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.
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
16 comments
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
Hey Chirag, Ur asnwer is correct but the way to solve is wrong. ~ Ankit
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
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.
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.
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
hi
and the next person to shoot would be obiviously No.3 cause he wouldnt get a confirmation from No.1.
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
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
OK, so person 2 shouts white, because he can see hat 3 is black and assumes his is different. Then person 3 shouts black because he also assumes person 1 couldn't differentiate between the colours. BUT I still don't understand how person 1 and/or person 4 work out which one is which! Please can someone enlighten me?
Answer is 2. As shown in the picture There is only one case. B W B | W 1 can not shout as he sees 2 & 3 wearing W & B resp So he may be wearing B OR W CAP. 2 shouts as he is sure A. 1 can see two different colour( W & B) hats on top of 2 & 3 resp. SO 1 is not sure which cap he is wearing. B. Since 3 is wearing B cap. 2 knows it for sure that he is wearing W cap. 2 shots first
Hey.... this problem can only be solved with an assumption that Man 2 knows that only one person is standing behind him..... there might also be a case that he might assume there is none behind him and the rest are on the other side of the wall.....there is no supporting statement in the question which clarifies this part.....So I doubt if the above solutions of all hold good......please share your opinion on this....
Man 1 can see man 2 and man 3 but is not able to tell what color hat he wears because man 2 and man 3 wear different color hats. So man 1 will not shout out. Then from man 1's reaction, man 2 is able to tell that he (man 2) and man 3 wear different color hats. Since man 3 wears black color hat, so man 2 knows he himself wears white color hat.
Man two can only shout first See man1 sees two different color so he cant make out which color is he himself wearing,This tells man2 that he and Man 3 are wearing different colors because he can see man three he will know he is wearing opposite color.
Man 4 will shout first because no one can see him, and after all he is a criminal he can break all the rule and he might be take his hat off and after see the color of his hat he can shout without any confusion instead of Man1 & Man 2 and other Man 3 no role.