Enigma 1363: Hat stand
17 December 2013
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From New Scientist #2522, 22nd October 2005
My logical friends Paul, Quentin, Rene, Steve and Taina were standing in a queue, but not in that order. After letting them look around at the queue I told them that they must now only look to the front and not look at anyone behind them.
From a bag containing three white hats and three black hats I placed a hat on each of their heads without anyone seeing the colour of their own hat (although everyone could see the hats ahead of them in the queue).
This left one hat in the bag. I explained all of this to them and asked them to say their name when they knew the colour of their own hat.
After a pause we heard the declarations “Rene” and “Steve” simultaneously and that led to a further declaration “Quentin”. No one else could work out the colour of their own hat.
In fact Paul’s hat was the same colour as the one in the bag, and Rene could see at least one hat of that colour.
What, from front to back, was their order in the queue?