Every year at DefCon they have acontesttohack the badges. The contests are some combination of math or hardware hacking. (You can read writeups of some of the past years here:21,20, 19)
Wired has a cool write up about the guy behind the badges for the last few years:
http://www.wired.com/2014/08/defcon-2014-badges-revealed/
The winner of the contest gets this cool badge (below)
