What is a good board game to use for a programming competition
Robo Rally (rules) could be interesting. Amusingly, the game itself is programming a robot, one of several (up to 8) on a game board.

Each player gets 9 random instruction cards per round and chooses 5 to play.  Then all the robots' moves are evaluated simultaneously (more or less).  Your robot can get pushed around or damaged by other robots as well as by conveyor belts and other board elements.  First robot to hit all the checkpoints in order wins.

You should have a few knobs to tweak here to make the challenge easier or harder:


Do the players know the board in advance, or does their AI have to deal with it dynamically?
The damage rules could be left out for simplicity, or left in for more complexity


It's possible this is too complex, but it's pretty well suited for this kind of contest, I think.

It's also an excellent board game to play in person, especially with other programmers.