100 Prisoners, 100 lines of code

In math and economics, there is a long, proud history of placing imaginary prisoners into nasty, complicated scenarios. We have, of course, the classicPrisoner’s Dilemma, as well as 100 prisoners and a light bulb. Add to that list the focus of this post, 100 prisoners and 100 boxes.
In this game, the warden places 100 numbers in 100 boxes, at random with equal probability that any number will be in any box. Each convict is assigned a number. One by one they enter the room with the boxes, and try to find their corresponding number. They can open up to 50 different boxes. Once they either find their number or fail, they move on to a different room and all of the boxes are returned to exactly how they were before the prisoner entered the room.