You're reading the first installment in a brand new puzzle series here at io9 – and what better way to kick things off than with the world's most difficult logic puzzle?
Some months back, I posted a little brain teaser here on io9. People seemed to enjoy it. Encouraged by the positive response, I decided to float an idea I'd had bouncing around my head for some time: How would you all feel about me dedicating one post per week to a particularly dastardly puzzle or brain teaser?, I asked. Again, lots of positive response. The idea for The Sunday Puzzle was born.
I confess this idea was not entirely my own. The genre of public, published puzzling was arguably pioneered by the legendary Martin Gardiner and his 'Mathematical Games' column in Scientific American, and lots of places to this day post puzzles and riddles with some regularity. But the clearest inspiration for io9's Sunday Puzzle was the TierneyLab blog over at the New York Times, where John Tierney used to publish puzzles, and discussions surrounding previous weeks' puzzles, every Monday.
I'd like io9's Sunday Puzzles to follow a similar format to Tierney's, and for the comments to become a place for people to submit full or partial solutions, questions, ideas, future puzzles, and so on. I encourage you to also upload any drawings, calculations, or ideas you jot down in the course of your puzzling. I'm still sorting out the details (I like to think that our commenting system has the potential to be moderated in a way that will foster discussion and help people along in the puzzle-solving process, without always spoiling the solution outright – but how feasible this will be in practice remains to be seen), so recommendations on how to structure the column are of course welcomed and encouraged.
There's so much more I could say about this, but I'll refrain for now (or reserve it for future posts), save for one last thing: If you know a great brain teaser that you think would work well as a Sunday Puzzle, please feel free to drop me a line with "Sunday Puzzle" in the subject line. Or sound off in the comments. Please also indicate whether it is an original puzzle or one that you found elsewhere. Puzzles can be mathematical, logical, visual, computational, some combination thereof, etc. – but they should be challenging, and, of course, satisfying to solve. (More on what constitutes a satisfying puzzle in future posts.)
Alright. I'm going to stop talking now (can you tell I'm really excited about this?). Onto the puzzles.
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 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?
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!
Illustration by Jim Cooke