[Emi]

It also turns out that each legal move on Rubik's Cube always flips an even number of edges, and so the above state would be impossible to reach via legal moves. To establish this, it is necessary to decide on a frame of reference for correct edge orientation, regardless of where an edge is positioned on the cube. The most common frame of reference is to say that an edge in the wrong position has correct orientation if, when it is moved to its correct position using only the left, right, top and bottom faces, it would have correct orientation. Using this frame of reference, it is easy to see that any move on the left, right, top and bottom faces will always flip zero edges, which is an even number. The only remaining faces are the front and back faces. In both of these cases, a 90 degree move will flip all 4 edges, which is again an even number of flips. Therefore, it is never possible, using only legal moves, to flip an odd number of edges.

Quelle

Ich habs damit kapiert