nan1234
On The Way Up
Joined: 23 Jul 2007
Location: Chicago Area
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| Posted: Thu Jan 17, 2008 6:15 pm Post subject: Black White Hat Game |
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A king invited the smartest three people to his palace to play a game. He shows them 5 hats, 2 are white, the remaining 3 are black. He ties the three players to a chair and blindfolds them. The king then hides the white hats and places the 3 black hats on the head of each player. As the three players are blindfolded, the king tells them that he has placed a hat on each player and that after he removes the blinds, the player must guess correctly the hat he is wearing- the time limit is one hour and the punishment for an incorrect guess or no guess is death. The punishment for looking at your own hat or communicating with another player is death as well.
What will happen?
(This is a pure logic question, not another interview question)
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Frank
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| Posted: Thu Jan 17, 2008 6:29 pm Post subject: |
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Just to clarify, can they look at each others hats?
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nan1234
On The Way Up
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Location: Chicago Area
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| Posted: Thu Jan 17, 2008 6:44 pm Post subject: |
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Yes.
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nan1234
On The Way Up
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Location: Chicago Area
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| Posted: Thu Jan 17, 2008 8:25 pm Post subject: |
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Okay. Let me give some hint.
Suppose I am one of the three people. Other two are named X and Y.
If my hat is white, X will see it. X, then, assume his hat is white, and if so, Y will immedaitely guess that his hat is black. But since Y is hesitating, so X knows that his hat is black. But X is hesitating too. That means X doesn't know the color of his hat. Therefore, my assumption is wrong.
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Frank
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| Posted: Thu Jan 17, 2008 9:05 pm Post subject: |
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How about this Nan:
- X looks at Y , Z and sees black hats
- X thinks:
"If I (X) had a white hat Y would gauge Z's reaction, If Z hesitated then Y would have known he (Y) didn't have a white hat because Z would have said he (Z) had a black hat right away. Therefore Y deduces he (Y) has a black hat. BUT Y has not deduced this yet so therefore I (X) have a black hat"
X, Y and Z deduce the same. They subsequently deduce by each other's prolonged hesitations that a white hat does not exist on any of their heads (the white hat scenario).
I think a lot depends upon the hesitation period before someone deduces that all 3 must be wearing black hats. If someone answers to soon one of the three may deduce the 'white hat exists' scenario and skew/corrupt the whole outcome. And someone would die!
Am I making sense or totally off the mark?
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dirt2diamonds
Showing Great Promise
Joined: 31 Oct 2007
Location: Mississippi
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| Posted: Fri Jan 18, 2008 12:12 am Post subject: |
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O.K The answer is.........
I give up.
I would answer last to stack the deck in my favor.
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nan1234
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| Posted: Fri Jan 18, 2008 1:00 am Post subject: |
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Haha, you got it right, Frank! Excellent analyse.
They all wait until last minute and shout "Black!"
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Frank
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| Posted: Fri Jan 18, 2008 1:11 am Post subject: |
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Woohoo! And it only took me 20 minutes and some black and white objects for visualisation   Good one Nan.
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