## Tuesday, 21 April 2015

### Solution to the hats logic problem

Here is the solution to the easier logic problem in my previous post:

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 ...