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

[Nitefly]

Oooo further to my last post how about this?

Spoiler

Q.3 - will God A and God C always give opposing answers consistently?

It feels like I'm almost there nurrrrrgh! Probably miles away!

 

[dowie]

For induction to work all the dragons, on the first day, are "waiting to see if any one of the other dragons see no green eyed dragons", but they know this cannot be the case.

nope

try it for 3 dragons one with blue eyes... now try it for three dragons all with green eyes... now try it for four... now think again about the original

they're not waiting for anything to happen after the first night - they're waiting for something to happen after the 99th...

 

[dowie]

Ok, so I'm hoping to redeem my inability to read the dragon puzzle by offering some thoughts on the god puzzle.

Spoiler

One of the questions, probably the first question, must relate to something that you know to be factually true. For example, asking God A "does 2 +2 = 4?", would produce Ja or Da. A second question to the same god, God A, could clarify the answer to the first question e.g. "does the answer to Q.1 mean 'yes' in English?"

So this would be the results using the above answers:

"Ja" "Ja" - that god is either the truth god or the maybe god. This means you know factually that one of the other gods MUST be the false god.

"Ja" "Da" - that god is either the false god or the maybe god. This means you know factually that one of the other gods MUST be the truth god.

I'm stumbling at the last hurdle, but I think the last question must relate to the fact that the maybe god will not always give a consistent answer TOGETHER with the truth revealed by the previous two questions (see above). So something along the lines of asking God B 'will God A and God C always give a consistent answer?', or perhaps asking God B 'Will God A always agree with God C?'

What do you guys think? Hopefully with a bit of combined brainpower we can get there!

you're not getting enough information from the first two questions

div0 posted a helpful suggestion earlier

 

[Liampope]

My problem is that no dragon in this situation would ever say "'If my eyes are also not green, that other dragon can see no green eyed dragons, and will therefore conclude his eyes are green and will leave on the first night"

...

For the official theory to work, all the dragons have to fabricate a situation in their mind that they know does not exist. They would be coming to a conclusion based upon fabricated evidence.

You're getting really hung up on things that don't matter and don't make any difference to the problem. They are not 'fabricating evidence' - they are simply defining correct logical statements and testing them. Specifically, they are making IF statements (if my eyes are not green...) - in fact a chain of nested IF statements. The statements are then tested by the actions of the other dragons which allows conclusions to be made. It makes no difference whatsoever to the process that all the statements are proven false in this case (because all dragons have green eyes), nor does it make any difference that they already know (because they can see) what the outcome of all but the last test will be. Makes no difference. You need to let go of the idea that logical statements being proven false (even before they are tested) means the process doesn't work. A statement being proven false is as conclusive as a statement being proven true.

The process would work just the same if there were one or more blue eyed dragons in the population. In that case some of the IF statements would test out to be true. The process would always weed out however many green eyed dragons there were in the population in that same number of days.

I'm sure some clever programming type could write out the whole 100 dragon problem as a 100 level deep nest of IF statements, but I'm not a clever programmer type.

 

[Nitefly]

you're not getting enough information from the first two questions

div0 posted a helpful suggestion earlier

I just had a look, interesting ideas but I don't think you can identify anything from one question alone - the 'random' god just throws everything into the air, at least until you can qualify the answer.

 

[div0]

Nitefly, I'm pretty sure you can eliminate the random god with my approach.

Back home today, so can try to explain why it works in more detail later.

 

[Jono8]

You're getting really hung up on things that don't matter and don't make any difference to the problem. They are not 'fabricating evidence' - they are simply defining correct logical statements and testing them. Specifically, they are making IF statements (if my eyes are not green...) - in fact a chain of nested IF statements. The statements are then tested by the actions of the other dragons which allows conclusions to be made. It makes no difference whatsoever to the process that all the statements are proven false in this case (because all dragons have green eyes), nor does it make any difference that they already know (because they can see) what the outcome of all but the last test will be. Makes no difference. You need to let go of the idea that logical statements being proven false (even before they are tested) means the process doesn't work. A statement being proven false is as conclusive as a statement being proven true.

