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Coin tossing, probability and some logic, kinda


Swan Red

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so why haven't they already ?

 

Because they've been given new information. They can now rule out the possibility that they don't have green eyes, previously they couldn't

 

In the case of 2 dragons before that heard the "at least" comment they had no way of working out whether they themselves had green eyes. Now they can, see my correct, but uselessly worded explanation above

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Because they've been given new information. They can now rule out the possibility that they don't have green eyes, previously they couldn't

 

In the case of 2 dragons before that heard the "at least" comment they had no way of working out whether they themselves had green eyes. Now they can, see my correct, but uselessly worded explanation above

 

it's not new information

 

they can already see 99 dragons have green eyes

 

 

 

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Because they've been given new information. They can now rule out the possibility that they don't have green eyes, previously they couldn't

 

In the case of 2 dragons before that heard the "at least" comment they had no way of working out whether they themselves had green eyes. Now they can, see my correct, but uselessly worded explanation above

 

" At least one of you has green eyes "

 

One dragon looks at the other and thinks " it must be him ". No piff paff anything.

 

To realise they had green eyes they'd have to be told definitively ( and i include being given a clue which helps them come to a conclusion ) or see it for themselves.

Edited by Earl Hafler
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Swan Red's clue is the key - it only works if all 100 dragons are present to hear the announcement

 

I can only prove it to myself in the 2 dragon scenario, the new information is the "at least" bit. This allows them to confirm that they deffo have green eyes (by the fact that other dragon doesn't go PPP), before hearing this statement they couldn't progress any further than knowing the other one had green eyes

 

 

 

 

" At least one of you has green eyes "

 

One dragon looks at the other and thinks " it must be him ". No piff paff anything.

 

 

Here it is..

 

And if he's logical when the other one doesn't PPP he can work out that he's got green eyes as well.....because at least one of the feckers has

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Strip it down to 3 dragons.

Dragon A knows that dragon B and dragon C have green eyes.

Dragon A also knows that dragon B and dragon C know that at least one dragon has green eyes.

Dragon A DOESN'T know whether dragon B knows that C knows at least one dragon has green eyes (because if A has blue eyes then as far as A is concerned B wouldn't be able to assume that C can see another dragon with green eyes).

After the pronouncement dragon A definitely knows that dragon B knows that dragon C knows that at least one dragon has green eyes.

 

 

 

Now I've got a headache.

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Swan Red's clue is the key - it only works if all 100 dragons are present to hear the announcement

 

I can only prove it to myself in the 2 dragon scenario, the new information is the "at least" bit. This allows them to confirm that they deffo have green eyes (by the fact that other dragon doesn't go PPP), before hearing this statement they couldn't progress any further than knowing the other one had green eyes

 

 

 

Here it is..

 

And if he's logical when the other one doesn't PPP he can work out that he's got green eyes as well.....because at least one of the feckers has

 

Maybe he thinks the other dragon hasn't realised it ?

 

Easier with the 2 dragons. Less so with the 100 but the human is irrelevant.

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yeah Earl is kinda there

 

In the case of 3 dragons 1 with green eyes the dragon learns he has green eyes when the guy tells him and he turns into a sparrow the following day. However in this case there is new information because the green eyed dragon didn't know there were any.

 

In the case of 3 dragons 2 with green eyes, the two dragons with green eyes know that the other dragon they see with green eyes would have turned into a sparrow on day one had two dragons not had green eyes. They know dragon 3 doesn't so dragons 1&2 turn into sparrows on day 2. In this case all 3 dragons knew that at least one of them has green eyes.

 

In the case of 3 dragons all with green eyes, they know that had the other two dragons seen a dragon with non green eyes as per above they would have turned into sparrows on day two so when they don't all three dragons turn into sparrows on day 3.

 

What's kinda interesting about this is that it's one of those puzzles where even when the results are known it's counter intuitive enough for people to think it's wrong. It wrecked my head.

 

Common Knowledge

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yeah Earl is kinda there

 

In the case of 3 dragons 1 with green eyes the dragon learns he has green eyes when the guy tells him and he turns into a sparrow the following day. However in this case there is new information because the green eyed dragon didn't know there were any.

 

In the case of 3 dragons 2 with green eyes, the two dragons with green eyes know that the other dragon they see with green eyes would have turned into a sparrow on day one had two dragons not had green eyes. They know dragon 3 doesn't so dragons 1&2 turn into sparrows on day 2. In this case all 3 dragons knew that at least one of them has green eyes.

 

In the case of 3 dragons all with green eyes, they know that had the other two dragons seen a dragon with non green eyes as per above they would have turned into sparrows on day two so when they don't all three dragons turn into sparrows on day 3.

 

What's kinda interesting about this is that it's one of those puzzles where even when the results are known it's counter intuitive enough for people to think it's wrong. It wrecked my head.

 

Common Knowledge

 

Once focusing on it a bit and not multi tasking, the 2 is easy to grasp. The 100 less so - still takes some thought, although easier when you ignore some irrelevant stuff the mind throws up at you ( "What if..." ) and forget the mise en scene.

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2 dragons: dragon A looks at dragon B, sees that dragon B has green eyes and thinks dragon B can see my eyes and if my eyes are not green then dragon B would know that his own eyes must be green so he'd go piff-paff therefore my eyes must be green, uh oh! Piff-paff. Dragon B does exactly the same.

 

I assume this generalizes to 3, 4, 5,... dragons. Yes it does.

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The human is relevant.

If I'm a dragon, I know he's not giving new info to me. But I don't know whether he's giving new info to the other dragon. I find that out at midnight.

 

 

What does it matter ? The curse is already known to both dragons. Even if only one of them has green eyes, it's perfectly logical to assume that if there's a curse then at least one of them must have green eyes. The green eyed dragon sees that the other dragon hasn't got green eyes, realises it's him and so turns into a sparrow

Edited by Earl Hafler
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I'm talking about when there are two.

The human's words do add something then. It's not new info to either dragon, but it lets each ascertain whether it is new info to the other, which in turn tells each whether he himself has green eyes.

 

I think it might also work for more than two but it's hard to get my head around.

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but it lets each ascertain whether it is new info to the other, which in turn tells each whether he himself has green eyes.

 

They are all logical creatures - I don't see this

 

If I'm Dragon No.1 - I know the other 99 have green eyes, including you, Dragon No.2. But I don't know if I have green eyes.

 

You, Dragon No.2 know the other 99 dragons have green eyes, including me Dragon No.1 but providing we, and the other 98 dragons keep schtum and bathe in the ignorance of the colour of our own eyes, no-one turns into a sparrow at midnight.

 

The human adds nowt we didn't already know.

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