# Is a Rubik-Sudoku possible?

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?