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I have a rubik cube, which always have two swapped edges in the last layer. No matter which color I start with, there are always two edges in the last layer which remained swapped with each other.

How to solve this scenario. Or if this is an invalid scenario, please can somebody explain how is this an invalid scenario.

See this image for sample:

http://m.imgur.com/u8P9Sag

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  • $\begingroup$ Welcome to Puzzling SE! Please can you explain your question a little more clearly? I don't understand what "two flipped edges in the last layer" means. $\endgroup$ – Rand al'Thor Mar 22 '15 at 13:09
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    $\begingroup$ @rand I have included an image link, is the question still not understandable after looking at the image? I'm so sorry, English isn't my first language, couldn't find more appropriate words, however I'll try to further explain the question. $\endgroup$ – Syed Aqeel Ashiq Mar 22 '15 at 13:34
  • $\begingroup$ That makes it clearer, thanks! Maybe you should crop the image to just the relevant part though; there are a lot of cubes shown there, which could confuse things. $\endgroup$ – Rand al'Thor Mar 22 '15 at 13:39
  • $\begingroup$ I have a Rubik's "Void" cube where this can happen, but it happens because the "missing" centre pieces are in the wrong place! It's not possible on an ordinary cube. $\endgroup$ – not my job Mar 22 '15 at 16:30
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In a Rubik's cube, every legal move swaps a even number of dowels, so any legal configuration can be obtained only with a even number of swaps. In this configuration, the difference between a legal cube (the solved one) and the current status consists of 1 swap; since 1 is odd, this is a No Win Scenario.

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  • $\begingroup$ So you mean, although this is a valid combination, but this is an unsolvable scenario. Or you are saying that is not valid at first place? $\endgroup$ – Syed Aqeel Ashiq Mar 23 '15 at 9:28
  • $\begingroup$ If it is unsolvable, you can't even get that combination with a standard cube. $\endgroup$ – leoll2 Mar 23 '15 at 10:08
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    $\begingroup$ @dj Since all valid operations on the Rubik's cube are reversible, valid and solvable are the same thing. $\endgroup$ – not my job Mar 23 '15 at 20:03
  • $\begingroup$ So this is a limitation with physical implementation of Rubik's cube that this scenario isn't achievable with standard cube, and thus unsolvable. Otherwise, this color combination is one valid combination out of quintillions of possible combinations. Isn't it? $\endgroup$ – Syed Aqeel Ashiq Mar 25 '15 at 15:56
  • $\begingroup$ From a mathematical point of view, this is one of the possible combinations of colors that you can apply to a cube. From a realistic point of view, the ONLY way to achieve this pattern is disassembling the cube, then rebuild as you wish. $\endgroup$ – leoll2 Mar 25 '15 at 16:02
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It is possible to swap two edge pieces as per your diagram, but only if you also swap two corner pieces. Once the corner pieces are correctly positioned, you can only swap "double pairs" of edge pieces, including rotating a set of three edge pieces.

Basically, your cube is wrongly assembled.

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Hold your cube so that the pieces are in the upper-front and upper-back position. In the case here, have the orange face pointed directly at you and yellow pointed up. This should put the cube in the correct orientation. Use: R' U2 R U R' U R U' R' U2 R U R' U R

This will swap the front-middle-upper and front-middle-back edge pieces and keep their orientation. However, the corner pieces will be repositioned and you will need to redo those steps. You're supposed to get the edge pieces correct before working on the corners anyways.

EDIT
I decided to cheat and put it onto an online solver. It said it wasn't solvable. At first I thought that those moves would leave the corner pieces alone, but apparently not. I punched in a very similar pattern I had once and it solved it. So apparently your cube really is improperly manufactured. Just take the two pieces off of the cube and put them back in correctly.
/EDIT

For those who don't understand cube notation:
R = right face of the cube
U = upper face

X means to rotate that face in a clockwise rotation (90')
X' means to rotate the face in a counter-clockwise rotation (-90')
X2 means to rotate the face twice (180')

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  • $\begingroup$ Welcome to puzzling.se. Thanks for your effort to answer. Can you please elaborate your answer, so that people who are less familiar with a Rubik's cube can understand it? $\endgroup$ – Rohcana Aug 24 '15 at 19:01
  • $\begingroup$ @Anachor is that better? $\endgroup$ – tridecagon Aug 24 '15 at 22:06
  • $\begingroup$ I wasn't actually saying anything about the notation. I meant, you wrote the moves, but you did not say what the end result was. $\endgroup$ – Rohcana Aug 24 '15 at 22:12
  • $\begingroup$ If you took a solved cube and performed these actions, would they produce the image that the asker presented? The asker has a cube where the only thing still scrambled is two edge pieces. Is his cube solvable? $\endgroup$ – LeppyR64 Aug 24 '15 at 23:21
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Yes this happens when the cube is wrongly assembled... I have had the same problem...Usually when you drop the cube or whatever and the center pieces come out, you think you have put them back right.. But turns out not necessarily always. You have to put them back correctly. Here's how.

In the above case as shown in pic, just leave the yellow and white faces alone... And move the center piece (literally pull it out and move) of each face one-left until you have moved all four. In the above case as shown in pic it will be as follows:

Orange center moved to where green center is Green center moved to where Red center is Red center moved to where Blue center is Blue center moved to where Orange center is

Hope this helps. At least this is what I did and the standard algorithm works afterwards

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  • $\begingroup$ Thanks for the solution. Can confirm that this allows the unsolvable cube in the question above to become solvable again. $\endgroup$ – Shane Oct 3 '18 at 7:30

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