How about accurately simulating/calculating the orbit of the earth around the sun based on newtons inverse square law, the mass of the earth and sun, and a starting location/speed/direction for both the earth and the sun. See if you can do a calculation once per hour and come back to about the same place in space (ie. a stable orbit to within one hour of the real one) after 24*365+6 calculations.
Sounds simple, contains a couple of hidden issues and opens up a lot of additional fun things to do.
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