100 Prisoners and 100 Boxes
Level 6●●●●● Expert~12 min
Problem
100 prisoners are numbered –. In a room are boxes, each containing a distinct slip numbered – in a uniformly random arrangement. One at a time, each prisoner may open up to boxes, looking for their own number, then leaves without communicating and the boxes are reset. If *every* prisoner finds their number, all go free. With the obvious random strategy the chance is . Find a strategy giving survival probability over .