Logic Puzzles

[Kit-]

New thread because I have no idea where to find the old one, and I couldn't be bothered to search for it and bump it.

1. If you knew the answer beforehand, please don't spoil it for the rest of us.
2. Don't Google for answers, that defeats the whole purpose.
3. Don't bother with repost reposts like "Why did the man shoot himself after drinking repost soup?"

That being said, I'll kick it off with a really hard one. I don't think I've seen this anywhere else. It took me two hours to figure it out with a fairly big hint.

prty heug hint: Has something to do with a topic covered in group theory.

There are 100 people in prison with ID numbers from 1-100, and the warden makes them a proposal. There is a room with 100 boxes in a line, each with one of their ID numbers inside, and each person is allowed to open up to 50 boxes. If they can each find their own number within these 50 guesses, they're all set free. However, if even one person fails, they all die. They are only allowed to speak to each other beforehand; no information transfer takes place at any time after. So, for example, you can't tell the next person in line that his box is the 27th one by coming out after 27 minutes have passed, even though no actual speaking is involved. The room is reset to its original state after each person exits. What is the only strategy with at least a 30% success rate given an equal probability of any configuration?