One Man & His Desk : notes for recordings
Here are a just a few notes to accompany the recorded segment for CNI Radio on October 14th 2009
Three men, five hats puzzle (original author unknown)
There are 3 men and five hats, three red and 2 white.
Each man is wearing a hat and the other two are hidden from view.
Each man can see the other two but cannot see his own hat, so picture the 3 men standing in a triangle.
Man A is asked “do you know what colour hat you are wearing?” to which he replies ‘No’
Man B is asked “do you know what colour hat you are wearing?” to which he replies ‘No’
Man C is asked “do you know what colour hat you are wearing?” to which he replies ‘Yes’
And before you get too excited and say that men A and B are both wearing white hats, therefore man C knows he is wearing a red hat, I can tell you that both man A and man B are wearing red hats.
Solution
Man C says, "let's suppose I am wearing a white hat".
"Man B would know from Man A's response that Man A cannot see two white hats, therefore he (man B) would know he was wearing a red hat".
So man C can deduce from the answers of man A and Man B that he cannot be wearing a white hat, therefore he is wearing a red hat.