Late in the day hypothesizing here. As the boxes are random, and the order is unknown, and there is no hidden information passed between each prisoner, and the

Late in the day hypothesizing here. As the boxes are random, and the order is unknown, and there is no hidden information passed between each prisoner, and the room is reset each time - the only controllable factor the prisoners can agree on ahead of time is the strategy for which boxes each one will open. Given the boxes are already randomized, using a random order is no more useful than using a sequential order. So assuming they know the layout of hte boxes (is it 100 in a line or 100 in a square... presumably this can be figured out or some other strategy accounted for so everyone approaches things the same way) - each person opening 50 boxes has the same odds of finding their name. To maximize the odds of the entire GROUP finding their name, we need to ensure that each box is opened the same number of times by the end of the exercise. As we can't pass any information back and forth, this is the best we can do. First 50 people open the first 50 boxes. Second 50 people open the second 50 boxes. Or - as they may or may not know their position - they only need a strategy that ensures that each box is opened an equal number of times by the end. To me that still looks like (1/2)^100..... which by definition isn't the answer - so I'm missing something. Eager to see the answer.