I have a couple of advertising cubes with pictures or diagrams on the faces. Solving these completely, requires getting the correct orientation of the center cubies for the faces. IIRC, half of the 4^6, or 2048, combinations of the face-center orientations are possible in an otherwise solved cube. The larger group size would add an expected log2048/log18 ~= 2.7 to the number of moves required. I've never seen anything discussed about this version of the cube that went beyond noting the group size. I have checked (too long ago) that there are move sequences that rotate centers of two faces by +90,+90 and also +90,-90, while leaving the rest of the cube untouched (or more accurately, restored). So the "full cube" problem can be solved. But my sequences weren't especially efficient, needing O(100) moves. [I think the moves were simply to rotate one face 90, and then the adjacent face 90 (or -90), and simply repeat till everything but the center cubie rotations was restored; the order of the double rotation happens to be odd.] Can any serious cubists tell me more? Rich
Tomas Rokicki: "The number of moves necessary to solve an arbitrary Rubik's cube configuration has been cut down to 23 moves". http://science.slashdot.org/article.pl?sid=08/06/05/2054249
Christian.
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