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Build a chess program. The simple version will just follow the rules, allow a user to make moves against the machine, and pick a random valid move. That should be pretty easy to defeat. It's probably also enough to pass a BSc thesis.
The next step is to add the simple minimax algorithm. As this requires an evaluation function, one will have to be written. A simple one is just number of pieces (Q=9, R=5, B=3, Kn=3, P=1).
