The Prisoners - Netflix

Series following repeat offenders released from prison over the course of a year as they try to live a life beyond bars.

The Prisoners - Netflix

Type: Documentary

Languages: English

Status: Ended

Runtime: 60 minutes

Premier: 2013-04-15

The Prisoners - 100 prisoners problem - Netflix

The 100 prisoners problem is a mathematical problem in probability theory and combinatorics. In this problem, 100 numbered prisoners must find their own numbers in one of 100 drawers in order to survive. The rules state that each prisoner may open only 50 drawers and cannot communicate with other prisoners. At first glance, the situation appears hopeless, but a clever strategy offers the prisoners a realistic chance of survival. Danish computer scientist Peter Bro Miltersen first proposed the problem in 2003.

The Prisoners - Examples - Netflix

Indeed, all prisoners except 6 (who succeeds directly) fail.

And in the following arrangement, prisoner 1 opens drawers 1, 3, 7, and 4, at which point he has to stop unsuccessfully:

The prisoners now act as follows: Prisoner 1 first opens drawer 1 and finds number 7. Then he opens drawer 7 and finds number 5. Then he opens drawer 5, where he finds his own number and is successful. Prisoner 2 opens drawers 2, 4, and 8 in this order. In the last drawer he finds his own number 2. Prisoner 3 opens drawers 3 and 6, where he finds his own number. Prisoner 4 opens drawers 4, 8, and 2, where he finds his own number. Note that this is the same cycle encountered by prisoner 2, but he isn't aware of it. Prisoners 5 to 8 will also each find their numbers in a similar fashion. In this case, all prisoners find their numbers. This is, however, not always the case. For example, the small change to the numbers of swapping drawers 5 and 8 would cause prisoner 1 to fail after opening 1, 7, 5, and 2 (and not finding his own number):

The reason this is a promising strategy is illustrated with the following example using 8 prisoners and drawers, whereby each prisoner may open 4 drawers. The prison director has distributed the prisoners' numbers into the drawers in the following fashion:

The Prisoners - References - Netflix