Originally Posted by Wikipedia

The prototypical Catch-22, as formulated by Heller, considers the case of a U.S. Army Air Forces bombardier who wishes to be excused from combat flight duty. In order to be excused from such duty, he must submit an official medical diagnosis from his squadron's flight surgeon, demonstrating that he is unfit because he is insane. According to Army regulations, any sane person would naturally not want to fly combat missions because they are so dangerous. By requesting permission not to fly combat missions, on the grounds of insanity, the bombardier demonstrates that he is in fact sane and therefore is fit to fly. Conversely, any flyer who wished to fly on combat runs implicitly demonstrated that he was insane and was unfit to fly and ought to be excused, and to be excused this person would only need to submit a request. Naturally, such flyers never submitted such requests. Of course, if they did, the "Catch" would assert itself, short-circuiting any such attempt to escape from combat duty.

Originally Posted by DivideBy0

I'm trying to find solutions to this problem, and I've got one so far,

When you try to get out of flying your mission, they will say you're sane, but you say that you do not want to fly your mission because it's not dangerous enough, hence proving that you are crazy. If they then try to make the mission more dangerous, it's already too late, because you've proven you're crazy and you can now leave freely.

What do you think? Any catches?