What is the Colour of the Hat? - Answer

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What is the 

Colour of the Hat? 

- Answer

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The question was:

"There are 3 black hats and 2 white hats in a box. Three men (say A, B and C) have a random hat placed on their heads. They cannot see what colour hat they have.

The men are situated in such a way that A can see the hats on B and C's hats, B can only see the hat on C's head and C cannot see any hat.

When A is asked if he can identify the colour of his hat, he refuses. Next, when B is asked the same question, he refuses too. 

However, C, who couldn't see anyone else's hat, says yes and correctly identifies the colour of the hat on his head. 

How did he know and what was the colour of his hat?"



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Now coming to the Answer!

We know that there are 3 black hats and 2 white hats. 

A, who can see the colour of the hats worn by B and C, is unable to identify the colour of his own hat. If B and C both had white hats, A could have confidently identified his own hat as black. However, since he wasn't able to, now B and C know that either only one of them has white or both have black.

Next, B, who can see C's hat, is unable to identify the colour of his hat as well. If C had a white hat, B would have confidently identified his hat as black, for only one of them can have white (from A's response). However, since he couldn't identify his hat, C now knows that he must be having a black hat.

So the possible combinations are - 

A - Black, B - Black, C - Black
A - Black, B - White, C - Black
A - White, B - Black, C - Black
A - White, B - White, C - Black

Therefore, C's hat is black.

***

If you have got the same answer in any other way, then do let me know in the comments section!

If you have interpreted this question in another suitable way, then do let me know in the comments section again!

If I have made any significant errors, let me know about that too, and I will be sure to make the necessary changes!
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With Warm Wishes,
Lavanya


 

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