The 100 Prisoner's problem

[Aoi Magi]

In fact if the director put the numbers in the boxes following this pattern (the number in the box is the number of the box plus 1, and the number in box 100 is 1) then he would guarantee that the first prisoner would not find their number, even if the first prisoner was chosen at random.

By the 20th time though, most prisoners would recognize the pattern.   It'd be a good test though.

But a prisoner wouldn't know what the others chose or what pattern they saw. In this case the prison warden has a much higher chance of detecting what pattern the prisoners are using than the other way around.