Sudoku

I have recently taken up an interest in Sudoku and I it made me wonder about the mathematics of the game. How many possible Sudoku games are possible in the standard 9x9 grid? How many squares must be given to ensure at unique solution? Is there always a unique solution in the games usually published? How are the difficulty rankings determined? How hard would it be to write a program to solve Sudoku puzzles?

I found a good article with some of the answers. Its amazing that we don't know the answers to some of these questions. For example, with a 9x9 grid we know that with less than 8 (3^2-1)given numbers their must be at least 2 solutions. But that doesn't answer the question. If you have 10 given numbers must there be a unique solution? The answer is we don't know. One researcher is guessing that the magic number is 17, but he hasn't been able to prove it yet.

Good stuff.