Solving a Logical Puzzle through Critical Thinking and Deduction

Mattamkiran
Hi all,

Here is a small puzzle for you as my gift on this weekend. Work on it and think about it before you scroll down completely for the answer.

PUZZLE:

4 criminals are caught and are to be punished. The Judge allows them to be freed if they can solve a puzzle. If they do not, they will be hanged. They agreed.

The 4 criminals are lined up on some steps. They are all facing in the same direction. A wall separates the fourth man from the other three.

So to summarize: Man 1 can see men 2 and 3. Man 2 can see man 3. Man 3 can see none of the others. Man 4 can see none of the others.

The criminals are wearing hats. They are told that there are two white hats and two black hats. The men initially don't know what color hat they are wearing. They are told to shout out the color of the hat that they are wearing as soon as they know for certain what color it is.

They are not allowed to turn around or move. They are not allowed to talk to each other. They are not allowed to take their hats off.

Who is the first person to shout out and why?

PS: There is no trick to the question, just logical deduction.

The solution to the puzzle:

The man who calls out is Number 2.

Why?

After a short time, Number 1 has not shouted out what color hat he is wearing. Because of this, number 2 knows that he cannot be wearing the same color hat as the person in front of him. If he was, then number 1 would see two black hats and would therefore know that his hat must be white.

Armed with the knowledge that he isn't wearing the same color hat as the man in front and the man in front is wearing a black hat, number two can confidently shout out that the hat he is wearing is white. Easy, wasn't it!

Regards,

Kiran.
Mattamkiran
Yeah... It is really one of the best puzzles I have ever come across. The simple way to find the solution for this is to picturize their postures in your mind or draw them on a piece of paper with the information given. You really need a pen and paper to solve these kinds of puzzles.

Regards, Kiran.
Mattamkiran
Hi Rupa,

I have puzzles like this, but they are scattered all over my mail IDs. I need to search for them, but I am not getting time due to my heavy schedule. I will post them once I find time to search and locate them.

Regards,
Kiran
hrx_pbs
Hi Kiran,

The logic of the solution is perfect. However, it has been based on two assumptions that are not provided in the question, namely:

1. After a short time, Number 1 has not shouted out what color hat he is wearing.
2. The man in front is wearing a black hat.

It has not been stated that Number 1 does not say anything until some time has passed or that Number 3 is wearing a black hat. Conclusions can only be drawn from the data provided, isn't it...?

These two assumptions have been made without any reasoning behind them.

Regards,
Smita
sacalaarun
Same question was asked by my professor, but we are not able to answer it. I am happy that I finally got the answer from you. Thank you, post more. Bye bye, Arun Kumar SG.
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