The Prisoner Problem

Explore a simpler version of the Prisoner Problem as featured in Matt’s video. What’s the probability that the prisoners will survive? What is it that makes their strategy a good one?

Curriculum Topics Covered

Permutations, Probability. 

More information

The puzzle in these activities is a simpler version of the Prisoner Problem featured in Matt’s video.

In Matt’s video there are 10 prisoners and 10 cabinets and cards, whereas we have only 4 of everything. We give students the prisoners’ strategy and ask the question ‘What is the probability that the prisoners survive using their strategy?’

We find that there is a 42% chance that the prisoners will survive if they use their strategy. This is amazing! If the prisoners were choosing randomly and independently of each other, they would each have a half chance of getting their card, and therefore they would be a one in sixteen chance of them all getting their cards and surviving.

The Worksheets – this download contains the following worksheets:

The Prisoner Problem‘ – this outlines the problem that the prisoners face and the strategy that they decide to employ.  

‘The Prisoner Problem Investigation’ – here students investigate in which of the different arrangements the prisoners would survive and in which they would die. It involves being systematic and spotting patterns. Can your students find the chance that the prisoner will survive?

The Prisoner Problem Cycles’ – this activity is an alternative to the one above. It introduces students to the cycle representation from the start and leads them to use this representation to work out the probability that the prisoners survive. 

The Solutions – this download contains solutions and notes on each of the activities. 

Excerpt from ‘So You Think You’ve Got Problems?’, Alex Bellos – Matt’s prisoner problem video is inspired by the prisoner problem featured in Alex Bellos’ book ‘So You Think You’ve Got Problems?’. In this version there are 100 prisoners. Alex has kindly given us the extracts from the book with the problem and solution. We have included these as a separate download.