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

[Jono8]

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?

Thank you

 

[Destination]

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.

and theres the answer

 

[dowie]

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.

I've said all along I don't understand why he sees an issue

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?

how can they figure it out sooner..

consider 99 green, 1 blue or 98 green 2 blue etc..

If you're struggling then try 3... or 4 and we'll work through those

 

[div0]

Guys it really doesn't help to keep rehashing the same 'proof' and expect someone to simply accept that extrapolation applies.

I know it's not easy to come up with alternative ways to explain it, but it wouldn't be on a website called 'hardest riddles' (or whatever the site is) if it wasn't at least slightly unintuitive.

Jono, hope my post above helps. But I accept it's not exactly a clear explanation. Best I could do though.

 

[dowie]

Well yeah that's why it would be easier to start with three dragons. He's said he can see it applying to two dragons but not more than two... It is a lot easier to explain any misunderstanding by working through the whole thing with diff combinations of 3 or say 4 dragons.

The idea that they'd all change after the first night because they can see 99 green eyes is flawed - you can see the flaw more easily if you consider say 99 green eyed dragons and 1 blue... the blue one can't change after one night just because it has seen 99 green eyed dragons.

 

[Destination]

Your post is rather clear div0, dowie didn't seem to understand I was trying to rephrase Jono8's question rather than I didn't get the induction extrapolation. So he asked me to struggle with 3 and 4 as well.
Giving people the same explanation when they already understand that bit doesn't help at all, even if you say it 12 times, or shout it very loudly.

 

[Jono8]

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.

Why would that require discussion?

 

[dowie]

Your post is rather clear div0, dowie didn't seem to understand I was trying to rephrase Jono8's question rather than I didn't get the induction extrapolation. So he asked me to struggle with 3 and 4 as well.
Giving people the same explanation when they already understand that bit doesn't help at all, even if you say it 12 times, or shout it very loudly.

The other poster hasn't said that he understands the solution for 3 or 4 dragons... he said he didn't understand it for greater than 2.

 

[dowie]

Why would that require discussion?

Seriously - it would be much easier to work through if you clarified your issue with 3 or 4 dragons to start with?

Failing that... as you seem to be dodging the question - when do you believe they'd all be able change with the 100 dragon problem?

 

[Jono8]

The other poster hasn't said that he understands the solution for 3 or 4 dragons... he said he didn't understand it for greater than 2.

I have told you countless times i understand the official answer

 

[dowie]

I have told you countless times i understand the official answer

OK I'll rephrase... what issue do you have with the solution as it applies to 3 or 4 dragons?

Or do you just have an issue as it gets to a larger number of dragons - if so - at what number do you start to have an issue with the solution?

 

[Liampope]

Why would that require discussion?

Because it isn't supported by pure logic alone.

Make no mistake - they've all got it 'figured out' on day 1, cos they're perfect logicians, right? They fully understand the problem, have figured out the inductive solution that takes up to 100 days to resolve.

They know more than that - they can each see 99 green-eyed dragons. They all know nothing will happen until day 99. On day 99, either the 99 green eyed dragons they can see will leave, or they wont, then they'll all leave on day 100.

But being purely logical beings, they are compelled to follow the whole solution they have deduced. To skip forward 99 days would be a conscious decision outside of strictly following the solution, and they would have to be certain all other dragons would make the same decision to shortcut the process. That would require some discussion and agreement, like 'right guys we all know what's going on here - anyone who can only see 98 green eyed dragons, leave tonight. If you can see 99 then stay. If we all stay tonight, we'll all leave tomorrow'. This is against the rules pure and simple. There is no solution based on pure logic alone, that allows this shortcut. That's why it has to take the full 100 days.

 

[div0]

I have told you countless times i understand the official answer

Did my post help at all with why they can't all start the induction process from 98?

Dowie, all that is being asked is, if all dragons know the other dragons see at least 98 green, why would they not all assume any dragon who sees two blue eyes would change on day 1. None change. On day two any dragons that see 1 blue eye change. None change. On day 3 all dragons change.

It is fairly easy to see why some people struggle with this.

Jono, take a look at my post above and see if it helps.

 

[Nitefly]

Try it with 3... you've said you can see it working for 2 but not greater than two - try it with three and outline your issue with it - we'll go from there

yup - you still don't understand it - like I said.. start at 3 - if you struggle solving 3 then post the issue you're having

yes

so what is your issue with the solution for 3 dragons?

so - 3 dragons - try to figure it out otherwise post the issue you're having

so what is your issue with the solution for 3 dragons?

