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Label all six faces of a standard Rubik cube with a free-chosen permutation of the digits $1,2,3,4,5,6,7,8,9$ (instead of colorizing the cubelets). Now there are $10^{20}$ or so configurations of the cube, can you still do the labeling such that only this starting configuration (modulo symmetry operations of the physical cube) preserves that no digit occurs twice on a face?

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You may wanna check https://en.wikipedia.org/wiki/Sudoku_Cube ... "The Sudoku Cube or Sudokube is a variation on a Rubik's Cube in which the faces have numbers one to nine on the sides instead of colours."

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  • $\begingroup$ Ah, I should have known that someone already had the idea. Note a small difference: The rotation of the numbers helps in solving. $\endgroup$ – Hauke Reddmann Sep 22 '16 at 12:09

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