The Math Behind Sudoku

OT: has anyone tried Sudoku as a two player game?

One way this could be done would be to start with a blank playing field and the players take turns adding digits. If a player is unable to add a digit anywhere without causing there to be a duplicate on a row, column, or in a square that player loses.

That would be suitable for playing on paper. If playing on a computer a more difficult variation could be played. Players alternate adding digits, and after each digit is added the computer checks to see that it is still possible to finish. If it is not, the player who placed the digit that made it unsolvable loses.

This latter variant could also be played by more than two people.