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Coloured Hats

  1. Aug 3, 2004 #1
    We have a box in which there are 2 white and 3 blue hats.
    The light is turned out and 3 boys take at random one hat each and places it on his head.
    The light is turned on again.
    Each boy can see the colour of the hat of each of his colleagues but not his own.
    The first boy is asked the colour of the hat he is wearing.
    He thinks and says he does not know.
    The second boy is asked the colour of his hat.
    He thinks and says he does not know.
    The third boy is now asked and he says 'Blue'.
    What was the logic of the third boy's reasoning?
    I believe the logic will also apply to red and green hats.
  2. jcsd
  3. Aug 3, 2004 #2


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    First boy could not have seen 2 Ws or he would have known he was B. So, one of either 2 or 3 is B.

    Second boy knows this. So, if he sees a W on 3, then he will know that he is a B. The fact that he does not know means that 3 is not W, hence B. :biggrin:
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