Can You Solve 'The Hardest Logic Puzzle In The World'?

It is correct, and VERY logical, but very hard to explain

100 dragons, they all change on day 100
200 dragons, they all change on day 200

they know the colour of their own eyes, based on what they observe from the other dragons. Since none of the other dragons change, they are able to logically determine that they themselves have green eyes. They all realise 100 days after the starting point, which was set in motion by the human making that comment.

for it to work though, all dragons have to hear the humans comment on the same day else it won't work
 
Greboth said:
The question isn't 'Why would they change?' it is 'Why wouldn't they change?'. The only reason each dragon wouldn't change is because each can see the same number of green eyes so assumes they don't have green themselves. For this to happen all of them must have green eyes.
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They don't talk about it do they? So how would they know how many green eyes each dragon can see?

Lets use the 3 dragon example for ease.

Dragon 1 is told atleast 1 dragon has green eyes.

He can see 2 dragons with green eyes.

He also knows that these two dragons can see the other dragons green eyes.

He then concludes that these two dragons will not change because they can see each others green eyes.

He then stops worrying about it.
 
balky12 said:
They don't talk about it do they? So how would they know how many green eyes each dragon can see?

Lets use the 3 dragon example for ease.

Dragon 1 is told atleast 1 dragon has green eyes.

He can see 2 dragons with green eyes.

He also knows that these two dragons can see the other dragons green eyes.

He then concludes that these two dragons will not change because they can see each others green eyes.

He then stops worrying about it.
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You're missing the point completely.

Dragon 1 would be told the information, however the other 2 dragons don't change at midnight following their rule as the other 2 dragons won't know they have green eyes, as they never changed the dragon would then realised that it itself has green eyes following the new information, and once a dragon know's it's own eye colour it changes.

HOWEVER, all 100 dragons heard the new information, thus all 100 change on day 100.

Can we move onto the 2nd one now?
 
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cheesyboy said:
Why would 100 dys make a difference?

What new information can logically be gained on day 2, 3 , 4 etc?

As far as I see, day one, you see a load of green-eyed dragons, and know that the other dragons all see a load of green-eyed dragons. You wouldn't expect anyone to change into a sparrow, because they are in the same boat as you: you don't know your own eye-colour, and you can see at least one green-eyed dragon.

Day 2 changes nothing. day 100 changes nothing
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I am with you.

Why would they think that others would change just because they can see others have green eyes? They all knew that all the others had green eyes anyway. :confused:.

They all knew that "at least one of them had green eyes" anyway.
 
Wait, I understand it!

3-dragons:
Dragon 1 knows that if he (1) doesn't have green eyes, dragon 2 will know he (2) must have green eyes if dragon 3 doesn't change at midnight - because dragon 1 knows that dragon 2 would see his (1) non-green-eyes, and Dragon 3's inaction would mean he must see green-eyes on dragon 2 (since dragon 2 knows Dragon 1 has non-green-eyes).

Therefore, no activity from dragon 2 and 3 means Dragon 1 knows he (1) has green eyes.

And this spirals out for scenarios of more than 3.

i.e. (4-dragons)
Dragon 1 knows that if he (1) doesn't have green-eyes, then dragon 2 will see 2 green-eyes. Dragon 1 knows that Dragon 2 won't know if he (2) has green eyes, but will know dragon 1 doesn't, and that dragon 2 would know that dragon 3 will see 1 green-eyes if he (2) and 1 doesn't. Dragon 3 will see....

Their inaction ultimately informs Dragon 1 of his own green eyes

etc
 
ThaReaperGuy said:
You're missing the point completely.

Dragon 1 would be told the information, however the other 2 dragons don't change at midnight following their rule as the other 2 dragons won't know they have green eyes, as they never changed the dragon would then realised that it itself has green eyes following the new information, and once a dragon know's it's own eye colour it changes.

HOWEVER, all 100 dragons heard the new information, thus all 100 change on day 100.
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You're missing a key point in what I said.

Dragon one accepts that Dragon 2 and Dragon 3 will not change because they can see each others green eyes.

That's when he stops caring.