The process would work just the same if there were one or more blue eyed dragons in the population. In that case some of the IF statements would test out to be true. The process would always weed out however many green eyed dragons there were in the population in that same number of days.

I'm sure some clever programming type could write out the whole 100 dragon problem as a 100 level deep nest of IF statements, but I'm not a clever programmer type.

Bit each dragon knows that each dragon knows that each dragon can see 98 green eyed dragons. If that is the case and they are completely logical, why do they start the whole process by testing the 'theory' - "If anyone can see no green eyes today then they will turn in to a sparrow tonight"? Why would they all not start by saying:

I know that there are at least 98 green eyed dragons, so if anyone looks out today to see 97, they must be green eyed also and turn into a sparrow at midnight - they don't

Ok I know that there are therefore at least 99 green eyed dragons so if anyone looks out to see 98 green eyed dragons then they will know they have green eyes and turn into a sparrow - they don't

Ok, I now know that there are therefore at least 100 green eyed dragons - everyone turns into a sparrow.

Why don't they all turn on the 3rd day? Why do they test it for 97 days drawing conclusions that they already know the answer to. Conclusions that they also all know that the others know the answer to.

I would still have difficulty with the above though as well because it means a dragon who can see 99 green eyed dragons has to say " if anyone can see only 97 green eyed dragons..." which he knows is impossible, and therefore the information he finds out from it should not be new information and help him in anyway to come to a conclusion.

 

[Threepwood]

I am there. *whoot!* It all hinges on..

Spoiler

making the true god always say 'da' & making the false god always say 'ja'

Here is my attempt at explaining how it is done.

Spoiler

Ask any god "Would you say 'da', if you were the truthful god & I asked you, are you the truthful god?'"

The truthful god can only answer 'da' to this question.

The false god can only answer 'ja' to this question.

The random god will answer 'ja' or 'da' to this question.

.
.
If T and da = yes then da (because yes he is truthful so he would say no - da)
If T and da= no then da (because yes he is truthful so he would say no - da)

If F and da = yes then ja (because if I were truthful I would say yes - da, but i'm false so ja - no)
If F and da = no then ja (because if I were truthful I would say yes da, but i'm false so ja - no)

If R then da or ja (because )
.
.


So if you ask two gods the same question... you will either get ja&ja, da&da or a mix of ja&da/da&ja.


If you get da&da you know that the two gods that you asked a question of, are either the true or the random god. So the one who was not asked a question must be the false god.

If you get ja&ja you know that the two gods that you asked a question of, are either the false or the random god. So the one left out must be the true god.

If you get da&ja/ja&da you know that the two gods that you asked a question of, are the true and the false god. The one left out must be the random god.

.

.

.

So!

If you get a mix of 'da/ja', you now have the Random god pegged, so the question to ask either of the two remaining gods (false and true) is...

...the same question!!! WOW. Because Truthful will always say 'da' and False will always say 'ja'.

This is great, it means we now who everyone is but we still do not know what 'Da' or 'Ja' means!!!

Really fun. Thats like getting the key word in the crossword that makes the crossword come alive and tell a story...if anyone gets what I mean there.




But...Alas... the story is not over! For that is only the solution to getting a mix of 'da&ja'



If we get 'ja,ja'... we know that False and random have been asked, so True is left!

How to make true say only 'da' if asked about the False god and only 'ja' if asked about the random god? (or vice-versa)...

...so we ask True, "Would you say 'da' if I asked you if this god *puts hands on shoulders of god other than Truthful god* is the False god?"

If my hands are on the shoulders of the false god he will say always say 'Da' and if my hands are on the shoulders of the random god he will always say 'Ja'.


I'm finding it very difficult to explain exactly why he has to say 'da' or 'ja', but if you visualise putting your hands on the gods shoulders and then asking the True god that question. it works.

Or this might help...

