The above cube is in the solved state (each of the 6 faces has identical color). I now take some paint and paint over two squares so that the resulting cube now looks the image below,

Notice that essentially we swapped the position of a red with that of a blue square. The top face and the three faces hidden from view are unchanged. Show that, using the normal pivoting and rotating operations of Rubik's cube, it is not possible to return the cube to the solved state like that of the first image.

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## bushindo

Let's consider the following 4x4x4 Rubik's Cube,

The above cube is in the solved state (each of the 6 faces has identical color). I now take some paint and paint over two squares so that the resulting cube now looks the image below,

Notice that essentially we swapped the position of a red with that of a blue square. The top face and the three faces hidden from view are unchanged. Show that, using the normal pivoting and rotating operations of Rubik's cube, it is not possible to return the cube to the solved state like that of the first image.

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