A special Math Problem of A New Century's puzzle

[josdavi]

Please teach me:

I made a new puzzle 5 months ago and found a special
mathematical problem, this problem is still unsolved.

The Puzzle -
consists of eight 3-D connectable cubes
with a solid colour sticker on each of the face of
each cube.

I can twist the layers like twisting the Rubik's cube's layers;

I can shift the layers of the puzzle:
shift the Top layer to be the new Bottom layer,
shift the Right layer to be the new Left layer,
shift the Front layer to be the new Back layer.

I can Overturn the layers of the puzzle:
separate a layer from the Cube Puzzle, turn over this
layer and connect this layer with its opposite side
to the Cube body again.

I knew that there are 8! X 24 ^ 8 = 4438236667576320
different combinations of the 8 cubes, but I don't know
how to calculate the probabilities when we constrain
the manipulations on the Cube, just 3 kinds of
operations are allowed - Twist, Shift, and Overturn.

Is it possible we use just 3 kinds of operations
(Twist / Shift / Overturn) to manipulate the 8 cubes
to form all the combinations ?

How to solve a scrambled such cube puzzle ?

Thank you very much.

[Captain Obvious]

The problem is that most of those combinations are just rotations of each other... Each cube has 8 different flavors (determined by the three exposed sides, one for each possible position, everything else is a rotation) and you need to remove all rotations of your initial selection which limits it to 8! * 8! = 1,625,702,400

[josdavi]

Thank Captain Obvious.

Prof. Maurizio Paolini had solved this puzzle and proved in Italian.
Please take a look at the link -

http://www.dmf.bs.unicatt.it/~paolin...e/tsengpuzzle/

[josdavi]

This puzzle is a real puzzle based on the "Magic Attractor", the first item in market is selling
on ebay. If you are interested to see more pictures, please take a look at this links -

http://www.geocities.com/dynamic_toys/josdavi_09.html

http://cgi.ebay.com/ws/eBayISAPI.dll...tem=1782381251

Thanks.