I have a 3x3x5 cuboid in the position shown (all pieces correct except for the two edges you can see. The must be a parity issue, but I can't get around it whatever I try. The only parity issue that seems possible is having a pair of middles pieces from rows 2 and 4 swapped, but I can't see how I can get a single pair to swap.

Current Position

I've contacted the guy that wrote the app. He says that scrambles are formed by applying legal moves only, so there should be a solution.

Any ideas?

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    $\begingroup$ I don't think this is possible on a 3x3x5 (except by disassembly), though it definitely is possible on a 3x3x4. Imagine removing the stickers from the 2nd and 4th layers so you can ignore those pieces, and you are left with what is essentially a 3x3x3 Rubik's cube. It is not possible to do a clean swap of two edge pieces on a 3x3x3. $\endgroup$ – Jaap Scherphuis Oct 23 '17 at 6:12
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    $\begingroup$ Based on solving the 3x3 cube, for the edge pieces on the top layer, Id always have either none correct, one correct or all four correct, but never two. You indeed seem to have a parity issue, where some of the (indistinguishable) pieces from second, third and fourth layers are 'mixed up'. I'm afraid I can't help you much with a solution, but I don't see a way to build on the 3x3 mechanics to start building a solution either. $\endgroup$ – Tim Couwelier Oct 23 '17 at 7:00
  • $\begingroup$ @Jaap Scherphuis I can discount disassembly, it's a virtual cube. The app has never given me an impossible position on any other cube, so I'd be surprised if this were one. $\endgroup$ – user164587 Oct 23 '17 at 18:31
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    $\begingroup$ I think you would have to rotate the top face 90 clockwise. Then you've got 3 edges out of place which you can fix with two swaps. But then you have to fix all four corner pieces. But even on a 3x3x3, that's as good as you can do. $\endgroup$ – Dr Xorile Oct 24 '17 at 3:54
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    $\begingroup$ @DrXorile This comment might be a good idea to make into an answer, so OP can give rep+credit where rep+credit is due Nice job :) $\endgroup$ – Rubio Oct 25 '17 at 1:32

Done! @Dr Xorile's idea leads to success. Once each top edge is 90 degrees from where it needs to be:

FB' UD' f U'D F'B

solves. The middle "f" rotates the four corner pieces without moving anything else.

To recreate the position in the question from a solved cube: FB' UD' f U'D F'B FB' UD' B' U'D L2 F'B U FB' L2 UD' B U'D F'B U2

The "f" moves rotates the four corners independently of the rest of the cube. All other moves are of slices next to the centres.

| improve this answer | |
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    $\begingroup$ As far as I know, that move that only shifts the corners is not possible on the real-life versions of this puzzle. $\endgroup$ – Jaap Scherphuis Oct 24 '17 at 13:30

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