Working on this problem:

100 people are in a room. In the next room, there are 100 identical boxes. Each box contains one person’s name (and each person’s name is in exactly one box). One at a time, each person can go into the box room and open up to 50 boxes. Then, they must return the box room to its original state (no re-ordering boxes, no marking boxes in any way). They leave the room and don’t communicate with anyone else. Individually, each person is asked, “which box had your name.” Fabulous riches are showered down on the group if all 100 people answer correctly. Are there strategies they can use to improve the odds that they answer right?