# Prisoners Problem - Page 1

The jail is getting rather crowded, and the jailor is thinking about setting some of the prisoners free. However they have to solve a challenge. If they fail, then they go back to their cells, and another group of prisoners will get a go. The challenge goes like this.

Ten prisoners will be selected, and have the challenge explained to them. They are allowed to confer at this stage, and plan their strategy. Then comes the challenge...

The prisoners will be lined up in a single file, all facing the same direction. The prisoner at the back can see all nine prisoners in front of him. The prisoner at the front cannot see any of the other prisoners, since they are all behind him. The prisoners standing in the rest of the line will only be able to see the prisoners in front of them, not the ones behind them.

Once the prisoners are standing in line, each prisoner will have a hat placed on their head. The hat will be either black or white. The choice of colour in each case is completely random. No prisoner can see the colour of their own hat. A prisoner can see the colour of the hats worn by any prisoners standing in front of him, but cannot see the colour of any hats worn by prisoners standing behind him.

Each prisoner then has to guess the colour of the hat they are wearing, and speak their choice out loud. They can only speak a single word, either 'white' or 'black'. The first prisoner to guess must be the prisoner standing at the back of the line. Then the prisoner in front of him, and so on. The last to speak will be the prisoner standing at the front of the line.

The jailor knows that this is a tough challenge. He will allow a maximum of one mistake, so long as the other nine guesses are correct. In which case, all ten prisoners will be released. However if there is more than one mistake, all the prisoners will be returned to their cells.

What is the best strategy the prisoners can adopt? What are their chances of getting free?

The answer is on the following page...

There are no tricks. Just mathematics.

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