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 Post subject: How to solve a cube 3x3x3 only with one algorithm
PostPosted: Sun Nov 10, 2013 11:37 am 
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How to solve a cube 3x3x3 only with one algorithm without additional moves.
Author of idea – Eugene Benek from Kazakhstan.

For solving we will use a J-permute algorithm: λ = R U' L U2 R' U R U2 L' R' U

Sequence of solving:
  1. Solving all edges around centers
  2. Solving all corners

My demo-video for this "crazy" method - http://youtu.be/7SopDBFCusI Yes!!! I did it!!! :D

Total, on solving of the cube was required:
605 / 11 = 55 λ
where:
605 - total number of movements
11 - count of moves in this algorithm (λ)

It is very interesting task! I recommend to try.

Rules: It is forbidden to use any additional moves except this algorithm! Also it is forbidden to use the mirror version of this algorithm!

Tricks with λ-algorithm:
  • U = λ y λ y λ
  • U' = λ y' λ y' λ
  • U2 = (λ y2 λ y λ y2 λ) or (λ y2 λ y' λ y2 λ)

In my demonstration I didn't use tricks with U, U', U2.
If to emulate algorithms by means of these tricks you need bigger quantity of J-permute. I so think. In this case the algorithm is used as a picklock and the task loses any interest. I use it as a key. 8-)

PS. Eugene Benek can only with this algorithm solved cubes of any size!!! Too without additional moves. He likes very hard puzzles - a big bandaged cubes and etc.
One of his topics at the Russian forum - http://twistypuzzles.ru/forum/index.php/topic,305.0.html

The correction from Eugene for big cubes:
On the big cubes he uses another version J-permute: λ = R2 U D' R2 U R2 U' R2 D R2 U' R2 U
In this algorithm need to replace U/D on u/d - λ = R2 u d' R2 u R2 u' R2 d R2 u' R2 u (i.e. instead of external, we twist inside layers) - http://twistypuzzles.ru/forum/index.php/topic,305.msg3296.html#msg3296

This method should be considered as an additional task on the Rubik's cube. For example, as a knight's move on a chessboard. The cube can be used and thus without any physical modifications (bandaging, morphing, etc). Here we limit ourselves to conditions and such tasks sometimes too are interesting and difficult.


Last edited by menshov_s on Mon Nov 11, 2013 10:38 am, edited 1 time in total.

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 Post subject: Re: How to solve a cube 3x3x3 only with one algorithm
PostPosted: Mon Nov 11, 2013 2:17 am 
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For those who used a U-trick, one more task from Evgeny which excludes opportunity to use simply a U-trick with λ.
Modified version of λ-algorithm: λ = D R2 U' L U2 R' U R U2 L' R' U R' D'
Video from Eugene about it - http://www.youtube.com/watch?v=B_di2vm682w


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 Post subject: Re: How to solve a cube 3x3x3 only with one algorithm
PostPosted: Mon Nov 11, 2013 7:38 am 
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Joined: Tue Aug 11, 2009 2:44 pm
I must be missing something. If you are allowed to orient the cube, then you can trivially solve the cube with only one "algorithm" -- R. So... do you mean, you can solve the cube using only reorientation and a single sequence greater than some (?) minimum length?


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 Post subject: Re: How to solve a cube 3x3x3 only with one algorithm
PostPosted: Mon Nov 11, 2013 8:12 am 
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bhearn wrote:
I must be missing something. If you are allowed to orient the cube, then you can trivially solve the cube with only one "algorithm" -- R. So... do you mean, you can solve the cube using only reorientation and a single sequence greater than some (?) minimum length?


Yes, in this task uses only a λ-algorithm and turns of the cube (x, y, z).
This method should be considered as an additional task on the Rubik's cube. For example, as a knight's move on a chessboard. The cube can be used and thus without any physical modifications (bandaging, morphing, etc). Here we limit ourselves to conditions and such tasks sometimes too are interesting and difficult.

The single move (for example - R) and turns of cube (x, y, z) isn't admissible so since thus it is possible to reproduce any algorithm:
R
R R = R2
R R R = R’
therefore, I think, single movement can't be considered as algorithm.


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 Post subject: Re: How to solve a cube 3x3x3 only with one algorithm
PostPosted: Mon Nov 11, 2013 4:24 pm 
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Joined: Wed Jan 09, 2013 8:39 am
Interesting exercise. But i also think that having the freedom to rotate the cube there are many "algorithms" to solve it.

There is another similar approach that solves it using a single algorithm (T-perm) + setups moves, it was used basically to solve it blindfold and invented by stephan pochmann. It is an exercise similar to your :) .

Here you can find some information: http://www.stefan-pochmann.info/spocc/blindsolving/3x3/old.php


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 Post subject: Re: How to solve a cube 3x3x3 only with one algorithm
PostPosted: Tue Nov 12, 2013 1:46 am 
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Joined: Mon Sep 30, 2013 2:16 am
psi wrote:
Interesting exercise. But i also think that having the freedom to rotate the cube there are many "algorithms" to solve it.

Yes, you are right! A cube possible to solve with many different algorithms it is only one of examples. Each algorithm sets the different problems. Ability to solve such problems can be useful for example for solving of bandaged cubes.

I know about Blindsolving. :wink: There similar methods are used.


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 Post subject: Re: How to solve a cube 3x3x3 only with one algorithm
PostPosted: Wed Nov 13, 2013 6:49 am 
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Joined: Wed Oct 23, 2013 7:39 am
I think this algorithm works well to fully solve 3*3*3 Cube Puzzle:
U'RU'R2F'U2FR2U2


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 Post subject: Re: How to solve a cube 3x3x3 only with one algorithm
PostPosted: Wed Nov 13, 2013 10:56 pm 
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sumitsharma wrote:
I think this algorithm works well to fully solve 3*3*3 Cube Puzzle:
U'RU'R2F'U2FR2U2

There is no mistake?
I don't understand what does this algorithm.


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