  We introduce SudoQ, a quantum version of the classical game Sudoku. Allowing
the entries of the grid to be (non-commutative) projections instead of
integers, the solution set of SudoQ puzzles can be much larger than in the
classical (commutative) setting. We introduce and analyze a randomized
algorithm for computing solutions of SudoQ puzzles. Finally, we state two
important conjectures relating the quantum and the classical solutions of SudoQ
puzzles, corroborated by analytical and numerical evidence.
