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# A special Math Problem of A New Century's puzzle

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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.

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• 2 months later...

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

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Thank Captain Obvious.

Prof. Maurizio Paolini had solved this puzzle and proved in Italian.

http://www.dmf.bs.unicatt.it/~paolini/varie/tsengpuzzle/ 