If F = true & da = yes then da (because he is false and since da equals yes, I would say 'da')

or

If F = true & da = no then da (because he is false and since ja equals yes, I would not say yes I would say no...which is 'da')



Again, we have seperated T,F and R...Without knowing what yes or no is yet!



Now....I am presuming that it is just as 'easy' to figure out what to ask the false god if you get him as the singled out god.

But I'm going to look into that after some coffee...Oh my days! I've not been able to sleep more than a few hours without waking up with this lot in my head.


After coffee, I'm going to think about if the given answers can be used to find out what da and ja mean, or not.


Might post a photo of my crazy man workings out too!



Time for the music to play .....

Omg, I hope I have not made a mistake and all that is wrong!

*quivers*

 

[div0]

I think you're close, but this doesn't make sense:

If you get da&ja/ja&da you know that the two gods that you asked a question of, are the true and the false god. The one left out must be the random god.

You could have asked truth+random, or false+random.

But you're on the right lines (if my solution above is indeed right). And I think you can eliminate random with only one question (similar to your thought process already).

 

[Kosmiche]

no

 

[Threepwood]

No, no, no!

You mean, it is not over???

Whyyyy!!!!



Okay! So the error is that...

If you get da&ja/ja&da you know that the two gods that you asked a question of, are the true and the false god. The one left out must be the random god.

Is false, and should read..

If you get da&ja/ja&da you know that the two gods that you asked a question of, are the true and the false god. The one left out must be the random god.

or

you know that the two gods that you asked a question of, are the true & random. leaving false.

or

you know that the two gods that you asked a question of, are the false & random. Leaving True.



So we have three possibles out of the mix R+TF, T+FR and F+RT and not only R+TF.

Okay, am on it like a car bonnet..

 

[Threepwood]

double post

 

[Greboth]

Glad we are finally talking about the God problem, interested to have a more detailed explanation div0 as all my methods get screwed over by random god.

 

[Judgeneo]

I think you're close, but this doesn't make sense:

If you get da&ja/ja&da you know that the two gods that you asked a question of, are the true and the false god. The one left out must be the random god.

You could have asked truth+random, or false+random.

But you're on the right lines (if my solution above is indeed right). And I think you can eliminate random with only one question (similar to your thought process already).

Yeah I think I figured this out on the train earlier too, I'll try writing it all down later to confirm my thoughts, and post tonight.

 

[TheBDog]

no

I disagree

 

[div0]

Ok here goes:

God problem

Spoiler

Question 1 To God A - If I asked you if God B is random, would you say ja?

Random: If God A is random, then you will randomly get Ja/Da


True: If God A is true, then by asking him a question in the format 'If I ask you X, would your answer be Ja', then we get:

Assuming ja=yes and da=no.
If he responds with ja(yes), this means the truthful answer to X is ja(yes)
If he responds with da(no), this means the truthful answer to X is da(no)

Assume ja=no and da=yes.
If he responds with ja(no), this means the truthful answer to X is da(yes)
If he responds with da(yes), this means the truthful answer to X is ja(no)

False: If God A is false, then by asking him a question in the format 'If I ask you X, would your answer be Ja', then we get:

Assuming ja=yes and da=no.
If he responds with ja(yes), it means that his answer to X is da(no). But because he is lying, this means the truthful answer to X is ja(yes)
If he responds with da(no), it means that his answer to X is ja(yes). But because he is lying, this means the truthful answer to X is da(no)

Assume ja=no and da=yes.
If he responds with ja(no), it means that his answer to X is ja(no). But because he is lying, this means the truthful answer to X is da(yes)
If he responds with da(yes), it means that his answer to X is da(yes). But because he is lying, this means the truthful answer to X is ja(no)


As you can see, in both of the above cases the God A will say 'Ja' when God B is the random god.

So if God A say 'Ja', you know that God B is the random god, or you are talking to the random god already. Either way you know that God C cannot be random.

Similar applies to if he answers 'Da'. This tells you that you're either already talking to the random God, or that God B is not random. Either way, you can deduce that B is not random.


Question 2 To the non-random God identified above (ie True or False god)

If I asked you if you're true, would you say ja?

