PUZZLES

Please post some interesting puzzles in this thread and let other hubbers find the answer by their intelligent brain.

Let me begin with a puzzle:

Three Gentlemen

There are three men standing in a row. All are wearing hats. The hats were chosen from a set of three black and two white hats. Nobody knows which color he himself is wearing. But the man at the back knows the colors of other men's hats and the man in the middle knows the color of first man's hat.
The last man was asked whether he knew the color of his own hat. "No",he said.
The man in the middle was asked the same question and he too said,"No."
Now the first man was asked the same question and he said,"Yes,I know."
Did he really know? If yes, what was the color? and how did he arrive at the answer?

Can anyone crack this out?

Quote:

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Originally Posted by sgokulprathap

Please post some interesting puzzles in this thread and let other hubbers find the answer by their intelligent brain.

Let me begin with a puzzle:

Three Gentlemen

There are three men standing in a row. All are wearing hats. The hats were chosen from a set of three black and two white hats. Nobody knows which color he himself is wearing. But the man at the back knows the colors of other men's hats and the man in the middle knows the color of first man's hat.
The last man was asked whether he knew the color of his own hat. "No",he said.
The man in the middle was asked the same question and he too said,"No."
Now the first man was asked the same question and he said,"Yes,I know."
Did he really know? If yes, what was the color? and how did he arrive at the answer?

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The third man knew that the second man knew that the first man did not see two white hats (if he had he would have said he- the 1st man- would have known his hat is black). The second man thus figures that between himself and the 3rd man there i at least one black hat. If the 3rd had a white hat on, man 2 would have been able to deduce that his hat is black. The fact that he couldn't conclude that tells the 3rd man that his hat is black.

Mustn't claim I solved this like that. This is famous classroom example in Information Theory.

Why a new thread for 'puzzles'? The old one is going strong, isn't it?

Please continue here
http://www.forumhub.mayyam.com/hub/v...=6263&start=45