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 Post subject: Barrel Cube Problem
PostPosted: Mon Jan 19, 2004 8:09 pm 
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Location: New York, USA
Hey all,

I have a Barrel cube that I scrambled from the solved position, thus meaning it should be entirely possible to solve. So far, I've solved everything except for the FD edge and the BD edge. They need to be swapped and twisted. After many hours of working on the problem and checking various lists and programs on the internet based on the Rubik's 3x3x3 cube, I've found that technically this position is unsolveable. I know that this cannot be true. I never took the cube apart, switched the stickers, and I started from the solved state, scrambled the cube, and then solved it to the current position. Any thoughts?

Sincerely,
Trevor Sayre


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 Post subject: Re: Barrel Cube Problem
PostPosted: Mon Jan 19, 2004 10:10 pm 
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> technically this position is unsolveable.

You are worried about the parity of the permutation? The problem is that you have two of the "cut down" columns swapped -- this is an odd permutation -- so the (normal-looking) pieces you are stuck on are in an odd permutation (even though the overall permutation parity of the cube is even).

So swap your 2 edges AND the edges of a pair of cut-down columns. You then just need to swap two pairs of corners from the cut-down column.


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 Post subject: Re: Barrel Cube Problem
PostPosted: Tue Jan 20, 2004 1:22 am 
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Location: Delft, the Netherlands
Mike G wrote:
> you have two of the "cut down" columns swapped
> So swap your 2 edges
> AND the edges of a pair of cut-down
> columns. You then just need to swap two
> pairs of corners from the cut-down column.

If you solve the puzzle in layers, with one octagonal face on top and are trying to solve the other octagonal layer on the bottom, then the sequence RL D2 R'L' will do the trick. It swaps the back-right and fron-left shaved columns, as well as the front and back edges of the bottom layer.

Some people prefer to solve it in layers but with the octagonal faces on the left and right. That way the final layer has two whole shaved columns and so will always be solvable without needing to rearrange the top two layers.

Jaap


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 Post subject: Re: Barrel Cube Problem
PostPosted: Wed Jan 21, 2004 12:26 am 
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Thank you so much for the help. I had to get over the mental barrier of seeing the shaved pieces as being easily translated at edge pieces.

Is there a sequence that allows you to just swap shaved columns?

Trevor Sayre


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 Post subject: Re: Barrel Cube Problem
PostPosted: Wed Jan 21, 2004 1:22 am 
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Well, there you go -- 2 much neater solutions!


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 Post subject: Re: Barrel Cube Problem
PostPosted: Wed Jan 21, 2004 3:41 am 
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i tend to solve the non shaved pieces first. the cross on top and bottom. then place the shaved pieces. this usually works out in solving the barrel most of the time

Adam


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 Post subject: Re: Barrel Cube Problem
PostPosted: Fri Jan 23, 2004 7:12 pm 
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Well, as you'll realize, you can't swap a single pair of columns. But the even perms of columns are

R' D2 R2 D' B' L2 F L2 D2 L2 B L2 F' D' R2 D2 R'
which swaps the columns FR FL and BR BL (not very pretty)

L2 F2 L2 R2 F2 R2
which swaps FR BL and FL BR

R2 B2 R' F' R2 B U' B2 U B' R2 F R'
which does the 3-cycle BL -> FR -> BR -> BL

These were found using Kociemba's Cube Explorer, but I don't know if they are optimal once you take into account the fact that you can't see whether the cut-down edges have been flipped. You'd need something like Josef Jelinek's ACube program to check that...


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 Post subject: Re: Barrel Cube Problem
PostPosted: Sat Jan 24, 2004 7:12 pm 
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Thank you for the ideas. I'm working with them, and they seem to be lending the right information. I'm at least able to swap what I need.

Trevor Sayre


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 Post subject: Re: Barrel Cube Problem
PostPosted: Mon Jan 26, 2004 9:18 pm 
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You know, I wonder why Jaap hasn't put these on his site. They'd be really helpful.

Trevor Sayre


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 Post subject: Re: Barrel Cube Problem
PostPosted: Mon Jan 26, 2004 9:55 pm 
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> I wonder why Jaap hasn't put these on his site

I suppose they are a little too specialized, and not essential for solving the puzzle. And for the 3x3x3-like puzzles there are enough programs around to help you DIY.
E.g., an optimized sequence for the column swaps FRFL and BRBL is

L2 U F B U2 L2 D2 L2 F' B' R2 U2 R2 U L2 (15f)

which was found quite quickly by ACube, then checked by solving the "invisibly flipped" cases using Cube Explorer 2.25 -- I hope I covered them all. Haven't tried to check the 3-cycle for optimality. [The other (6-turn) double-column swap was already optimal.]


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 Post subject: Re: Barrel Cube Problem
PostPosted: Tue Jan 27, 2004 9:55 pm 
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> Haven't tried to check the 3-cycle for optimality.

Just tried it in another orientation, in the hope that the pruning would be more effective. It was -- ACube proved the 13-turn sequence to be optimal after a few seconds.

I'll shut up now.


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 Post subject:
PostPosted: Tue Feb 10, 2004 2:16 am 
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I'm just posting here to say that all of the above posts by "TM-Trevor Sayre" are me. This is just a sample. I hope Sandy can find a way to convert all these to my new screen name here. I'm posting this as a note/reminder. If it's not possible, I understand, but it would be nice.

_________________
How to solve the Rubik's Cube 3x3x3:
:scrambled: :arrow: :solved:

See? It's not so hard.


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