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  1. Aug 16, 2009 #1


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    an emperor judged three prisoners to be executed, but he gave an exception to whomever gives the correct answer to his riddle will be set free. first, he asked them to line up, in a way where the first can’t see the two behind him, the second can see the one on front of him, and the third can see both [they choose their positions, the emperor didn’t interfere]. he then brought four hats, two black ones and two white, he puts a white hat on the first person’s head [remember the first person can’t see what’s on his head, but the other two behind him do], and puts another two hats on the others’ heads and he hides the forth hat [none of them see/know what color is that hat], now only one of them is 100% sure of his hat color, who’s that person and what color is his hat???
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  3. Aug 16, 2009 #2


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    The only way one person can be 100% sure of his hat color is if he sees two hats of one color; he therefore knows he has the other color. The only person who can see two hats is the last man. Since we know the first man has a white hat, the second man must also have a white hat; ergo, the third man wears a black hat.
  4. Aug 16, 2009 #3


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    hint: the emperor is an honest man!

    that would be a direct help from the emperor to the third person, don't you think?
  5. Aug 17, 2009 #4
    If the first two have the same colored hats, the third instantly knows the color of his hat is not that color. If not, the second would be the only one to have certainty of knowledge of the color of his hat, because if the third person says nothing, this means that the colors must be different. Since the second man knows the color of the hat on the first, he then knows that his hat is black.

    This is way too simple. :(
  6. Aug 17, 2009 #5


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    didn't say it's hard, though it could’ve been if I didn’t mention the 100% sure thing, and of course without the hint :biggrin:
  7. Aug 18, 2009 #6
    Actually, the "100% sure" part is pretty presumptuous. If the first two people received white hats, and the 3rd prisoner was rather dumb, or if the 3rd prisoner wanted the 2nd prisoner to incorrectly guess that his hat was black, the 3rd prisoner could just sit there and wait for 5 minutes before saying anything, even though he has all the data necessary to guess his own hat color.

    For that matter, we're assuming that the prisoners are "100% sure" that the emperor told them how many of each color hat there would be, and that he was telling the truth when he did so. The emperor could have lied and simply given them all white hats.

  8. Aug 21, 2009 #7
    what if the third person sees 2nd guy wearing a black hat and the 1st a white.

    edit nevermind.
  9. Aug 27, 2009 #8
    Ya. this riddle as stated is impossible. Nowhere in the riddle do you say that the prisoners are then expected to speak out loud, so that the other prisoners can hear, in real time if they know what hat they have. In fact you don't say anything about the prisoners being able to communicate or being able to see/hear if another prisoner is answering the emperor.
  10. Aug 27, 2009 #9
    ITS THE MIDDLE GUY, or the last guy

    IF guy 1&2 were wearing hats of the same color guy 3 would know and say "i have the answer"
    but if he dosn't - that because guy 1&2 wear hats of a different color, so the middle guy says "i have the answer" and knows his hat is the opposite color to the guy in front
  11. Aug 29, 2009 #10
    Last guy raises hand and says BLACK hat? lol
  12. Aug 31, 2009 #11
    The only person who is sure, it seems, is the Emperor.

    The first man may have a white hat, but this allows that the second man has a black hat. Leaving the 3rd man with the possibility of having either color.

    Or so it seems
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