I know this one too, and I'm pretty sure a set of problems containing this one was posted on hn a long while back. I suggest using the constraints of the probl

I know this one too, and I'm pretty sure a set of problems containing this one was posted on hn a long while back. I suggest using the constraints of the problem to your advantage. There's only a limited number of ways one could choose boxes to open, and there's a limited amount of information to work with. Here's a hint: If the prisoners cannot communicate after deciding on the strategy, is it possible there's any benefit of prisoners performing different strategies? Beyond that, try to consider the different ways to select 50 boxes. They are randomized, so picking any 50 boxes at once will give you a 50% success rate, which with 100 ppl is unacceptably low. What other ways are there to select boxes? Are there any ways to pick boxes using information that's given?