We actually have a Challenges section which wound down because people stopped actually participating. Some of them were pretty decent and a couple were somewhat flawed (like my SADMEP challenge, back before I had any adequate knowledge of math :P).
It would be pretty neat to see that actually running again.
EDIT: Here's a cool idea:
Challenge idea: WordForge
Bah! Who needs math when you have English? In this challenge, you must make a program that will turn five inputted letters into a real English term! The judge will give your program five letters (2 or 3 of which must be vowels excluding y) which will always be able to form an English word. Your program must then rearrange those letters into any five-letter English word. For instance, if KASTE is given, SKATE, STEAK, STAKE, or TAKES would all be appropriate outputs. Ten sequences will be tested, and whoever has the most points (best out of 10) wins! In the case of a tie, the smallest program will win.