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Given a standard 3x3 rubik's cube, is it possible to scamble it and then paint a solved sudoku cube configuration on it - with all the digits on each face orientated the same way - such that when the cube is solved w.r.t to the colours, the digits on each face will all be orientated the same way?

i.e. when solved w.r.t colour, it is a super cube due to orientation of digits. When it is solved as a sudoku cube, the colours will not be solved, but the digits will all be orientated the same way?

I am interested in the answer as well as a method of writing the digits on the cube - if possible.

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    I'm not sure how it affects the orientation of the centre pieces, but you can do things like [swapping centre pieces](http://www.instructables.com/id/Rubiks-Cube-Tricks-center-piece/), then as long as all the centre pieces have the same number the cube will remain solved in the sudoku sense while being scrambled in colour. [rotating centres](http://www.alchemistmatt.com/cube/rubikcenter.html) may solve the orientation problem. I assume you want the scramble to swap at least some edges and corners though? – 2017-01-11
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    @RobertChamberlain when the cube is solved using the colours, the cube doesn't have to be solved in the sudoku sense - just that all the digits are orientated in the same away a la super cube – 2017-01-11

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