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100 Green Eyed Dragons

10 years ago

Taken from io9's puzzle series, which I just found, but which has been around since October 2014. So far, I haven't solved any of the four puzzles I've tried. Grrrr. No cheating.

http://io9.com/can-you-solve-the-hardest-logic-puzzle-in-the-world-1642492269

 

Sunday Puzzle #1: 100 Green-Eyed Dragons

UPDATE: SOLUTION

This week's puzzle is an old favorite of mine. It's been around for a long time, and existed in various forms, but the version we'll be solving I originally encountered in a handout given to physics students at Harvard, and is called "Green Eyed Dragons."

XKCD's Randall Munroe tells a version of this puzzle, called "Blue Eyes," that he's dubbed "The Hardest Logic Puzzle In The World." The puzzle is fundamentally identical to Green-Eyed Dragons, but Munroe's version includes some wording that provides what I think is a fairly big clue, so if you find yourself struggling with the dragons, head on over to XKCD and give his rendition a go. Here, now, is what I believe to be the most challenging version of the puzzle:

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 tearfulfarewell you thank them for being such hospitable dragons. Then you decide to tellthem something that they all already know (for each can see the colors of the eyes ofthe 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?

I will make the same closing points here that Munroe does: This is not a trick question. There's no guessing or lying or discussion by or between dragons. The answer does not involve Mendelian genetics, or sign language. The answer is logical, and the dragons are perfectly logical beings. And no, the answer is not "no dragon transforms."

We'll be back next week with a breakdown of the solution – and a new puzzle!

100 Green Eyed Dragons

10 years ago
Not sure, but what about the water? Wouldn't they all be able to see their eyes in the reflection? I mean they're on an island.

100 Green Eyed Dragons

10 years ago
It would depend on how clear the water is. If you live in Australia, you've probably never seen the Atlantic, which is as murky and grey as the pacific is clear and blue.

100 Green Eyed Dragons

10 years ago

They can't see their own eyes; there are no mirrors of any kind on the island. The water is all murky and dark and non-reflective.

100 Green Eyed Dragons

10 years ago

They haven't seen a human in centuries. They are all blind.

Edit: Nevermind. Apparently, they could see the eyes of the other dragons.

100 Green Eyed Dragons

10 years ago
"infallible logic"

100 Green Eyed Dragons

10 years ago

There's no trick question here, there is nothing to do with Mendelian genetics, etc. The dragons are all completely logical.

100 Green Eyed Dragons

10 years ago
Yeah, I saw the solution, so I can't discuss it anymore here. I feel stupid now.

100 Green Eyed Dragons

10 years ago

That's how I felt. Look at some of the other puzzles. The newest one has no solution yet. It's a pie one.

100 Green Eyed Dragons

10 years ago
My curiosity also outweighed my perseverance.

100 Green Eyed Dragons

10 years ago

Yeah, that keeps happening to me. Check the newest one, there is no solution posted yet.

100 Green Eyed Dragons

10 years ago
Interesting, I saw how to get the seven on the third slice, but I'd have to take awhile to maximize six slices. I should probably finish my writing quota for the day before I lose myself in this though.

100 Green Eyed Dragons

10 years ago

None of them turn into sparrows, because not even other dragons want to tell a flying, magic-casting, firebreathing lizard with axe-blocking armor and venomous breath that they have to give it up in order to become a pussy-ass bird for the sake of age-old racism.

100 Green Eyed Dragons

10 years ago

Maybe... All of them transform?

Because if they all see each-other with the green-eye, then they know that everybody has green eyes except for them. If the man tells them that at least one of them has green eyes ('at least' means potentially more than one), and they all know that all the other dragons have green eyes, then maybe they'd deduce that the human isn't just saying what he said randomly, and each of them will begin to wonder about themselves and finally reason that the human was indeed referring to them.

I dunno, don't like my logic either.

100 Green Eyed Dragons

10 years ago

I guess maybe I don't know much about logic, but the dragons puzzle seemed incredibly easy to me?  

100 Green Eyed Dragons

10 years ago

You turn into a sparrow, having relatively...green eyes?  They could see differently!

That, or some dragons, due to having slight differences in green in their eyes, do transform after being told they have relatively...greener eyes than the others.

100 Green Eyed Dragons

10 years ago

None of them transform. They can already see that the others have green eyes, so the guys answer has no effect.

100 Green Eyed Dragons

10 years ago
"And no, the answer is not 'no dragon transforms.'"

100 Green Eyed Dragons

10 years ago

Sorry, I missed that.

100 Green Eyed Dragons

10 years ago

That "hint" is slightly disingenuous, since the correct answer does involve none of them transforming at first.

100 Green Eyed Dragons

10 years ago

Spoiler:

But, ultimately, it proves true. That's where the extra bit in "Blue Eyes" comes into play.

100 Green Eyed Dragons

10 years ago

My friend has actually told me this one a while ago (because he REALLY likes puzzles things like them), but I can't quite remember what the answer was...

I think it had something to do with process of elimination, or something. Like one dragon says:"Aw man this dragon has green eyes so hes gonna turn into a bird at midnight!", and then he doesn't and the first dragon goes down the line and says: "I must be the one with green eyes!", but all of the other dragons are doing this at the same time so they all turn into birds at the same time.

As I said before, its been a while since I heard this one. And looking back at my answer, it doesn't really make any sense, so I wouldn't take my exact words for it, but that was the gist of what the answer was, I'm sure.

100 Green Eyed Dragons

10 years ago
Where have you been?

100 Green Eyed Dragons

10 years ago

In your mom's attic.

I've been busy.

100 Green Eyed Dragons

10 years ago
Oh, okay.

100 Green Eyed Dragons

10 years ago

Thank you for asking.