Hackaday announced this comp a few weeks ago, I am thinking of entering myself.
The prizes are pretty cool, should be fun!
Simply design a project around an LM555 timer or timers.
http://www.555contest.com/
I had thought of using an LM555 as the basis for a self oscillating Class-D audio amplifier. I had the basic design in my head and when I searched for prior works someone has already done this! Bugger! Back to the drawing board...