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The Stairs of Execution
Three people are standing on some stairs. They are each wearing a hat. They are only allowed to face forwards, so they cannot see the colour of their own hat, only the colour of the hat of the one or two people in front of them (depending in which position they are). The hats they are wearing have been chosen from a pile of two red hats and two blue hats.
All three men will be shot in one minute unless one of them shouts out (correctly!) the colour of their own hat. Who shouts out and how do they know the colour of their hat? (Work out the answer for the most difficult situation!)
Assume the easy situation when both the people at positions two and three are wearing the same colour hat. Who shouts out? Now assume the difficult situation where they are not wearing the same colour hat.
The person at position two knows that the person behind (in position one) wants to save their own life and would shout out if they knew the colour of the hat they were wearing.
The person at position two knows that the colour of their own hat is different to the person's in front of them (position 3) and therefore shouts out.
The person at position one can see two hats. If both hats are the same colour, their hat is clearly of the other colour (as there are only two hats of the each colour). Let's assume the difficult case, when they are not the same colour. Now, the person at position one cannot tell the colour of their own hat and so cannot yell out.
The person at position two (realising the situation of the person behind him!) will listen for them to shout out. When they do not, that person knows that they are wearing a different colour hat to the person in front of them, and so can shout out their own colour.
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