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A fine old logic problem

  1. Nov 4, 2014 #1
    You visit a remote desert island inhabited by one hundred very friendly dragons, all of whom have green eyes. They haven't seen a human for many centuries and are very excited about your visit. They show you around their island and tell you all about their dragon way of life (dragons can talk, of course).

    They seem to be quite normal, as far as dragons go, but then you find out something rather odd. They have a rule on the island which states that if a dragon ever finds out that he/she has green eyes, then at precisely midnight on the day of this discovery, he/she must relinquish all dragon powers and transform into a long-tailed sparrow. However, there are no mirrors on the island, and they never talk about eye color, so the dragons have been living in blissful ignorance throughout the ages.

    Upon your departure, all the dragons get together to see you off, and in a tearful farewell you thank them for being such hospitable dragons. Then you decide to tell them something that they all already know (for each can see the colors of the eyes of the other dragons). You tell them all that at least one of them has green eyes. Then you leave, not thinking of the consequences (if any). Assuming that the dragons are (of course) infallibly logical, what happens?

    If something interesting does happen, what exactly is the new information that you gave the dragons?
  2. jcsd
  3. Nov 7, 2014 #2
    1. If there really is only one green eyed dragon: They don't unanimously already know that one of them has green eyes; the green eyed dragon had no idea. He/she now realizes that he must be the green eyed dragon, as none of his buddies have green eyes (something he surely would have noticed). What's more, the rest of the dragons don't know their own eye color, so they can't be sure that the GED (green eyed dragon) they know about is the only one, they could be a second and would never know it. End result: single GED turns into a sparrow as he realizes everyone else has blue eyes, so he must have green eyes.

    2. If there is more than one GED, no dragon can ever be certain it is them. Let's say Dragon X and Dragon N both have green eyes. D(x) can see D(n)'s eyes, and vice versa. However, while D(x) can be sure of the color of D(n)'s eyes, he can never be sure of the color of his own eyes, as there remains the possibility that D(n) is the only dragon with green eyes on the island. It would end here, but D(x) will see that D(n) does not sparrow-ify, so he must assume that D(n) has had the same thought process. They both realize their eye color, and promptly feather up at the next available midnight.

    3-ish. They never talk about eye color, and yet they have a rule which is based off of eye color. Not sure if this is meant to be part of the answer, but nothing would happen, as none of the dragons would ever know of the rule regarding eye color, so it's completely meaningless.

    Edit: I am stupid - didn't read the part about them all having green eyes.

    Reconsidering the question:

    Okay, this makes it a bit more complicated, but the same logic for point #2 should apply, right? The only difference is that D(a1)-D(d5) all have green eyes. Each night they can rule out a specific dragon, so at the 100th night they all find out what it's like to live as one of their less intimidating worldly counterparts.
    Last edited: Nov 7, 2014
  4. Nov 9, 2014 #3


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    Staff: Mentor

    http://www.thescienceforum.com/mathematics/6536-hardest-logic-puzzle-world.html [Broken]
    Last edited by a moderator: May 7, 2017
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