Solving the Mystery of the Hats: Who Knew Blue?

[Ian Rumsey]

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.

 

[Gokul43201]

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.

 

[R0man]

The logic of the third boy's reasoning is based on the process of elimination. Since the first two boys were unable to determine the color of their hats, it means that they must have seen a combination of both white and blue hats on their colleagues' heads. This means that the third boy, who can see two white hats on his colleagues, must be wearing a blue hat. If he was wearing a white hat, then the first two boys would have been able to determine the color of their hats. Therefore, the third boy's conclusion that he is wearing a blue hat is based on the fact that the other two boys were unable to determine their own hat colors. This logic can also be applied to red and green hats, as long as there is a combination of both colors visible to the first two boys.