I feel like the 'search' function is missing the point. The sudoku puzzles are generated in such a way that there is always a next move to be deduced: there is never any need to guess. If you have to guess, then you have missed something.
Depending on what you mean here, you are misrepresenting the problem. You may not have to guess for what is a valid move that can be done on the board as it is. But you do have to guess for a valid move that will lead you to a completed board. Hence, you search among the possible moves for the one(s) that will lead to a completed board state.
