In honour of Patricia C. Wrede

Today at work we bandied about an interesting logic puzzle, and understanding the answer totally blew my mind. It goes like this:

All dragons have either red eyes or green eyes. If a dragon ever knows its own eye color, it will die on the next stroke of midnight. Moreover, dragons, like all mythical beasts, are perfect logicians. That is to say, if it is possible to infer a fact from what is already known, dragons cannot help but make this deduction.

There is a town in which n dragons live, where n is small enough that every day, every dragon interacts with every other dragon. One day, an oracle, renowned for always speaking the truth, comes to the town. She gathers together all the dragons, looks at each one, and then loudly proclaims, “At least one dragon here has red eyes!”

  1. What happens in the town?
  2. Suppose that at least three dragons have red eyes. Now, not only does every dragon already know that at least one dragon has red eyes, they also know that every other dragon knows this, too. What information does the oracle add that the dragons didn’t have already?
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4 Comments

  1. sneaselcouth says:

    I didn’t know you read Wrede! I should go back and read some of her work – I really dont remember it at all but I remember loving it as a kid.

    Well doesnt this puzzle have me frustrated…

    • Alan says:

      Yeah, Dealing With Dragons and the rest of the series were wonderful books, and I really enjoyed reading them when I was younger. Interesting fact: Wrede lives in Minneapolis, and is friends with Lois McMaster Bujold.

      This puzzle is much harder than it looks; three friends and I discussed it for about an hour before we all agreed on an answer. so don’t worry if you don’t get it right off. For the first part, start small and try to work up a pattern. What happens if there’s 1 dragon in the town? What about 2 dragons? 3? Remember that every day, all surviving dragons learn which dragons died the night before, and which dragons didn’t die. For the second part, suppose there are 3 dragons in town, and they all have red eyes. What happens before the oracle arrives?

  2. eve_wyoming says:

    Lovelovelove Patricia C Wrede. Also found a book of short stories by her that I enjoyed while I was home last Christmas break. SO glad to see you liked her as well!

    In other news, I don’t really think oracles should do that. Poor dragons.

    And in other other news, I really like hearing about everything you’re up to, even if I don’t understand about half of it…
    MUAH

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