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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. $\endgroup$ Commented Oct 23, 2017 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. $\endgroup$ Commented Oct 23, 2017 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
    Commented Oct 23, 2017 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
    Commented Oct 24, 2017 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
    Commented Oct 25, 2017 at 1:32

1 Answer 1

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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.

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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. $\endgroup$ Commented Oct 24, 2017 at 13:30

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