Just a small side note, you can solve any such sudoku in the same way you can fill a blank sudoku grid with a valid game state. Take the first 3x3 square and fi

Just a small side note, you can solve any such sudoku in the same way you can fill a blank sudoku grid with a valid game state. Take the first 3x3 square and fill it with consecutive numbers 1,2, ..., 9. Then take the next 3x3 square and fill it with 2, 3, ..., 9, 1. Do the same for each next square and you'll end up with a valid board. To solve the one-number-only sudoku you would then simply take the 3x3 square the number is in, fill it with consecutive numbers around the given number, and then fill the rest of the board similar to the above.