Expert: Rohit Agarwal - 1/28/2009

Question
I was given this riddle in one of my classes and I thought I had the answer and that I couldn't be wrong, but I was.

There are three students sitting in a circle so they can all see each other. One student is completely blind, another student has one eye patch, and the third student can see perfectly.

Their teacher tells them that there are 2 white hats and 3 red hats and places one of a random color on their head. They cannot see which hat they are wearing on their own head but can see the two other students' in front of them.

The students are told to answer which color hat they have on their head based on what they see.

So which student speaks up and knows what color hat they have on their head and how do they know?

Answer
There are three cases possible:
(W stands for White and R for Red)

Case I: 2W, 1R
In this case, the person with the red hat will see 2 white hats. He knows that 3W isn't possible, hence he must be wearing a red hat.

In case no one speaks up for some time, we can assume Case I doesn't hold true.

Case II: 1W, 2R
In this case,the people with the red hat will see 1W&1R hats. They know that 3W and 2W aren't possible. Hence, there's only one white hat, hence they must be wearing a red hat.

In case no one speaks up for some time, we can assume Case II doesn't hold true.

Case III: 3R
In this case, people will already assume Case III to be true, hence each person must be wearing a red hat.

Also, in case only one person declares that his hat is red, the other two must be white. Also, in case two people declare that their hats are red, the third one must be white.