AboutRohit Agarwal Expertise I can answer questions related to numbers and logic easily. However I sometimes face problems when solving questions that require a lot of creative thinking. I am not good at puzzles which involve a play with words, so please don't ask me to solve such puzzles for you.
Experience I have read a couple of good books containing puzzles and can now claim to have an "expert" in this field. I have been invited to become a member of Mensa.
Organizations INDIAN INSTITUTE OF TECHNOLOGY, DELHI
Education/Credentials Currently doing Dual Degree (B.Tech M.Tech) in Electrical Engineering Department from INDIAN INSTITUTE OF TECHNOLOGY, DELHI
Awards and Honors Numerous certificates recognizing my ability in Mathematics and Logical Thinking
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.
