How many possible unique ways are there to generate a Sudoku Puzzle?? I can think of only two possible ways 1) Take a solved Sudoku puzzle and shuffle the rows and columns 2) Generate a random number and check if it violates any Sudoku constraints, repeat untill number does not violate any Sudoku constraint for every square(theoretically possible but normally it leads to deadlocking )
Are there any other ways?
Here is a 20-page PDF, titled "Sudoku Puzzles Generating: from Easy to Evil", that you'd probably find useful in your quest.
To answer your question:
Are there any other ways?
Yes. Yes there are.