1. Some variant on the Busy Beaver problem- (say) create a Turing machine of 4 states which does as many state transitions as possible then quits, leaving the tape in the same state as it was initially.

2. Quick fractal preview. Create the closest approximate image of an escape-time fractal (eg the Mandelbrot set) only doing a fixed number of iterations (not shortest time, to avoid making people write the loop in assembler).

3. Assisting Bayesian spam-checking. Many spammers have resorted to mangling works (eg V1.agr4). Write a program to map mangled words to their closest dictionary equivalent.

4. Optimizing simple linear code. Given a sequence of simple expressions, produce an optimized version doing any of dead-code elimination, constant-folding, etc. IOW, given:

a = b + 2
b = a * 3
b = b * 2
b = b + 0

produce:

a = b + 2
b = a * 6

5. Write a program to play Tetris (take a stream of shapes on standard input, output moves you plan to make as "left, turn, down" etc).

6. Write a program to play Rocket Mania.