In particular I would like to know:
- is it possible to say if a sudoku is solvable only having the initial scheme? If yes, what are the condition for which it is solvable?
- Given the initial scheme of a solvable sudoku the final solution is always unique?
- There exist some simple free codes to solve a sudoku?
- Is there any deep mathematical theory behind or connected with a sudoku (some theorem of group theory or number theory) or it is only a simple and pretty game?
- What are the smartest means and strategies for solve a sudoku?
I am also interested in the pure mathematics behind my questions, so if you know some article or book in which the sudoku theory is explained, please let me know.