I have solved 3x3x3 cubes as well as 4x4x4, 5x5x5, 6x6x6, 7x7x7 and the megaminx from some time now but this one is really bugging me. I won't consider my self an expert but I have not experienced anything like this before. One of my students messed around with the cube and suddenly the corners won't orient correctly. I tried solving it several times but without being able to solve the corners. My first thought was that she must have twisted the corners too quickly but it does not help when I twist them back either way. I am really stuck. I do hope someone can help. I have taken pictures of the cube from all sides. As you can see all corners are twisted wrong. Cheers from Peter
Answer
It’s very unsolvable. The centers are not movable, and there is no possible way to orient the corner piece in the first picture so that it would align with the centers.
Most likely, the caps on the center pieces have been swapped.
My 3D visualization isn’t perfect, but I think swapping two opposing centers (no matter which) might fix this.
This is based on the observation that each corner has a possible spot with correct neighboring center colors, but two of the colors are always the wrong way, and you would need a mirror image of the corner piece to fit. (Even taking apart the cube wouldn’t help). The most likely reason is that the centers’ order has been mirrored, which happens when any two opposing centers are swapped.
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