This page will appeal to those who like a good puzzle. I mean, a puzzle probably several orders of magnitude above what you're used to puzzling upon, but, upon solving any of them you can pretty much count on a scholarship and some serious bragging rights with your friends. Your reputation will be made. Mind you, many of these might not be as tough as they initially appear, and just require a fresh perspective to lay them to rest. Should that be the case with you, try and limit your solving of them to one a day, to give the rest of us a chance . . . .
Link: (Wolfram) http://mathworld.wolfram.com/UnsolvedProblems.html