Quote from: fumblingperch on December 27, 2015, 10:22:48 AM

i think i got it now...

so, if 1 silver and 2 gold is not fair to the guy using the silver crown, because he can`t know if he`s using silver (2) or gold crown (3)

the option 2 isn`t fair too

the option 3 is the unique valid fair to all 3 guys

So all 3 guys using a Gold Crown..., and the clever guy who notice that and said he`s using a Gold Crown

Exactly.

Quote from: Jeremycoin on December 27, 2015, 02:09:59 PM

Wait what? my answer is correct?

You were the first to suggest the answer to be three golden crowns, so yes.

But you didn't explain on the second and more important part of the question.

Winners:

fumblingperch : 6 mBTC

loyce : 2 mBTC
Explanation of the first part correct.

Jeremyroll : 2 mBTC
Gives the correct answer first.

The original question:
The King's Wise Men: 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 one, two, or three blue hats, but not zero. 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 correctly 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. What did he say, and how did he work it out?

The solution:
Suppose that there was one blue hat. The person with that hat would see two white hats, and since the king specified that there is at least one blue hat, that wise man would immediately know the colour of his hat. However, the other two would see one blue and one white hat and would not be able to immediately infer any information from their observations. Therefore, this scenario would violate the king's specification that the contest would be fair to each. So there must be at least two blue hats.
Suppose then that there were two blue hats. Each wise man with a blue hat would see one blue and one white hat. Supposing that they have already realized that there cannot be only one (using the previous scenario), they would know that there must be at least two blue hats and therefore, would immediately know that they each were wearing a blue hat. However, the man with the white hat would see two blue hats and would not be able to immediately infer any information from his observations. This scenario, then, would also violate the specification that the contest would be fair to each. So there must be three blue hats.
Since there must be three blue hats, the first man to figure that out will stand up and say blue.

tl;dr
Scenario 1, One gold crown and Two silver crown. Does not take "very long" time to figure out and the contest would not be fair, for the one with the gold crown gets an advantage.
Scenario 2, Two gold crowns and One silver crown. The contest would not be fair, for the ones with the gold crown gets an advantage while the one with the silver cannot infer anything.
Scenario 3, Three gold crowns, as the only possible scenario remaining and that which satisfies all conditions.
Reference: https://en.wikipedia.org/wiki/Induction_puzzles#Solutions