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Green Eyed Dragons Riddle
https://forum.nogoblinsallowed.com/viewtopic.php?f=14&t=20030
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Author:  Ragnarokio [ Mon Nov 06, 2017 6:06 pm ]
Post subject:  Green Eyed Dragons Riddle

I am guessing a lot of you have already heard this but i just encountered it today and thought it was pretty cool so i decided to share it.

There are three dragons, each with green eyes in a room. They can each see each other's eyes, but not their own. The following statement is said aloud and the dragon's regard it as true: "There is at least one dragon with green eyes". What new information do each of the dragon's gain from this statement?

Author:  UselessCommon [ Mon Nov 06, 2017 6:48 pm ]
Post subject:  Re: Green Eyed Dragons Riddle

1) There is a mysterious speaker in a room.
That's not all there is to it, is it ?

My logical skills fail me...

Author:  Ragnarokio [ Mon Nov 06, 2017 6:54 pm ]
Post subject:  Re: Green Eyed Dragons Riddle

nope, its not really a trick question, i think.

Author:  YingLung [ Tue Nov 07, 2017 9:34 am ]
Post subject:  Re: Green Eyed Dragons Riddle

Assuming that having green eyes makes everything you see look green, the each dragon learns that it has green eyes.

Author:  Lord LunaEquie is me [ Tue Nov 07, 2017 9:46 am ]
Post subject:  Re: Green Eyed Dragons Riddle

You forgot the part where the dragons are only allowed out if they have green eyes.

Author:  YingLung [ Tue Nov 07, 2017 9:57 am ]
Post subject:  Re: Green Eyed Dragons Riddle

Having looked up the solution, it appears that the green eyes is merely a pigmentation of their irises.

The version I read had the condition that when a dragon realises they have green eyes, they must transform into a bird at midnight of that day.

Author:  Yarium [ Tue Nov 07, 2017 11:28 am ]
Post subject:  Re: Green Eyed Dragons Riddle

Also looked up solution, and I can confirm that a REQUIREMENT in the stating of this riddle is that the Green Dragons must leave the room when they discover they have green eyes. Without that, there is no logical reason that the Green Dragons learn any new information.

Author:  Tevish Szat [ Wed Nov 08, 2017 5:56 pm ]
Post subject:  Re: Green Eyed Dragons Riddle

I looked at this thread without having heard the solution, but knew that, from a meta-logical standpoint, each dragon must be able to derive its own eye color as green. There is no other hidden information to a dragon and it wouldn't be much of a riddle if the answer was "nothing happens". However, I couldn't arrive at the mechanism by which this would occur. I looked up the answer, and yeah, the automatic midnight birdification is kind of necessary to the puzzle because it creates the feedback loop of information that eventually leads the dragons to derive their own eye color

Author:  Ragnarokio [ Wed Nov 08, 2017 6:03 pm ]
Post subject:  Re: Green Eyed Dragons Riddle

The bird clause isn't necessary and the solution to this puzzle is different from the solution to the puzzle from which this is derived from. The answer is:

Spoiler

Author:  Yarium [ Thu Nov 09, 2017 8:23 am ]
Post subject:  Re: Green Eyed Dragons Riddle

Ragnarokio wrote:
The bird clause isn't necessary and the solution to this puzzle is different from the solution to the puzzle from which this is derived from. The answer is:

[spoiler]Each dragon learns that from the possible perspective of another dragon, the third dragon can't possibly think that all three dragons have non-green eyes.[/spoiler]


response + answer to the other riddle

Author:  Tevish Szat [ Mon Nov 13, 2017 11:24 am ]
Post subject:  Re: Green Eyed Dragons Riddle

Yarium wrote:
Ragnarokio wrote:
The bird clause isn't necessary and the solution to this puzzle is different from the solution to the puzzle from which this is derived from. The answer is:

[spoiler]Each dragon learns that from the possible perspective of another dragon, the third dragon can't possibly think that all three dragons have non-green eyes.[/spoiler]


response + answer to the other riddle

Spoiler

Author:  Ragnarokio [ Mon Nov 13, 2017 9:30 pm ]
Post subject:  Re: Green Eyed Dragons Riddle

Yarium wrote:
Ragnarokio wrote:
The bird clause isn't necessary and the solution to this puzzle is different from the solution to the puzzle from which this is derived from. The answer is:

--


response + answer to the other riddle


Spoiler

Author:  Knifethrower [ Sun Apr 08, 2018 6:43 pm ]
Post subject:  Re: Green Eyed Dragons Riddle

I agree that you need the mechanism to signal what the dragons' know about their own eye color. Without knowing if a dragon knows it's own eye color, I don't see how you derive new information.

