write
Quote:
In this case, carry out an edge piece series using the 4th top edge currently in the center, the middle top edge, and either of the other top edges. Make sure you finish with three top edges facing the top. When you're done, you will have the situation in either case 3 or case 4.
So, if you are very unfortunate and make wrong choices, you can toggle between Case 4 and Case 1. Or what am I missing?

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 Post subject: Re: Solving Puzzles Using Ultimate Solution
PostPosted: Wed May 18, 2011 5:50 am 
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Hi Konrad

First, thankyou very much for taking the time to "test" the site for me. Knowing your skill in cube solving, I'm well aware this probably would have been quite tedious for you! I was hoping that if there were inconsistencies, they might be picked up.

Now your questions

Quote:
Hi rline, in your Step3 Case 4 description you write
Quote:
In this case, carry out an edge piece series using the 4th top edge currently in the center, the middle top edge, and either of the other top edges. Make sure you finish with three top edges facing the top. When you're done, you will have two of the top three correct relative to each other, and can go to Case 2 or 3.

I have not seen an explanation for "middle top edge". In the video you say "any two top edges". If I really use "any" two, the result can be Case 1. In Case 1 you write

Quote:
In this case, carry out an edge piece series using the 4th top edge currently in the center, the middle top edge, and either of the other top edges. Make sure you finish with three top edges facing the top. When you're done, you will have the situation in either case 3 or case 4.

So, if you are very unfortunate and make wrong choices, you can toggle between Case 4 and Case 1. Or what am I missing?


First, the phrase "middle top edge" was meant to indicate this: on the top there were 3 yellow edges with their yellow stickers on the up face. The middle top edge means the yellow edge piece in the center. The central one of the three. Perhaps I should change it to "central".

Second, regarding the infinite potential loop between case 1 and 4. Hmmm. After a little experimenting myself, I see you are right. :oops: That would be a pretty long solve...

When I do it myself, I always make piece 1 the yellow edge currently in the middle layer. When that happens, what I have on the site is true. It always goes to case 3 or 4. But if I make one of the top yellow edge pieces piece 1, I see that it is possible to get case 1.

Now, the reason I have the instructions for case 1 is this: when I first went through Marshall's site, I spent literally hours going over and over what he'd written and trying to make sense of it. When I came to the explanation for "all 3 are correct relative to each other", it said

This arrangement is converted to one in which all four white edge pieces are in the proper order on the top face by a series of replacements.

We begin by replacing a white edge piece on either end of the three on the top face with the white edge piece in the center section. For example, rotate the top face in Fig. 6d by 90o clockwise giving Fig. 6e. Rotate the green face 90o clockwise giving Fig. 6f. The white/red piece is replaced by the white/yellow piece and the former moves to the center section.

Now turn the top face 90o counterclockwise (Fig. 6g) and replace the white/green piece with the white/red piece (i.e. rotate the green face by 90o counterclockwise) to give the cube shown in Fig. 6h. Continue in this fashion until, in the fourth turn of the green face the last white edge piece (in this case the white/orange piece) returns to the top face of the cube and the fourth center section edge piece moves into place at front/right.


I confess that this made pretty much no sense to me. But I discovered that if I just substituted one of the 3 yellow edges on top with the one in the middle, then within 1 or 2 edge piece series, I'd get to case 2 or 3, both of which are solvable. So I was happy with that.

Then, quite recently, I find out about an alg no doubt well known to most people on the forums for swapping two outer edge pieces on the crazy earth. U (R U R' U R U R' U). Someone then pointed out that case 1 on my site was the case where we had to swap two edge pieces, so shouldn't that alg work there? I went back and re-read his description, and finally worked out that his description of "a series of replacements" is in fact U (R U R' U R U R' U). And this is why in Marshall's original method, case 1 will always be solved and will never loop back and forward with case 4.

I should probably do an updated video using this method.

Anyway, I hope that helps explain things and am happy to be alerted to any more issues.

