# Never Reassemble Your Cube "Complete" Again



## blgentry (Apr 16, 2008)

Most (all?) of us are aware that there are a variety of "illegal" positions on a nearly solved cube. A single rotated corner, for example, is not achievable by twisting the faces. Only disassembling the cube and reassembling it "wrong" can produce this, or any of the other "illegal states".

So I read on wikipedia that there are actually 12 different "cubie orbits" that account for these states. One of the 12 orbits is the one we all work with, which allows a fully solved cube; the other 11 will not yield a fully solved state. I got to wondering: Just how "wrong" will one of these orbits look when I try to solve the cube in the wrong orbit? Will I even be able to get it close?

I was cubing with a friend yesterday and we decided to try it. We both disassembled our cubes and reassembled them in a random configuration. Reassembling a cube, without having to look for the "right" pieces is SO much faster! Probably 30 to 40 seconds without really even trying.

We both finished assembly and solved. His came up fully solved with no pieces out of place. It was a one in 12 chance. Mine came up with (I think) one rotated corner and one flipped edge. Fixing that was very easy, as you can imagine.

We repeated the experiment a few times and always ended up with just a few things out of place. In thinking about it, I believe the worst case scenario is three things: One rotated corner, one flipped edge, and two swapped edges. 

All in all, I find this process of reassembly far more satisfying. Instead of hunting down cubies, I just put it back together fast and then I get to do a solve. 

I will never reassemble my cube "as solved" ever again.

Brian.


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## Pedro (Apr 16, 2008)

blgentry said:


> In thinking about it, I believe the worst case scenario is three things: One rotated corner, one flipped edge, and two swapped edges.



I'd add 2 corners swapped, as is the same as 2 edges swapped...

well, I think you'll always get really close to solved...the other scenarios I can think about are 3 edges flipped, 2 corners flipped in the same direction and...I guess that's it. That would be 6 "wrong" orbits, and of course the solved one. Can't think about the other 5 now...


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## PatrickJameson (Apr 16, 2008)

I'll also add that on 4x4's, the only thing that can be changed is the twisting of the corners. Everything else can be fixed with parity algs

When i assemble a 4x4 I always put the pieces in randomly except I orientate the corners like I do in bld.


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## shelley (Apr 16, 2008)

I always assemble my cube randomly. It's a lot faster to assemble, solve, then pop open to fix any wrong pieces than it is to look for specific pieces and assemble it solved.

And yeah, nice thing about 4x4 is that you only have to worry about corner orientations.


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## hait2 (Apr 17, 2008)

uhh yeah..
basic cube principles

in case you're wonering why 12..
on the 3x3x3,
2(permutation, correct and incorrect)*3(corner orientation, correct and 2 ways of being incorrect)*2(edge orientation, correct and incorrect) = 12

you can only solve a cube if 
your permutation is solvable (1/2) and your corner orientation is solvable (1/3) and your edge orientation is solvable (1/2) = 1/12

any cube can be reduced to one of those 12 states (obviously).

ill list them out since it seems uh, there's some misunderstanding about the basics of the cube (aren't algorithms great.. you don't even have to know what you're doing anymore!)

shorthand: cw = clockwise twisted, ccw = counterclockwise twisted

1 - solved cube
2 - flipped edge only
3 - flipped edge + cw corner
4 - flipped edge + ccw corner
5 - cw corner only
6 - ccw corner only
7 - 2 swapped pieces
8 - 2 swapped pieces + flipped edge
9 - 2 swapped pieces + flipped edge + cw corner
10 - 2 swapped pieces + flipped edge + ccw corner
11 - 2 swapped pieces + cw corner
12 - 2 swapped pieces + ccw corner


any cube can be reduced to one of those 12 states (they are obviously mutually exclusive due to the way the face turn affects the pieces)


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## Dene (Apr 17, 2008)

I don't see how this isn't obvious? Did you assume that if you put it back together randomly that you wouldn't even be able to get close to solving it? Any moderately experienced cuber should know that it isn't a problem. It's kind of like when people think that, if you scramble it by doing exactly 1 million rotations, it'll be a hell of a lot harder to solve than if you did 25 rotations. These people obviously have never thought about solving a cube or how it works.


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## blgentry (Apr 17, 2008)

I'll try to not be insulted by the mildly condescending remarks here.

This was a new concept to me. I'm sure at some point in your life this was a new concept to you as well. I thought it might be fun to share with others that are interested in the cube. I still think it's neat. 

As for my "experience level", I think I've been solving for around 12 weeks now, maybe give or take one week. So, I feel like I have a solid handle on how to solve and can do so fairly quickly, but I do not feel I have any sort of "mastery" of the cube.

Brian.


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## Lucas Garron (Apr 17, 2008)

Let's see what I have to add...
Megaminx has separate parities for edges and corners. 

Also, this was a mystery puzzle once.


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## coopersacatfilms (Apr 17, 2008)

What I have found is that you can get through all F2L and you really notice it when you get to your OLL because when my cube Pop's if I put it back wrong I know all OLL so I can easily tell if a Piece is swapped or sometimes it will come up in the PLL you never know but it is always in the OLL or the PLL well..... Most of the time =]


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## Dene (Apr 17, 2008)

It should be obvious. You can't have 3 corners, 1 edge or 3 edges orineted.


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## alltooamorous (Apr 17, 2008)

I've been doing that for a while now >.>


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## Kenneth (Apr 17, 2008)

When poping in competition you put the pices back in as you like and then solve the cube as much as possible, then in the end you are allowed to fix the pices that came in wrong but not more than three pices may be changed.

So you can always solve all but three of them.


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## Swordsman Kirby (Apr 17, 2008)

shelley said:


> I always assemble my cube randomly. It's a lot faster to assemble, solve, then pop open to fix any wrong pieces than it is to look for specific pieces and assemble it solved.
> 
> And yeah, nice thing about 4x4 is that you only have to worry about corner orientations.



You do 4x4? Since when?


Dene said:


> It should be obvious. You can't have 3 corners, 1 edge or 3 edges orineted.


... 3 corners oriented?


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## Dene (Apr 18, 2008)

Swordsman Kirby said:


> Dene said:
> 
> 
> > It should be obvious. You can't have 3 corners, 1 edge or 3 edges orineted.
> ...



Yes... You can't have only 3 corners oriented.


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## shelley (Apr 18, 2008)

Swordsman Kirby said:


> You do 4x4? Since when?



Since last weekend 
(Well, competed in 4x4 for the first time last weekend anyway)


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## Lucas Garron (Apr 18, 2008)

Dene said:


> Swordsman Kirby said:
> 
> 
> > Dene said:
> ...


RU2R'FUF'

EDIT: 7 corners is the only impossible.


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## Dene (Apr 18, 2008)

Lucas Garron said:


> Dene said:
> 
> 
> > Swordsman Kirby said:
> ...



With the F2L completed...


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## masterofthebass (Apr 18, 2008)

Dene, have you not heard of the Sune algorithm? You can have 3 misoriented corners as long as they are all in the same direction...


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## Cubie Newbie (Apr 18, 2008)

Yes, but Dene's point is not that you can't have three corners MISoriented. You simply can't have three LL corners oriented (or orineted). This is simple to realize, as the seven corner OLLs don't include such a case.


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## Mike Hughey (Apr 18, 2008)

It occurs to me that this might be a fun thing to try - randomly reassemble your cube, then solve it BLD. It would be part of the challenge to recognize what pieces are in wrong during memorization, and then at the end pop the cube, reassemble a few pieces, and fix it before removing the blindfold. One case in 12 would be decidedly easier than the other 11, though.


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