100 Prisoners Puzzle
Here's an interesting puzzle:
A cabinet with ten drawers, each numbered 1 to 10, stands in an otherwise empty room in a prison. The warden enters the room, writes the name of 10 different inmate numbers on separate cards & distributes the pieces randomly so that each drawer contains one prisoner's unique number.
Said inmates with their numbers placed were invited to a room in shackles. They're tasked to enter the room, one after the other, and given 5 tries (opening 5 drawers) to find their inmate number among the cabinet. When they're done, they will exit to an isolated waiting room where they cannot speak of their findings to anyone that has yet to attempt the task.
The warden adds a hope-inspiring, yet harrowing condition - If every prisoner is able to find their own inmate number, everyone will be freed; but if even one person fails to find their number, everyone will be killed.
The prisoners are allowed to communicate among themselves, on what strategy they can employ for such a tenuous task. But once the task begins, they will not be allowed to communicate. And, leaving breadcrumbs or hints for the ones after would be pointless (and at times even misleading) since the guards will reset the room to a random configuration every time.
Can you derive / find a strategy, that gives you a chance of survival that exceeds 30%?