100 mathematicians and 100 boxes
100 mathematicians are challenged to a deadly game. There is a room into which there are 100 boxes numbered from 1 to 100, each of them containing the name of 1 of the 100 mathematicians. (so that each name is contained in a box, and we assume that no two mathematicians have the same name)
The mathematicians are to go into the room one after the other has come out. Once inside, each of them will have to open at most 50 boxes, in any order, until they find their name. They are not allowed to change the places of the names, nor can anyone who comes out of the room give any information on the contents of the boxes to his fellow mathematicians. If one has not found his (why not her ?) name, all 100 mathematicians instantly die.
The mathematicians are allowed to agree upon a common strategy before beginning the game, is there any way they can improve their chances of surviving ?