Hardest Logic Puzzle in the World

[rsnomar05]

This logic puzzle, which has been making the rounds on the internet lately, is given to incoming physics students at Harvard. A friend e-mailed it to me, so I figured I'd post it here to see if people could solve it:


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.

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?

https://www.physics.harvard.edu/uploads/files/undergrad/probweek/prob2.pdf

[Sportsforever]

Re: Hardest Logic Puzzle in the World

This logic puzzle, which has been making the rounds on the internet lately, is given to incoming physics students at Harvard. A friend e-mailed it to me, so I figured I'd post it here to see if people could solve it:


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.

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?

https://www.physics.harvard.edu/uplo...week/prob2.pdf

I think I have the answer:

Spoiler

They will all turn into sparrows. Up until this point they didn't know what the color green was, so when they saw that everyone else was green it didn't occur to them that it was green. When told that at least one of them has green eyes, they will assume that since everyone else's eyes are the same (and they haven't turned to sparrows) that they are the one with the 'different' green eyes, thus discovering they have green eyes.

I'll see if I can find the answer on the 'net, but that's what jumps out at me at first.

[SPTO]

Re: Hardest Logic Puzzle in the World

Spoiler

They either all turn into sparrows because you introduced the concept of "green" to them or maybe they're all color blind? I dunno.

[Knight165]

Re: Hardest Logic Puzzle in the World

I think I have the answer:

Spoiler

They will all turn into sparrows. Up until this point they didn't know what the color green was, so when they saw that everyone else was green it didn't occur to them that it was green. When told that at least one of them has green eyes, they will assume that since everyone else's eyes are the same (and they haven't turned to sparrows) that they are the one with the 'different' green eyes, thus discovering they have green eyes.

I'll see if I can find the answer on the 'net, but that's what jumps out at me at first.

If this is the answer...I would have a problem with it.
It says they have a rule on the island about having green eyes.
I would assume they would know what green was if they are going to have a rule about it.

M.K.
Knight165

[FlyingFinn]

Re: Hardest Logic Puzzle in the World

Spoiler

On the hundredth night they all turn into sparrows.

[TheMatrix31]

Re: Hardest Logic Puzzle in the World

Spoiler

Are they color-blind? If they have a rule about finding out they have green eyes, they can see each other's eyes. If they need a human to tell them.....

Either that or they kill each other to make sure they don't turn into sparrows.

Just read the solution. Well, I guess my answers give a bit of insight into my 4:45am mind, eh?

[slickdtc]

Hardest Logic Puzzle in the World

My best guess is nothing changes. All the information they give you is just trying to keep you from thinking simple. Especially since it's a Harvard puzzle, the brainiacs are going to assume it's a complex answer.

They're all blissfully ignorant as it is, so they know all others have green eyes (besides knowing if they themselves do). But because they never speak of it, they'll still never be able to tell one another. So none will ever discover they have green eyes. They'll remain dragons if they don't talk about it. An outsider would have to tell a dragon that they specifically have green eyes. This human said at least one, but did not tell which one. There's a code of silence already, so nothing changes. They all already knew all others had green eyes. You gave them no new information.

That's my best effort.

Read the solution: meh.