Now how about trying with 3 dragons as you're clearly not getting your head around 100?

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.

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?

So lets start there - what is your issue with the solution to 3 - or do you now accept the solution for 3 dragons?

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?

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

Lets make this simple - do you understand and agree with the solution as it applies to 3 dragons?

If yes then do you understand and agree with it as it applies to 4 dragons?

I've said all along I don't understand why he sees an issue

how can they figure it out sooner..

consider 99 green, 1 blue or 98 green 2 blue etc..

If you're struggling then try 3... or 4 and we'll work through those

Well yeah that's why it would be easier to start with three dragons. He's said he can see it applying to two dragons but not more than two... It is a lot easier to explain any misunderstanding by working through the whole thing with diff combinations of 3 or say 4 dragons.

The other poster hasn't said that he understands the solution for 3 or 4 dragons... he said he didn't understand it for greater than 2.

OK I'll rephrase... what issue do you have with the solution as it applies to 3 or 4 dragons?

Oh my god.

Just... oh my god.

 

[dowie]

Dowie, all that is being asked is, if all dragons know the other dragons see at least 98 green, why would they not all assume any dragon who sees two blue eyes would change on day 1. None change. On day two any dragons that see 1 blue eye change. None change. On day 3 all dragons change.

It clearly just doesn't work like that and is much easier to illustrate with a lower number... however if that is his question then the answer is that it is incorrect to assume that a dragon seeing two sets of blue eyes would change - that dragon would have no information about its own eye colour and so on.

 

[dowie]

Oh my god.

Just... oh my god.

well if he outlined his problem with 3 or 4 it would make things easier....

 

[Liampope]

Did my post help at all with why they can't all start the induction process from 98?

Dowie, all that is being asked is, if all dragons know the other dragons see at least 98 green, why would they not all assume any dragon who sees two blue eyes would change on day 1. None change. On day two any dragons that see 1 blue eye change. None change. On day 3 all dragons change.

It is fairly easy to see why some people struggle with this.

Jono, take a look at my post above and see if it helps.

If that is what jono is asking (is it???) the answer is simple. That assumption does not logically follow from the human's statement. There's no logical basis to start with that assumption. There is only one solution - the full solution, and the only way the inevitable at least 99 days of thumb twiddling could be skipped is by agreement. But that is against the rules.

 

[div0]

If that is what jono is asking (is it???) the answer is simple.

Only he can answer that. I'm just trying to show that simply saying the same things over and over doesn't help if the someone doesn't quite get the starting point.

I started replying to this.

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....."

He has said he understands the induction process and it seems clear he does. I just think he's struggling to understand why they don't already know enough information to jump further down the chain.

Personally I can understand why it isn't immediately obvious. My previous post tried to explain why they actually start with very little info about what other dragons think other dragons are thinking.

 

[dowie]

Well if he's not prepared to consider at what number of dragons he believes the process breaks down and can be shortened then the short cuts can be eliminated by considering some blue eyed dragons mixed in with the 100... i.e.

What would be the shortest number of days 95 green eyed dragons and 5 blue eyed dragons figure out their eye colour - How about 96 and 4... (consider that the green eyed ones would act in the same way as a blue eyed one from the 95+5 example..)

(obviously it is easier to consider with lower numbers - but the idea of a shortcut can be dismissed by introducing a blue eyed dragon(s) and considering that green eyed dragons in that problem will behave in the same way as any blue eyed dragon in a problem involving 1 more blue eyed dragon.)

 

[Jono8]

If that is what jono is asking (is it???) the answer is simple. That assumption does not logically follow from the human's statement. There's no logical basis to start with that assumption. There is only one solution - the full solution, and the only way the inevitable at least 99 days of thumb twiddling could be skipped is by agreement. But that is against the rules.

There is every logical basis to start with that assumption. In fact surely it is illogical not to?

I find the official theory to be rather tenuous because of this. The whole official answer relies on all the dragons only coming to one logical conclusion - that they must start the induction process with the disingenuous testing of a theory that there is only 1 green eyed dragon, when they know full well this is not the case and know full well that all the others know this is not the case either.

Basically it is discounting their ability to follow logical deduction and only taking in to account their ability to follow logical induction.