Swap 2 corners

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Swap 2 corners

Postby qwertyuiop » Sat Oct 19, 2013 12:45 pm

My cube is solved besides 2 corners in each others positions on the same layer. How do I complete the solve?
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Re: Swap 2 corners

Postby borginator2 » Sat Oct 19, 2013 6:02 pm

This swaps front right and back left corner pieces on top level as well as swapping left and back edge pieces. You'll have to solve them afterwards.

Y-Perm: F (R U' R' U') (R U R' F') (R U R' U') (R' F R F')

Here is a video demonstrating this stage:

http://www.youtube.com/watch?v=z430AQtdMFY

Cue through to about 1:40. Here's where I show the Y-perm.

If the corners solved are next to each other, go with the case before on the video.
Please take off topic discussion off this forum. Thanks.
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Re: Swap 2 corners

Postby Zeotor » Mon Oct 21, 2013 1:11 am

If only two corners are swapped on a 3x3x3 cube, and everything else is solved, then it is unsolvable. You can find out how to fix this situation in the following topic - How to fix that unsolvable cube. If other pieces are unsolved though, borginator2's approach above will work. (On other cubes, such as the 4x4x4, two corners can be swapped.)
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Re: Swap 2 corners

Postby kidologist » Sat Nov 23, 2013 5:17 pm

Zeotor wrote:If only two corners are swapped on a 3x3x3 cube, and everything else is solved, then it is unsolvable.

This is not true. I've been going nuts because I often end up with my Cube completely solved, except for two adjacent corners swapped, but the rest solved. In Dan Harris' book this is not included as one of the possibilities. But it is. Online I read that this is impossible, your stickers were moved, or peices taken out - but that's wrong. It is a brand new Cube, and if I scramble and re-solve it, I can solve in under a minute now, but every 20-30 times I end up this way and would LOVE to find how to fix it without just starting all over. I've tried combinations and swap BOTH sides and swap diagonal, but without luck.

On my Void, I know it is parity and I just move the middles over 90 degrees, but what about on the normal Rubix' Cube, someone more experienced than me has to have an answer. The video above shows swapping two oppsite corners with the edges are not yet solved. (a different method) I solve Dan Harris' method, top two layers, cross on bottom, bottom edges, solid on bottom, and then last corners. His book says you will either have one corner in place, or need to do one of the 2 corner swaps (both adjacent corners) or both corners diagonally.

No one seems to know (that I can find) how to swamp just two corners.

This 13 year old kid shows it on his page, but the algorithm doesn't work, ironically, but he at least acknowledges that it is possible:
http://cubefreak.weebly.com/beginner-solution.html

HELP! (and thanks!!)
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Re: Swap 2 corners

Postby Zeotor » Mon Nov 25, 2013 4:04 am

If you can, kidologist, please post a picture of this situation when it happens again.

My reasoning as for why I think what I do can be found in this post on another forum. The post is quite long. However, I think that you only need to go through it until the following.
Now consider a Rubik's cube. Again, looking at the locations of only the edges and corners, a single move (90 degrees!) cycles 4 edges and 4 corners. A four cycle: ABCD -> BACD -> BCAD -> BCDA takes three swaps so is an ODD parity! [...] take an ODD number of 90-degree moves to solve 8-) )

:)
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Re: Swap 2 corners

Postby kidologist » Wed Nov 27, 2013 12:08 am

Thanks for the link! LOVED your post over on TwityPuzzles.com - not only the detail on parity, but the humorous way it was written. I registered and am currently awaiting with baited breath to see if I shall be "approved" by the gods of that site to be worthy of membership! :?

I will post a pic the next time it happened, by Murhy's Law of Cubing, it will probably never happen again now! ;)

However, I have since learned a second way to solve, and have discovered if I just switch methods, it seems to work.

If you are curious, I will explain. If not, just click away now, and you are free to roam about the Internet as you were previously before I briefly interrupted whatever you were doing. (a tip to your post)

I learned to solve: 1st 2 layers, cross on bottom, line up bottom center edges, then solid bottom, then permute corners, which is when I get the above issue at times. I just learned that Patrick Bossert, the 12 year old who solved the Cube and published the first book and sold 1.5 million copies in 1981 did corners first - so I learned his method: 1st 2 layers, cross on bottom, (skip: line up bottom center edges) then solid bottom, then permute corners, finally permute center edges.

Still deciding which I like better, but when I get "parity" (or should I say, "apparent parity"?) I just switch to the other method and it seems to self-correct.

Loving that all this help is available and amazed that I solved this myself as a kid.

Wrote about it here, in my Leadership Lessons from the Rubix Cube: http://kidology.org/rubixleader
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Re: Swap 2 corners

Postby Zeotor » Sat Nov 30, 2013 7:39 am

The post that I linked to was not written by me.
(I thought that it was a great post too.)

kidologist wrote:[...]then permute corners

If I understand correctly, at this point in the solve, there are still unsolved pieces. Those would be the top corners (because they still need to be oriented), the top edges, and the middle layer's pieces. Two corners can be swapped at this point in the solve. They can't be later on if everything else is solved. The following quote (from that post that I linked to before) basically states this, but with different words.

This also explains why it is impossible to solve a cube with just two swapped edges or just two swapped corners, but entirely possible to solve a cube with BOTH two swapped edges and two swapped corners

You can go back to that post for the logic preceding that statement.


That forum is a great place to be if you enjoy solving puzzles. By that, I mean you enjoy the process of figuring out how to solve puzzles, such as the Rubik's cube. As you can tell from what you've seen, it has some very knowledgeable members. (It is also great for other puzzle-related interests too.)
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