## Rubik’s nxnxn Cube Algorithms

The Professor’s Cube is an extension of the Rubik’s Cube and the Rubik’s Revenge. It is made of ﬁve rotating slices, from which it follows that the Professor’s Cube is composed of 98 cubies: 8 corner cubies (possessing 3 stickers each), 36 edge cubies (2 stickers), and 54 remaining center cubies (one sticker only).

At an ﬁrst glance the Professor’s Cube turns out to share a remarkable feature with the Rubik’s Cube: one cubie in each face, namely the most central one, is ﬁxed.

### Rubik’s nxnxn Cube Algorithms

The ‘even cube’ always 8 corner cubies (3 possible orientations), while the number of edges and centers depends on n. It is not difficult to check that the number of centers, as well as that of edges, is even. In particular, the number of center cubies isc= 6(n−2)2,(5)while the number of edges is= 12(n−2). (6)In the special case of the Rubik’s Revenge (n= 4), we have c=e= 24. Notice that in the limit case n= 2 we get a cube with no edges nor centers (only corners!), which is exactly the case of the 2 ×2×2, the so-called Pocket Cube.

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