Sometimes, when solving the Void Rubik's Cube using the standard beginner method, it gets "stuck." What I mean by this is that the top edge of one face and the top edge of an adjacent face's colors are swapped.
Typically, I've just turned random faces until the cube is sufficiently messed up and then started over. However, there must be a better way - what is it?
Answer
When you work with a void cube, you've de facto lost a degree of visibility. The algorithm to take you out of this position is M' U M' U' M U' M U2 M' - then you just solve the remaining edges as-is, and I'm going to attempt to briefly explain why this works.
You, as you know, can no longer see the centers on the void cube. However, it's important to bear in mind that they're actually still there, just hidden. When the 'virtual' centers are rotated incorrectly - that is to say, you're attempting to solve the cube around an invalid position - the pieces won't line up. In the case you're seeing, the centers along one axis have been rotated 90 degrees out of position.
To see for yourself why this might be, attempt to solve a regular Rubik's cube with one row of centers rotated 90 degrees. You'll find yourself in an equivalent position on the 3x3. (Note: a position which is mathematically equivalent to the one you are in is where two corners are swapped; if you end here, you're in literally the exact same position.)
This algorithm moves them back into a legal position, and, though it disrupts a couple edges in the process, actually allows you to solve it regularly again.
This can also be done intuitively. Simply do a middle slice along any face, then keep one corner fixed in your mind relative to the three virtual centers (i.e., keep it in the same place relative to them), and solve the cube again.
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