Dragon 'X' can see 2 dragons with green eyes. Dragon 'X' realises that they can see each others green eyes and so will not change, as only atleast 1 dragon has to have green eyes.

They do not all talk about it.
 
Greboth said:
So you as Dragon 1 think I wont change because I haven't got green eyes and but I know the other 3 have green eyes and expect all 3 to change. Dragon 2, 3 and 4 all come to the same conclusion though so don't change. Therefore, again as Dragon 1, you must conclude that you were wrong in the beginning and you also have green eyes. The day at which Dragon 1 realises this 2, 3 and 4 also do too.

Edit: I give up trying to explain this :(
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Your logic is here that because the others haven't changed must mean I have green eyes.
NO
It simply means the others don't know they have green eyes as they can't confirm it 100% (anything over 3 dragons works)

Lets assume the below
D1 - Blue eyes, sees 3 green
D2 - Green eyes, sees 1 Blue 2 Green
D3 - Green eyes, sees 1 Blue 2 Green
D4 - Green eyes, sees 1 Blue 2 Green

If Every Dragon assumes they are Dragon 1, then they can all see 3 Green and assumes the other dragons can see at least 2 green, so therefore cannot work out there own eye colour, so no-one changes.

I accept that my logic might be flawed here somewhere however, and am ready to be proven wrong :)
 
Jono8 said:
I am with you.

Why would they think that others would change just because they can see others have green eyes? They all knew that all the others had green eyes anyway. :confused:.

They all knew that "at least one of them had green eyes" anyway.
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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.

Because of this rule, they've been told that at least one dragon has green eyes which means by their logic of the rule, at least one dragon should change to a sparrow but as none of them know their own eye colour they don't change until day 100, when they all then realise that themselves have green eyes as no other dragon changed although they were told at least 1 dragon has green eyes.

The bold parts are important to the logic.
 
Before the visit, all the dragons know that there are 99 dragons with green eyes. Being told at least one of them have green eyes is nothing they don't already know. Therefore nothing changes.

If there were only 2 then yes, they could deduce that they had green eyes on the second day when the other fails to change. when there are 3 or more each dragon can see another dragon looking at a third dragon and thinking "phew, that one has green eyes so I don't have to worry."
 
balky12 said:
You're missing a key point in what I said.

Dragon one accepts that Dragon 2 and Dragon 3 will not change because they can see each others green eyes.

That's when he stops caring.

Dragon 'X' can see 2 dragons with green eyes. Dragon 'X' realises that they can see each others green eyes and so will not change, as only atleast 1 dragon has to have green eyes.

They do not all talk about it.
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dude, don't worry....it took me a while to figure it out. Think of the dragons as a computer algorithm instead. Reading the original article a couple of times helped. It's logical.
 
MassiveJim said:
Your logic is here that because the others haven't changed must mean I have green eyes.
NO
It simply means the others don't know they have green eyes as they can't confirm it 100% (anything over 3 dragons works)

Lets assume the below
D1 - Blue eyes, sees 3 green
D2 - Green eyes, sees 1 Blue 2 Green
D3 - Green eyes, sees 1 Blue 2 Green
D4 - Green eyes, sees 1 Blue 2 Green

If Every Dragon assumes they are Dragon 1, then they can all see 3 Green and assumes the other dragons can see at least 2 green, so therefore cannot work out there own eye colour, so no-one changes.

I accept that my logic might be flawed here somewhere however, and am ready to be proven wrong :)
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That exaclty how I interpret it.

Dragon 'X' sees two greens. Realises that they in turn can see one green therefore neither will change.
 
Gruber said:
"phew, that one has green eyes so I don't have to worry."
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And when that dragon doesn't change when you expected it to?
Suddenly you think, I must have green eyes, as they'll be thinking the exact same of you, which was "Phew, that one has green eyes so I don't have to worry".

Dragon 1 = Dragon 2 = Dragon 3 with their logical thinking.

balky12 said:
That exaclty how I interpret it.

Dragon 'X' sees two greens. Realises that they in turn can see one green therefore neither will change.
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Except, they've been told at least one dragon has green eyes, which means ONE DRAGON HAS TO CHANGE following their rule.
 