Author:  Ragnarokio [ Mon Apr 09, 2018 3:39 am ]
Post subject:  Re: Green Eyed Dragons Riddle

You don't derive new information, the dragons do. Tevish's post is a good explanation.

Author:  cathydec04 [ Tue Aug 07, 2018 8:12 am ]
Post subject:  Re: Green Eyed Dragons Riddle

I looked at this thread without having heard the solution, but knew that, from a meta-logical standpoint, each dragon must be able to derive its own eye color as green. There is no other hidden information to a dragon and it wouldn't be much of a riddle if the answer was "nothing happens". However, I couldn't arrive at the mechanism by which this would occur. I looked up the answer, and yeah, the automatic midnight birdification is kind of necessary to the puzzle because it creates the feedback loop of information that eventually leads the dragons to derive their own eye color

All this seems to me too metaphysical, but I would still like to understand the concept if someone devotes himself to explain it to me.

Author:  Aaarrrgh [ Tue Aug 07, 2018 9:35 am ]
Post subject:  Re: Green Eyed Dragons Riddle

Imagine that there are only two dragons, both with green eyes. All dragons have either red or green eyes, and any dragon who knows their own eye color leaves the island at midnight.

If you tell them that at least one of them has green eyes, and they both know that the other has green eyes, they will each expect the other one to see red eyes, deduce that their own eyes are green, and leave. In the morning, when the other dragon is still there, that means it could not deduce its eye color, which means it also saw green eyes. Thus, day two is when both dragons deduce they both have green eyes, and they both leave.

Although it seems counterintuitive, this logic actually expands to any number of dragons. So with 99 green eyed dragons, they will be able to deduce their eye colors on day 99, but not sooner. It's odd, but it really works.

Author:  Ragnarokio [ Tue Aug 07, 2018 11:37 am ]
Post subject:  Re: Green Eyed Dragons Riddle

and for the other version of the riddle consider that dragon A is evaluating the possible perspective of the other dragons, so they draw up a chart.

Quote:
+----------------------+------------------------+------------------------+--+--+
| ############# | Dragon B's Perspective | Dragon C's Perspective | | |
+----------------------+------------------------+------------------------+--+--+
| Dragon A's Eye Color | Green or Red | Green or Red | | |
+----------------------+------------------------+------------------------+--+--+
| Dragon B's Eye Color | Green or Red | Green | | |
+----------------------+------------------------+------------------------+--+--+
| Dragon C's Eye Color | Green | Green or Red | | |
+----------------------+------------------------+------------------------+--+--+


note that dragon B and Dragon C, in reality, knows that dragon A has green eyes, but Dragon A doesn't know which of these the other dragon knows, and so when making their chart they can't put down either green or red in that cell.

Now dragon A imagines that dragon B is making a similar chart. It would look something like this:

Quote:
+----------------------+------------------------+------------------------+--+--+
| ############# | Dragon A's Perspective | Dragon C's Perspective | | |
+----------------------+------------------------+------------------------+--+--+
| Dragon A's Eye Color | Green or Red | Green or Red | | |
+----------------------+------------------------+------------------------+--+--+
| Dragon B's Eye Color | Green or Red | Green or Red | | |
+----------------------+------------------------+------------------------+--+--+
| Dragon C's Eye Color | Green | Green or Red | | |
+----------------------+------------------------+------------------------+--+--+


Dragon B does not know their own eye colour, so they do not know what dragon C sees them as. The rest of the logic remains the same.

In this analysis, it is thus possible for Dragon A to believe that Dragon B believes that Dragon C believes that all dragons have red eyes. This is one hefty sentence so I'll break it up a bit logically.

-Dragon A begins with the assumption that it has red eyes (which is possible from its perspective).
-Dragon A then begins thinking about what Dragon B sees. Dragon B will see that Dragon A has red eyes and that Dragon C has green eyes.
-Dragon A then begins thinking about what Dragon B thinks about Dragon C's perspective.
-Dragon A posits that Dragon B makes the assumption that it has red eyes. (which is possible from dragon B's perspective)
-Dragon A posits that Dragon B then imagines that dragon C sees two dragons with red eyes, and does not know its own eye colour
-Dragon A posits that Dragon B then posits that dragon C can believe that all three dragons have red eyes

Thus, from Dragon A's perspective, it is possible that Dragon B's analysis of the situation could result in the possibility of dragon C believing all dragons could possibly have red eyes.

When all dragons learn that there is at least one dragon has green eyes, this possibility obviously collapses, and so Dragon A's analysis of the situation changes.

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