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

dowie said:
It doesn't matter...you brought it up in the first place! I have answered your questions..

Now how about trying with 3 dragons as you're clearly not getting your head around 100?
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You haven't answered it at all. Why does it matter that no dragon will see 97 green eyed dragons in my example?
 
It doesn't matter.. what do you want me to say? Its just irrelevant really....

Now - 3 dragons.... why won't you try with 3? It would make it much easier to understand if you're struggling with 100.
 
3 dragons - 1 blue eyes and 2 green eyes

visitor says 'at least one of you has green eyes'

for each green eyed dragon - they can see 1 blue eyed and 1 green eyed dragon

the blue eyed dragon can see 2 green eyed dragon

the green eyed dragons can deduce there are either one or two green eyed dragons
the blue eyed dragon can deduce there are either two or three green eyed dragons

first night passes

no one turns into a sparrow....

green eyed dragons both realize therefore they have green eyes... blue eyed dragon still doesn't know if there are two or three green eyed dragons

second night passes

both green eyed dragons turn into sparrows, blue eyed dragon then realises that it has blue eyes


Can you follow the above?
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now all three have green eyes... their thinking will be the same as the blue eyed dragon in the above example except:

...
second night passes

none of the dragons turn into sparrows... they all realise they have green eyes
..........................

Can you now follow 3 green eyed dragons - you said before you couldn't follow it for greater than 2?
 
I understand the method of induction i do not agree that it would apply here. Can you tell me why starting at 97 dragons does not work?
 
In what way? I mean do you not follow the 3 dragon example... lets just deal with that one for the moment as it will make things easier - what is the issue you have with the solution as it applies to 3 dragons?
 
dowie said:
In what way? I mean do you not follow the 3 dragon example... lets just deal with that one for the moment as it will make things easier - what is the issue you have with the solution as it applies to 3 dragons?
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Please answer my question. Can no one here answer it?

In the official answer, for the first 98 days, they are waiting to reach the conclusion that "there are at least 98 green eyed dragons". They all know that everyone else already knows this. So why not start with " if any dragon sees only 97 green eyed dragons, they will know they have green eyes and turn into a sparrow tonight"

All I want to know, is why that is incorrect.
 
I'm really not sure what you're getting at - I've already answered your questions... Like I said it would be much much easier to start with 3 - which I believe you've had an issue with too as you said you can only see it working for 2 dragons...

So lets start there - what is your issue with the solution to 3 - or do you now accept the solution for 3 dragons?
 
dowie said:
I'm really not sure what you're getting at - I've already answered your questions... Like I said it would be much much easier to start with 3 - which I believe you've had an issue with too as you said you can only see it working for 2 dragons...

So lets start there - what is your issue with the solution to 3 - or do you now accept the solution for 3 dragons?
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So you cannot answer my question basically?
 
Jono8 said:
So you cannot answer my question basically?
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I already have...

You said you can't see the solution working for greater than 2... so... lets try with 3 as it will be easier to work through it!

Now - what is your issue with the solution as it applies to 3 dragons?
 
back up the thread... I really don't see where you're going with this 97 dragons nonsense..

Main point is - you don't understand it applying to 3 dragons - right?

So... for the sake of clarity and to stop going round in circles or clogging up the thread with pointless nonsense... can you put the 97 dragons nonsense to one side and see if you can understand how the solution works for say 3 dragons...

What is the issue you had with the solution applying to 3 dragons?
 
dowie said:
back up the thread... I really don't see where you're going with this 97 dragons nonsense..

Main point is - you don't understand it applying to 3 dragons - right?

So... for the sake of clarity and to stop going round in circles or clogging up the thread with pointless nonsense... can you put the 97 dragons nonsense to one side and see if you can understand how the solution works for say 3 dragons...

What is the issue you had with the solution applying to 3 dragons?
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I don't think you are listening. I understand the official answer but i don't agree with it.

Please tell me why they cannot start of the induction with " there are at least 98 dragons....."
 
if you understood it you wouldn't have an issue with it

they can see 99 dragons - there are either 100 or 99 green eyed dragons

If you've got an issue with the solution for 3 dragons then please just post the issue you have with the 3 dragon solution - like I said it will be easier to start there
 
Jono, I think this might be why.

For simplicity I'll replace 'dinosaur' with 'd'.

d1, d2, d3 ... d100 = green.

Take any single perspective.

d1 knows there are at least 99 green.

d1 knows d2 can see at least 98 green eyes.

But d1 thinks, if I do have blue eyes, then d1 thinks d2 could think he also has blue eyes. So d1 thinks there is a chance d2 thinks that d3 will be looking at a maximum of 97 green.

Taking this further, d1 now thinks if I do have blue eyes and d2 does think he also has blue eyes. And if d2 thinks that d3 can also think he has blue eyes, then d2 could think that d3 thinks that d4 will see a maximum of 96 green.

And so it continues.

Note this is not d1's perspective of how he thinks each dragon perceive the others. But his perception of how each dragon thinks he might think, they think, another thinks of another's thoughts about another.

It is hard to get your head around, but before the man speaks it is actually possible that each dragon thinks that if they are blue, then any other dragon may think they are blue and then that dragon would think another dragon who also knew they themselves could be blue, may think that any other dragon .... keeps going until it is possible that any dragon thinking from another's perspective can form a chain of perspectives of perspectives which mean each dragon is concerned there could be a dragon who thinks there's a dragon, who thinks there's a dragon who thinks they could all be blue.

The man speaks and removes this possibility.

It is very hard to explain, apologies if it doesn't clear it up.
 
Lets make this simple - do you understand and agree with the solution as it applies to 3 dragons?

If no then what is the issue you have with it?

If yes then do you understand and agree with it as it applies to 4 dragons?
 
Jono you're right to point out, and I've already pointed out too, that no dragon is expecting to see anything happen on day 1, 10, 50 etc etc. The only uncertainty is what happens on day 99. But what you're missing, and the reason they dont all shortcut the inductive process and skip straight to that point, is that that would require discussion and agreement to do so. That is against the rules - simple as that. All each dragon can do is play out the full process, no short cuts, and rely that the others do the same. That's all there is to it.
 
Of course there isn't a shortcut... what if there were actually 99 green eyed dragons and 1 blue eyed dragon... would the blue eyed one turn overnight because it can see 99 green eyed dragons? Nope...
 
dowie said:
back up the thread... I really don't see where you're going with this 97 dragons nonsense..

?
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THERE finally you said it.
You don't understand.
You have jumped valiantly away for it only about 12 occasions on this thread page alone, by regurgitating the 3 dragon rule.

His question relates to timing I think.
Logical timing.
The question works for three, as there is a query in their head as to the number of green eyes that the other two dragons can see.
When you up the total to massive numbers, why do you need to wait for 100 nights, when all logical dragons know every other dragon sees either 98 or 99 other pairs of green eyes.
That is his question, why does the induction wait 100 days? Why don't they figure it out sooner?
 
dowie said:
if you understood it you wouldn't have an issue with it

they can see 99 dragons - there are either 100 or 99 green eyed dragons
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So you are saying that my suggestion does not work because they can all, in fact see 99 green eyed dragons?
 
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