*A, B and C are told that in a bag there are 3 red hats and 2 blue hats. B is blindfold, so is unable to see anything. One hat is put on each person's head and they have to work out what colour hat they are wearing. A and C can see the hats on the other two, but none of them can see their own hat.*

*A says: I do not know what colour my hat is.*

*C says: Nor do I.*

*B says: Then I am wearing a red hat.*

*How did B work that out?*

B considers the possibility that the hat on her head is blue.

Assuming this, when A says, I do not know what colour hat I am wearing, it follows that C must be wearing a red hat: because if C were wearing a blue hat, A would see two blue hats and know that her own hat would have to be red.

But C would also work this out! So C would be able to deduce that she is wearing a red hat.

But, even after A has spoken, C does not know what colour her hat is.

So B deduces that she cannot be wearing a blue hat.

Hence she knows that she is wearing a red hat.

Cheryl's birthday to be disclosed in my next post ...

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