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Trevor Sayre

Post subject: Barrel Cube Problem Posted: Mon Jan 19, 2004 8:09 pm 

Joined: Fri Sep 19, 2003 9:26 pm 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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Mike G

Post subject: Re: Barrel Cube Problem Posted: Mon Jan 19, 2004 10:10 pm 

Joined: Wed Oct 31, 2001 4:19 am Location: Manchester, UK

> 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 (normallooking) 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 cutdown columns. You then just need to swap two pairs of corners from the cutdown column.


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jaap

Post subject: Re: Barrel Cube Problem Posted: Tue Jan 20, 2004 1:22 am 

Joined: Wed Mar 15, 2000 9:11 pm 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 cutdown > columns. You then just need to swap two > pairs of corners from the cutdown 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 backright and fronleft 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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Trevor Sayre

Post subject: Re: Barrel Cube Problem Posted: Wed Jan 21, 2004 12:26 am 

Joined: Fri Sep 19, 2003 9:26 pm Location: New York, USA

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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Mike G

Post subject: Re: Barrel Cube Problem Posted: Wed Jan 21, 2004 1:22 am 

Joined: Wed Oct 31, 2001 4:19 am Location: Manchester, UK

Well, there you go  2 much neater solutions!


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Adam Zamora

Post subject: Re: Barrel Cube Problem Posted: Wed Jan 21, 2004 3:41 am 

Joined: Thu Nov 20, 2003 7:29 am Location: San Diego, California

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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Mike G

Post subject: Re: Barrel Cube Problem Posted: Fri Jan 23, 2004 7:12 pm 

Joined: Wed Oct 31, 2001 4:19 am Location: Manchester, UK

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 3cycle 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 cutdown edges have been flipped. You'd need something like Josef Jelinek's ACube program to check that...


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Trevor Sayre

Post subject: Re: Barrel Cube Problem Posted: Sat Jan 24, 2004 7:12 pm 

Joined: Fri Sep 19, 2003 9:26 pm Location: New York, USA

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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Trevor Sayre

Post subject: Re: Barrel Cube Problem Posted: Mon Jan 26, 2004 9:18 pm 

Joined: Fri Sep 19, 2003 9:26 pm Location: New York, USA

You know, I wonder why Jaap hasn't put these on his site. They'd be really helpful.
Trevor Sayre


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Mike G

Post subject: Re: Barrel Cube Problem Posted: Mon Jan 26, 2004 9:55 pm 

Joined: Wed Oct 31, 2001 4:19 am Location: Manchester, UK

> 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 3x3x3like 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 3cycle for optimality. [The other (6turn) doublecolumn swap was already optimal.]


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Mike G

Post subject: Re: Barrel Cube Problem Posted: Tue Jan 27, 2004 9:55 pm 

Joined: Wed Oct 31, 2001 4:19 am Location: Manchester, UK

> Haven't tried to check the 3cycle for optimality.
Just tried it in another orientation, in the hope that the pruning would be more effective. It was  ACube proved the 13turn sequence to be optimal after a few seconds.
I'll shut up now.


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Trevor Sayre

Post subject: Posted: Tue Feb 10, 2004 2:16 am 

Joined: Fri Sep 19, 2003 9:26 pm Location: New York, USA


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