3 heads 5 hats - puzzle

[gc791188]

I got this one long back.

In a small village in the middle of nowhere, three innocent prisoners are sitting in a jail. One day, the cruel jailer takes them out and places them in a line on three chairs, in such a way that man C can see both man A and man B, man B can see only man A, and man A can see none of the other men. The jailer shows them 5 hats, 2 of which are black and 3 of which are white. After this, he blindfolds the men, places one hat on each of their heads, and removes the blindfolds again. The jailer tells his three prisoners that if one of them is able to determine the color of his hat within one minute, all of them are released. Otherwise, they will all be shot. None of the prisoners can see his own hat, and all are intelligent. After 59 seconds, man A shouts out the (correct) color of his hat!

What is the color of the hat man A is wearing?

 

[wait485wait]

A wears white hat

 

[Marwari]

Well that's the only possible answer given that the reply came from "A". BUT as stated in the puzzle "and all are intelligent", in that case why it took "A" 59 seconds to reply???

Originally posted by wait485wait
A wears white hat

 

[lamborghini]

A is wearing white

that is why B said nothing - he can have either black or white

and that is why C said nothing he sees black and white or both white in front of him

as B and C say nothing it takes a 57 seconds to realize he is wearing white and 2 seconds to say it

 

[wait485wait]

I explain my reasoning:

The possible combinations of hats of A and B are:
1. B, B
2. B, W
3. W, B
4. W, W

A thought as follows:
For C, in situation 1 he will know everything, but confuse in 2,3,4.

For B, if he saw A has Black hat, and C does not know anything, B will know he wears White hat. so situtation 2 not exist.

Now only possible is 3 and 4. A knew he had white hat. He wait edfor the last second to say it to give B and C enough time to think.

 

[Marwari]

lamborghini,

as per your logic, A could be wearing Black and B could we wearing white also!!! Isn't it?

Originally posted by lamborghini
A is wearing white

that is why B said nothing - he can have either black or white

and that is why C said nothing he sees black and white or both white in front of him

as B and C say nothing it takes a 57 seconds to realize he is wearing white and 2 seconds to say it

 

[ric2]

A wears WHITE for sure. This is a famous muddy-childrin algorithm in distributed computing of computer science. Too easy.

3 rounds are needed to detect the color of A.

Round 1: Since C can see both A and B, the silience of C implies that A and B can not be both black. Otherwise, C will tell that his hat is WHITE. This become the COMMAN KNOWLEDGE among three prisoners after this round.

Round 2: Since B can see A, the silence of B implies that A can not be Black. Otherwise, B can tell that his hat is white since A and B can not be both black.

Round 3: The silience of B and C makes A believe that A must be WHITE from the common knowledge drawn from Ruond 1 and 2.