http://en.wikipedia.org/wiki/Fermi_problem
An absurdly whimsical and fairly basic Fermi problem, but, hey, why should physicists and engineers hog all the fun?
As for the practical applications of this problem: Any game which a) encourages people to estimate costs in terms of percentage of GDP and b) makes the point that GDP per capita tends to grow over time is a useful educational gambit.
http://en.wikipedia.org/wiki/Kardashev_scale
Let's just borrow a chapter from Ringworld, and move the Sun, dragging the Earth along. I don't have enough napkins for a calculation, but it may be possible to just trail the star as it clears debris ahead of us, while also keeping us warm. (Naturally, the exhaust would have to be redirected around Earth - I don't know if it would be easier to build something around the sun to do this, or to place a shield around the planet.)
AsteroidShell = 3For1Deal!
But we MUST discuss this idea, using only napkins for paper.
http://idea-sandbox.com/blog/2007/11/cocktail-napkin-noteboo...
But maybe I just don't get something about it.