# 3 Men and 5 Hats – Brainteaser

### Interesting Brainteaser

3 innocent prisoners were 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 executed. 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 man A‘s hat, and how does he know?**

suhaaaaan dont you study maths

i know the thing may be A must have peeped his eyes through the blind folding cloth

There are only 2 black hats. If both A and B were wearing black hats, then C would know for sure that he was wearing white.

But since C could not guess the colour, it means that not both of A and B are wearing black.

This means,

Either, one among A and B is wearing black and the other is wearing white

Or, both A and B are wearing white.

Now, if A was wearing black, B would know for sure that he was wearing white (as both A and B can’t be wearing black).

But since, B did not have an answer, it means A was not wearing black.

Therefore, A was wearing white hat, which he correctly answered.

A IS HOLDING BLACK

POSIBLITIES

A IS HOLDING WHITE BCOZ

A- B C

W W ======IN THIS C CAN PREDICT SO NOT POSIBLE

W B IN THIS C CANT PREDICT BUT B CAN AS C IS SILENT AND A IS HAVING WHITE

SO B OR C CAN PREDICT ONLY WHEN A IS HAVING WHITE SINCE THEY DID NOT RESPOND HENCE A WILL COME TO KNOW THAT HE IS WEARING WHITE

brilliant!!!!!!!!!!!!!!!!

Since “C” can see the users “A” & “B”, if the hat of ‘A’ & ‘B’ is white, he can say that the hat which he wears is Black as there is only two white hat and the rest three is black. When “C” confirms that he is wearing black, “A” & B can be sure that they are wearing White hat. As stated, all three are intelligent.

Though A cannot see but can very well ask B about the colour of his hat as there is not such condition in the question that they cannot ask each other. B’s replies is white. Hence A is wearing white. Answer is WHITE.

A is wearing white hat

as B and C cant predict becouse

C sees A AND B wearing white and dont know about his colour

B sees only A wearing white cant predict his colour’

so A can predict that he wear a white hat

Very Simple!!

A will see B’s hat.

B will see C’s hat

C will see A’s hat

kya baat kar diye cherry bhai……..!!!!

As informed in the puzzle “all are intelligent” the possibilities are as follows:

A B C

Black Black White C would have declared that he is wearing White

Black White ?(B/W) If C remains silent B can say he is wearing white

White White ?(B/W) C & B are silent hence A says he is wearing white

White Black ?(B/W)

Hence A is wearing white hat.

A is wearing white hat…..this is because if C didnt commented dat means the other two were weraing white hats which confused him…..

Also if A was wearing black hat B could have easily deduced dat he is wearing a white hat based on C’s answer but he himself was confused…….

Due to these reasons A waited till 59 seconds so he could make sure if anybody can comment and answered dat he is wearing a white hat.

If it is BB for A&B then C’s hat must be White. C didn’t speak coz A&B have either WW or WB or BW. Now A & B are left with below choices.

A B

W W

W B

B W

IF A is holding Black hat then B’s hat must be White. B Didn’t speak coz A is holding White hat and B may have either White or block.

Now the choice left is A having White hat.

Shalin.. there are no red hats in the question.

C won’t know his hat if he sees A & B either wearing both white or one white one black

now B khows C didn.t answer so he is sure that the colour of his hat & A’s is both white or 1 blck 1 white

now B won’t b able to answer if he sees the colour of a’s hat to b white

this A khows

so he answers the ques

C dint say nythng ths means A n B hav hat combinations as WW or WB or BW

now B dint say nythng ths means A is nt wearng black…….cz A==Black means his hat has to b White.This shows A wearng White

Thus A’s hat==White:)

Shalin.. there are no red hats in the question.

HES WEARING RED HAT.

IF C SEES A & B WEARING BLACK HATS , HE COULD SAY HE IS WEARING RED HAT. HE DOESNOT SAY. SO A & B BOTH ARE WEARING RED HATS OR ONE OF THEM HAS A BLACK HAT.

IF B SEES A WEARING A BLACK HAT , HE CAN SAY THAT HE HAS A RED HAT. BUT EVEN HE IS NOT ABLE TO DECIDE.

SO A MUST BE WEARING A RED HAT.

buddy bhai, where r u bringing this red hat from???

what an idea sirji