[math-fun] Re: sudoku and rubik

Combine puzzle genres; Start with sudoku designed to be etched onto 6 faces of a cube (with common numbers in all the edge positions of adjacent faces. Now move the whole pattern to a rubik's cube, so each cubie corresponds to a 3x3 sudoku cell. How likely are random positions of the rubik's puzzle to also be solvable as sudoku? My guess: not very likely, but probably very difficult to prove that only the intended solved rubik's state is also solvable as sudoku.