[jmg_]

Thinking back to some of the exercises that I did:

+ Calculate the nth term of Fibonacci Sequence

+ Comparing the efficiency sorting algorithms

+ Calculating the resulting angles of the hands of a clock based on a digital-time input.

You could probably apply many of the easier Project Euler questions for your competition with little modification.

Alternately, if you want more computer-related problems some of the /r/dailyprogrammer exercises might be applicable (however most require a computer and programming knowledge)