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| Acmlm's Board - I3 Archive - Brain Teasers - The King's Hats |
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rubixcuber Mole                    Since: 09-08-06 From: St. Louis, MO Last post: 6393 days Last view: 6393 days |
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| The King called the three wisest men in the country to his court to decide who would become his new advisor. He placed a hat on each of their heads, such that each wise man could see all of the other hats, but none of them could see their own. Each hat was either white or blue. The king gave his word to the wise men that at least one of them was wearing a blue hat - in other words, there could be zero, one, or two white hats, but not three. The king also announced that the contest would be fair to all three men. The wise men were also forbidden to speak to each other. The king declared that whichever man stood up first and announced the colour of his own hat would become his new advisor. The wise men sat for a very long time before one stood up and correctly announced the answer. How did he figure it out and what were the colors of the three hats? | |||
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Deleted User Banned     Since: 05-08-06 Last post: None Last view: 6284 days |
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| Because the other wise men had both white hats, thus he had the blue one? | |||
Ramon Bullet Bill Since: 11-25-05 Last post: 6283 days Last view: 6283 days |
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| I don't think so. He wouldn't have sat for "a very long time"...
Spoiler:
If he saw the others had a blue and a white one, he knew that if he had a white one, the one with the blue hat would know that he had a blue hat, because that one saw the other two had white hats. So he knew that if that one didn't know the color of his hat, then he had a blue one. If he saw the others had two blue ones, then he knew that if he had a white one, one of the other ones would know the color of their hat (see above). So he knew he had a blue hat. So the King either used 2 blue hats and a white one, or 3 blue hats. That's my guess...  I'm not sure though whether the "sat for a very long time" does mean that they had to think a lot because they couldn't see two white hats.  |
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rubixcuber Mole Since: 09-08-06 From: St. Louis, MO Last post: 6393 days Last view: 6393 days |
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| Ramon is very close. It is possible to determine the color of all 3 hats from the information given. And the sat for a very long time isn't especially important. | |||
Jagori 150 Since: 11-17-05 Last post: 6285 days Last view: 6284 days |
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| He could tell that nobody saw two white hats, or that person would have immediately known that his own hat was blue. This means there were at least two blue hats.
Since these were all wise men, the guy assumed the other two figured this out as well. If any one of them saw a white hat, he'd know that his own hat was blue. Again, since nobody answered, the guy figured that nobody saw a white hat. This means all 3 hats are blue, and therefore he knew the color of his own hat. |
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rubixcuber Mole Since: 09-08-06 From: St. Louis, MO Last post: 6393 days Last view: 6393 days |
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| Yey! A cookie for Jagori! | |||
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Alastor Fearless Moderator Hero  Since: 11-17-05 From: An apartment by DigiPen, Redmond, Washington Last post: 6283 days Last view: 6283 days |
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| Uh. There is a solution that is so much simpler than that.
The king announced that the contest will be fair to all men. Since anyone with a white hat is at a disadvantage due to how everything is set up, and since it is impossible for all men to be wearing white hats for the same reason, all men must be wearing blue hats. |
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Xkeeper Took the board down in a blaze of glory, only to reveal how truly moronical ||bass is. Since: 11-17-05 From: Henderson, Nevada Last post: 6284 days Last view: 6284 days |
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Originally posted by Alastor the Stylish You get the jumbo, fresh, chocolate cookie. |
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Deleted User Banned Since: 05-08-06 Last post: None Last view: 6284 days |
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| But, wouldn't Alastor the Stylish's solution make all three men figure that out at the same time?
... Just kidding, enjoy the cookie 
EDIT - Or make it that when 2 of the wise men were figuring out the complex version, the other wiser one figured out the simpler one. (edited by Uly on 09-24-06 11:52 PM) |
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rubixcuber Mole Since: 09-08-06 From: St. Louis, MO Last post: 6393 days Last view: 6393 days |
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| Only if they all thought at the exact same speed. The first one to figure it out wins. The solution I had did make use of the contest being fair, but it wasn't really that much simpler. The rigorous logic for "anyone with a white hat is at a disadvantage due to how everything is set up" isn't really that much easier. | |||
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Deleted User Banned Since: 05-08-06 Last post: None Last view: 6284 days |
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Originally posted by rubixcuber Not easier, SIMPLER to explain, my mother and sister agree as they were having problems to understand the original solution. |
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