I doubt it has anything to do with the prize, the classic "What To Do When The Trisector Comes"[0] seems applicable across a lot of mathematics problems and situations. Geometry of course, perpetual motion machines, prime number finding, quantum physics interpretations...

I guess if you're offering a financial prize rather than "merely" trying to teach mathematics, you're probably in too deep for any of its recommendations though.

[0] http://web.mst.edu/~lmhall/WhatToDoWhenTrisectorComes.pdf