Just another idea... There is a nice article
The Mathematics of Sudoku1) (PDF) by Tom Davis which explains common strategies that can be translated easily into algorithms. But apart from very easy Sudokus, these strategies bring you only to a certain point where e.g. backtracking is required (nice to visualise).
The grid structure of the game allows for straight forward visualisation.
1) an updated version might be available meanwhile...
Update: The keyword simulation mentionend elsewhere in this thread triggered this idea: Swarm Theory - relatively new, ideal for OO-implementation.