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Math Help - King's daughter can't decide who to marry

  1. #1
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    King's daughter can't decide who to marry

    The king's daughter had three suitors and couldn't decide which one to marry. So the king said, "I have three gold crowns and two silver ones. I will put a gold or silver crown on each of your heads. The suitor who can tell me which crown he has will marry my daughter." The first suitor looked around and said he could not tell. The second did the same. The third suitor said, "I have a gold crown." He is correct, but the daughter was puzzled: This suitor was blind. How did he know?
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  2. #2
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    Quote Originally Posted by novice View Post
    The king's daughter had three suitors and couldn't decide which one to marry. So the king said, "I have three gold crowns and two silver ones. I will put a gold or silver crown on each of your heads. The suitor who can tell me which crown he has will marry my daughter." The first suitor looked around and said he could not tell. The second did the same. The third suitor said, "I have a gold crown." He is correct, but the daughter was puzzled: This suitor was blind. How did he know?
    Spoiler:

    If the first or second sees two silver crowns, he would conclude that he would have a gold crown. Since he did not, the other two knows that there is at least one gold crown in between them.

    Suitor 3 also knows that

    • if suitor 1 and 2 both had silvers, he would have a gold one.
    • if suitor 1 had a gold and 2 had silver, 3 must have a golden one or suitor 1 would have concluded that he had a golden one
    • if suitor 2 had a gold and 1 had silver, 3 must have a golden one or suitor 2 would have concluded that he had a golden one.
    • if suitors 1 and 2 had a gold, 3 must also have a gold, for if he had silver, suitor 2 would know he has a gold crown (since suitor 1 must not have seen 2 silvers, suitor 2, seeing the silver on 3's crown would know he has gold)

    I hope this solution is somewhat coherent.



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  3. #3
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    Hello, novice!

    A slightly different explanation . . .

    Spoiler:

    If #1 saw two silver crowns, he'd know he had a gold crown.
    Since he didn't know, he must have seen at least one gold crown.

    #2 knows this, so if he saw a silver crown on #3,
    he'd know that he (#2) must have a gold crown.

    But he didn't know, hence he must have seen gold crown on #3.

    And that is how blind #3 deduced that he had a gold crown.



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  4. #4
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    Ha ha that was fun.
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  5. #5
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    Of course, 3 would know he had a gold crown as described above, but if the other suitors were a bit thick, how would he know that it wasn't possible for one of them to deduce their crown even if they said they couldn't?
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