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I haven't read any replies for the dragon one yet - but I'm throwing this down here anyway.

I'm ninja-redatcing it because I might have misread the problem
 
glen8 said:
dude, don't worry....it took me a while to figure it out. Think of the dragons as a computer algorithm instead. Reading the original article a couple of times helped. It's logical.
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I understand the logic. Honestly. I just don't think it actually applies to this scenario.

Remember this is all in the dragons heads as they can not talk about it.

Dragon 1 sees 2 green eyed dragons. But knows they can both see each other, so why would they change?

In Dragon 1's head he can see two green eyes dragons (satisfying the new information that atleast one dragon has green eyes) and he also knows that both of these dragons can see each others green eyes (again satisfying the rule). He then accepts that neither of these dragons will change?
 
MassiveJim said:
Your logic is here that because the others haven't changed must mean I have green eyes.
NO
It simply means the others don't know they have green eyes as they can't confirm it 100% (anything over 3 dragons works)

Lets assume the below
D1 - Blue eyes, sees 3 green
D2 - Green eyes, sees 1 Blue 2 Green
D3 - Green eyes, sees 1 Blue 2 Green
D4 - Green eyes, sees 1 Blue 2 Green

If Every Dragon assumes they are Dragon 1, then they can all see 3 Green and assumes the other dragons can see at least 2 green, so therefore cannot work out there own eye colour, so no-one changes.

I accept that my logic might be flawed here somewhere however, and am ready to be proven wrong :)
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You can't make assumptions, this is a logic question so you can only tackle this with fact....."why does dragon 1 think he has blue eyes?" This is where everyone is going wrong. Each dragon doesn't know what colour eyes they have. They are assuming nothing. They calculate what colour eyes they have by a process of elimination.
 
balky12 said:
I understand the logic.

You don't. :(

In Dragon 1's head he can see two green eyes dragons (satisfying the new information that atleast one dragon has green eyes) and he also knows that both of these dragons can see each others green eyes (again satisfying the rule). He then accepts that neither of these dragons will change?
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Re-read their rule, you'll soon understand, and then re-read all my replies to everyone that hasn't understood the rule.
 
This is as bad as the bloody airplane and moving runway. I will admit I had to read the answer and couldn't figure it out on my own, but I at least understand the answer so I feel okay about myself.
 
balky12 said:
I understand the logic. Honestly. I just don't think it actually applies to this scenario.

Remember this is all in the dragons heads as they can not talk about it.

Dragon 1 sees 2 green eyed dragons. But knows they can both see each other, so why would they change?

In Dragon 1's head he can see two green eyes dragons (satisfying the new information that atleast one dragon has green eyes) and he also knows that both of these dragons can see each others green eyes (again satisfying the rule). He then accepts that neither of these dragons will change?
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You are forgetting about the human influence though. That is key as it sets up the formula for a resolution.

If the human never visited the island, you would be correct. The fact is, the human said one of them has green eyes. This is nothing they didn't already know, but when 100% of the dragons heard that statement on the same day, they could calculate (they were very logical dragons) using the formula on the website that they themselves had green eyes.
 
cheesyboy said:
Wait, I understand it!

3-dragons:
Dragon 1 knows that if he (1) doesn't have green eyes, dragon 2 will know he (2) must have green eyes if dragon 3 doesn't change at midnight - because dragon 1 knows that dragon 2 would see his (1) non-green-eyes, and Dragon 3's inaction would mean he must see green-eyes on dragon 2 (since dragon 2 knows Dragon 1 has non-green-eyes).

Therefore, no activity from dragon 2 and 3 means Dragon 1 knows he (1) has green eyes.

And this spirals out for scenarios of more than 3.

i.e. (4-dragons)
Dragon 1 knows that if he (1) doesn't have green-eyes, then dragon 2 will see 2 green-eyes. Dragon 1 knows that Dragon 2 won't know if he (2) has green eyes, but will know dragon 1 doesn't, and that dragon 2 would know that dragon 3 will see 1 green-eyes if he (2) and 1 doesn't. Dragon 3 will see....

Their inaction ultimately informs Dragon 1 of his own green eyes

etc
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Good man. :D
 
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