Further details on the competition website reveal that astronauts might wear their pressure-sealed suits for up to 10 hours at a time, or for six days in a cataclysmic event. Right now, their only solution is wearing adult diapers. And while a convenient place to take a dump, a diaper proves a "temporary solution, and doesn’t provide a healthy/protective option longer than one day." Ask any baby -- actually, don't do that. Babies can't talk, so you won't get a response.
In case you were wondering what excretion of all sorts is like in space, definitely for shits and probably for giggles, here's a blurb that explains the problem:
"Well, in space there is no gravity to direct your urine away from your body when you release it. Same for poop. There is no gravity to pull it away when you release it. Menstrual fluid? At least some of it will exit a woman’s body. You don’t want that traveling around your suit.And don’t forget, you can’t always count on poop being solid, especially if you are up in space and nervous about the fact that your vehicle cabin has depressurized."
Nevertheless, NASA's ponying up a full $30,000 for your toilet thoughts, and you've got until Dec. 20, 2016 to help astronauts boldly go dookie where no one has gone dookie before: into a fancy space john that you invented.