Thanks again

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 Post subject: Re: Solving Puzzles Using Ultimate Solution
PostPosted: Wed May 18, 2011 9:12 am 
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Hi rline, thanks for the clarifications. When I read a description like yours, I try to scratch out everything I know already about the Cube and just want to follow the given instructions. :)
rline wrote:
...First, the phrase "middle top edge" was meant to indicate this: on the top there were 3 yellow edges with their yellow stickers on the up face. The middle top edge means the yellow edge piece in the center. The central one of the three. Perhaps I should change it to "central".
I think "the central one of the three" says it clearly.
rline wrote:
Second, regarding the infinite potential loop between case 1 and 4. Hmmm. After a little experimenting myself, I see you are right. :oops: That would be a pretty long solve...

When I do it myself, I always make piece 1 the yellow edge currently in the middle layer. When that happens, what I have on the site is true. It always goes to case 3 or 4. But if I make one of the top yellow edge pieces piece 1, I see that it is possible to get case 1.
I could easily find a Case 4 where piece 1 is in the middle layer, the central top piece 3 is at UF. piece 2 at UR. After R U' R' U I end up with Case 1!ImageProbably, you need to say that the central top edge has to be piece 2? Your current wording doesn't express that clearly (and in the video you say just "any" top edges.
rline wrote:
....Continue in this fashion until, in the fourth turn of the green face the last white edge piece (in this case the white/orange piece) returns to the top face of the cube and the fourth center section edge piece moves into place at front/right.
I confess that this made pretty much no sense to me.
Especially this part is not clear to me as well. :)
rline wrote:
...I went back and re-read his description, and finally worked out that his description of "a series of replacements" is in fact U (R U R' U R U R' U).
Actually Philip Marshall's sequence starts U R U' - Now turn the top face 90o counterclockwise (Fig. 6g) - R' (the part where he describes the moves precisely)

Especially the part with the last edges lets me think, that this method is not well suited for beginners.

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 Post subject: Re: Solving Puzzles Using Ultimate Solution
PostPosted: Wed May 18, 2011 7:39 pm 
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Hi Konrad,

Thanks again for the followup.

Quote:
When I read a description like yours, I try to scratch out everything I know already about the Cube and just want to follow the given instructions.

And for that I am very grateful to you!

I think what I will do is make a new video for case 1, showing how Marshall does it, using his series of replacements, seeing as it makes sense to me now (as opposed to when I first did the site a year and a half ago). I think it's valid since Marshall uses it, and also, I use that same sequence (his "series of replacements") when needing to swap two edges on the crazy earth.

Quote:
Especially the part with the last edges lets me think, that this method is not well suited for beginners.

Possibly. The way I taught my daughter to do it avoided this entirely. What I said was that when she got to that point, she needed to get the "back two" yellow edges correct. In other words, holding the cube with the 4th yellow edge at FR, look to see whether the yellow edges belonging at LU and BU were next to each other correctly. If not, cycle edges until that was the case. Then she'd have the last 3 yellow edges in position, and would be able to finish it with one edge piece series. She picked that up easily enough (she's 10). However, it's not how Marshall did the "Ultimate Solution", so I won't use that.

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 Post subject: Re: Solving Puzzles Using Ultimate Solution
PostPosted: Thu May 26, 2011 6:46 am 
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I've posted a new page showing how to solve the Crazy 4x4x4 II.

It's at http://rubiksultimatesolution.blogspot. ... x4-ii.html


To clarify...

1) My site is not claiming to offer the best method, nor the quickest method to solve cubes, simply the "Ultimate Solution" method. It's designed for those wanting simple ways to solve puzzles, where by simple I mean as minimal memorisation as possible.

2) As an example, if I use a corner piece series and then turn the whole cube about an axis and then another corner piece series (eg. in crazy 3x3x3 earth), I still class that as an "ultimate solution" method.

Any constructive feedback on the site is always welcome.

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 Post subject: Re: Solving Puzzles Using Ultimate Solution
PostPosted: Sat Aug 13, 2011 10:25 pm 
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For anyone interested, I've added lots of new video tutorial pages to my blog at

http://rubiksultimatesolution.blogspot.com/

Latest additions include

* all 8 of the crazy planet cube series
* crazy 3x3x2
* face turning octahedron
* rex cube
* skewb ultimate
* pyraminx crystal
* crazy tetrahedron standard

The blog's aim is to show how to solve a whole heap of different twisty puzzles using just the two basic algs found in the ultimate solution method.

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