Question 335127
here's the deal:


There are 3 red hats and 2 blue hats.


A sits behind B sits behind C


All look forward.


A says he doesn't know what hat he is wearing.


B says he doesn't know what hat he is wearing.


C says he knows.


The color of the hat C is wearing has to be red.


Here's how:


Assume C has a red hat on.


This means that B could have a red or a blue hat on.


A looks and sees either 2 red hats or 1 blue and 1 red hat.


A can't determine what color hat he has on because he cannot know unless both B and C had a blue hat on, which they don't.


So A doesn't know which means that B and C either have 1 red and 1 blue or 2 red.


B looks at A and sees a red hat.


This means that B could have a red hat on, or a blue hat on, so he doesn't know either.


C knows that the only way A would know is if both B and C had blue hats.


C also knows that the only way B would know is if C had a blue hat on.


C concludes he has a red hat on.