I'm in need of some assistance with my Sudokube. I've solved it many times in the past, but for some reason I keep finding myself in the same stuck spot near the end. I've scrambled and rescrambled it several times recently, but it's always the same parity-style situation on the final layer.

First of all, my Sudokube is the style where all the centres are 5s and the completed sides read 1 through 9 in order. My top (final) layer has the edges 2/2, 2/4, 2/6, 2/8 and corners 1/3/1, 1/3/3, 1/3/7, 1/3/9.

I can get my top cross, but the centre is rotated CCW 90 degrees (note: NOT 180 degrees). Also, when it's in this configuation, I can get only 2 of my corners in their right spots (not necessarily oriented correctly), but the other two corners are swapped like on a void cube or an even-numbered cube.

Again, I've successfully solved this very cube many times before, but I don't normally run into this situation. I am also positive that nobody has tampered with the cube in any way. Is there an algorithm to solve the state I've described?

Pick any two identical edges and swap them. This will force you to also swap two corners and it will rotate a center by 90 degrees. [R2, D', R', D, R', B2, L, U', L', B2] is a way to do this quickly.

Is that algorithm supposed to do all three things you mentioned (swap two edges, swap two sides, and rotate the centre)? Also, if I'm going to pick any two identical edges to swap, where should those two edges be in relation to me when I do the algorithm?

It swaps the FU and RU edges and the RFU and RBU corners as well as twists the U center by 90 degrees.

So when you get the puzzle into the position you described, put two identical edges between the two swapped corners and perform the sequence. Then undo the setups. In this way you'll fix everything at once.

I guess what I'm confused about is the "two identical edges" statement. The edges on my top layer are all different (2/2, 2/4, 2/6, 2/8). I left my cube at work, so I'll have to test this algorithm tomorrow. But, can you clarify the "identical" statement?

Yeah that makes sense. What you'll need to do is find a 2/2 or 2/4 or 2/6 or 2/8 edge elsewhere on the puzzle too. You must have a duplicate edge somewhere. You'd move it into the top layer (you could use a middle slice which would make it easy) and then do the sequence. Then you'd undo the setup moves.

Here is an example of setup moves:
[F'2, B'2, L'2, U', L', U, L', B'2, R, D', R', B'2, F'2, B'2]

Since all the center pieces are the same, you may be having the void parity, it is solved by rotating the "middle" layer (between U and D) 90 degrees and then returning the edges to the position they had before the turn. Then you should be able to solve the last layer.

You can simulate this situation on a normal 3x3 by doing the middle slice layer turn and returning the edge pieces to their "correct" places under the correct corner pieces. Then you will have the 2 last edges/corners swapped.

Like this:

Thanks for the help, guys. I'll give it a try tomorrow.

Alternatively, if there is no pair of identical edge pieces, you can just flip the 2/2 edge and that should also solve the parity issue.

Well, I don't know if I did exactly what I was instructed to, but it worked. All I had to do was a middle slice (M' U M) U2 (M' U M) with the identical edges on the FU and FB spots, then rebuild the cube from the bottom. Somehow it worked. 4 days of struggling brought to an end! Thanks again guys