4 Criminals problem : Logical Solution

Solve following :

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 hung. They agreed.

 

4Men-Problem.JPG

 

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

So to summarise :-
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 initally don’t know what colour hat they are wearing. They are told to shout out the colour of the hat that they are wearing as soon as they know for certain what colour it is.

They are not allowed to turn round 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?

 It should not take more than 5 minutes to solve.

~ Ankit  

Comments (10) left to “4 Criminals problem : Logical Solution”

  1. Mr.Chirag Mehta wrote:

    prob man wearing white || prob man wearing black
    Man1 50% 50%
    Man2 66% 33%
    Man3 50% 50%
    Man4 50% 50%

    so i think it man2 and white

  2. Ankit wrote:

    Hey Chirag,

    Ur asnwer is correct but the way to solve is wrong.

    ~ Ankit

  3. Mr.Chirag Mehta wrote:

    ITs not completely wrong The soln is based on logic and tht logic shows tht 66% chances are tht im right and 33% chances are tht im wrong So i can say tht my answer is scorrect in 2 out of 3 circumstances

  4. Vismay wrote:

    Chirags ans is write. But he can convince by saying :

    Since Man 1 can see 2 ppls hat, he wud shout only if both 2 & 3 are wearing the same hat. Since No.2 dont receive anything from him, he can conclude that since 2 & 3 have diff colors….. he’s not able to conclude.

    This makes man 2 to conclude tht his hat color is diff from tht of 3 viz. he shouts White.

  5. Vinod wrote:

    The man who calls out is no: 2

    Because after a short time, no: 1 has not shouted out what colour hat he is wearing. So no: 2 knows that he cannot be wearing the same colour hat as the person in front of him. If he was then no: 1 would see two black hats and would therefore know that his hat must be white.

    No: 2can confidently shout out that the hat he is wearing is white since he isn’t wearing the same colour hat as the man in front and the man in front is wearing a black hat.

  6. srinath wrote:

    Ankit,
    If you say what Chirag said was wrong, can you provide your solution to us. I find that the solution stated is proving to be more logical.
    Please advice

  7. ankit wrote:

    hi

  8. Anand wrote:

    and the next person to shoot would be obiviously No.3 cause he wouldnt get a confirmation from No.1.

  9. Sharad Agarwal wrote:

    Here is the answer of this question::

    2 shouts first. If 2 and 3 were wearing the same colored hats, 1 would know his hat color. Becasue 1 can only see two opposite colored hats, he can’t guess his own. When no one shouts anything, 2 knows that 1 must be seeing two different colored hats, and correctly chooses that his hat is the opposite of 3.

    ~SA

  10. rakendu sharma wrote:

    case 1
    1 2 3 4
    B B W W (FIXED)
    B W B
    W B B

    ———
    case 2

    W W B B(FIXED)
    W B W
    B W W

    GOING TRHU THE ABOVE RESULTS THE SECOND NO WILL WAIT FOR A WHILE FOR 1 PERSON TO RESPOND, IF HE DOESN’T HE WILL TELL THE OPPOSITE OF THE 3 RD PERSONS COLOR OF HAT.

    Rakendu

Post a Comment

*Required
*Required (Never published)
 

*
To prove you're a person (not a spam script), type the security word shown in the picture.
Anti-Spam Image