a brand new brainaching puzzle

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a brand new brainaching puzzle

Post by dante » Thu Apr 16, 2009 2:36 pm

Hello everyone,

I'm not a professional in asking puzzles but here's one more I like anyway. This time I've rearranged the wording of the puzzle I've found on the net to my taste and I hope it is a clear and unambiguous wording of the puzzle.

Three people are seated one behind the other, so that the first person can see neither of his colleagues, the second can see the colleague in front of him an the last can see both colleagues in front of him.

Each has a hat placed on his head from a selection of 5 hats, 2 of which are white and 3 of which are black. None of the three is allowed to see the color of the hat on his own head of course.

They are each asked to say the colour of the hat on his own head. After some time the first person in the line, who cannot see the other two persons, says the colour of his hat, and his answer is correct.

What is the colour of his hat and how did he know that ?
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Re: a brand new brainaching puzzle

Post by Wizard of Oz » Thu Apr 16, 2009 4:50 pm

.. if they were Michelin chef's hats now that would be worth puzzling over ..

WoZ planning a gourmet tour
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Signature: "The question is," said Alice, "whether you can make words mean so many different things."

Re: a brand new brainaching puzzle

Post by dante » Fri Apr 17, 2009 6:17 pm

Ok, since nobody is interested in solving this puzzle here's the solution . Here's why only the first guy knew the colour of the hat on his head.

He reasoned like this : if the third guy in the line ( who sees other two colleagues) saw two white hats he would say so immediately, knowing that on his head is a black hat (since there were only two white hats ). Since he's silent that can only mean that he doesn't see two white hats in front of him.

The guy in the middle also knows that the third one doesn't see two white hats or otherwise he would say that he has a black hat on his head. So, if this middle guy saw a white hat on the head of the first guy he would know that on his head is a black hat and he would say so. But he is silent too, and that only can mean that he doesn't see a white hat in front of him.
That's how the first guy in the line knew that he has a black hat on his head.
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Re: a brand new brainaching puzzle

Post by Shelley » Sat Apr 18, 2009 12:32 am

I like this -- never would have figured it out -- I think it's sneaky, though.

My limit on these things is the one about the dark room with all the socks.
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Re: a brand new brainaching puzzle

Post by dante » Sun Apr 19, 2009 8:02 pm

I'm glad you liked the puzzle Shelley :)
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End of topic.
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