Similar to above logic, both gods will answer Ja=Yes and Da=No.

Question 3 To the same god above

If I asked you if God A is random, would you say ja?

Again, Ja=Yes, Da=No.

You now know the identity of all gods.

 

[div0]

Glad we are finally talking about the God problem, interested to have a more detailed explanation div0 as all my methods get screwed over by random god.

See above, I have put my answer in SPOILER tags.

Hope it makes sense. If I've made a mistake I'd be raging, but I think it works!

 

[Judgeneo]

"To God A - If I asked you if God B is random, would you say ja?"

This I think is where the problem is. If you knew that ja/da = yes/no, then the question you have asked is "If I ask you X, will you say yes?"

Lets assume the answer for X is correct
Truthful God:
X = Yes (answering the first question). Yes * true = Yes (Applying the truth of the God), Yes*Yes = Yes (Answering the second question), Yes * true = Yes (applying the truth of the God
X = No. No * true = No, no*Yes = No, No * true = No

False God:
X = Yes. Yes * false = No, No * Yes = No, No* true = Yes
X = No. No * false = Yes, Yes * Yes = Yes, Yes* false = No

As you can see, the yes god and the no god would both answer the same, so you haven't gained anything by itself. Therefore you cannot guarantee that the second question is asked to the random god, and your solution falls over.

Back to the drawing board!

 

[div0]

As you can see, the yes god and the no god would both answer the same, so you haven't gained anything by itself. Therefore you cannot guarantee that the second question is asked to the random god, and your solution falls over.

No it doesn't.

You just want to avoid the random god with the second question. Not specifically to find out which god is definitely random.

Why don't you think it works? Your logic doesn't make sense to me.

/edit

"To God A - If I asked you if God B is random, would you say ja?"

This I think is where the problem is. If you knew that ja/da = yes/no, then the question you have asked is "If I ask you X, will you say yes?"

Lets assume the answer for X is correct
Truthful God:
X = Yes (answering the first question). Yes * true = Yes (Applying the truth of the God), Yes*Yes = Yes (Answering the second question), Yes * true = Yes (applying the truth of the God
X = No. No * true = No, no*Yes = No, No * true = No

False God:
X = Yes. Yes * false = No, No * Yes = No, No* true = Yes
X = No. No * false = Yes, Yes * Yes = Yes, Yes* false = No

I think you're getting confused about what knowledge I'm trying to gain from the question.

I am not trying to work out whether I am speaking to the true/false/random god. I am trying to find a way to word the question such that if a get a particular answer (ja/da), then I know that both the true and the false gods would be saying the same thing about X (yes/no).

Question 1 To God A - If I asked you if God B is random, would you say ja?

Broken down gives:

Q1a : Is God B random?
Q1b : Was your answer to Q1a, Ja?

Ja=Yes, Da=No

God A = Truth

If God B is random
Q1a = Yes (Ja)
Q1b = Yes (Ja)

If God B is not random
Q1a = No (Da)
Q1b = No (Da)

God A = False

If God B is random
Q1a = No (Da) - a lie
Q1b = Yes (Ja) - another lie

If God B is not random
Q1a = Yes (Ja) - a lie
Q1b = No (Da) - another lie


Da=Yes, Ja=No

God A = Truth

If God B is random
Q1a = Yes (Da)
Q1b = No (Ja)

If God B is not random
Q1a = No (Ja)
Q1b = Yes (Da)

God A = False

If God B is random
Q1a = No (Ja) - a lie
Q1b = No (Ja) - another lie

If God B is not random
Q1a = Yes (Da) - a lie
Q1b = Yes (Da) - another lie


As you can see:

In the case where God B is random - the overall answer to the question (Q1b answer) is always Ja from both True and False, irrespective of whether Ja=Yes/No.
If you get a 'Ja' answer, then you know that God B is random or the only other alternative is that you're speaking to the random god (God A). Either way God C cannot be random. So address your next question to him.

In the case where God B is not random - the overall answer to the question (Q1b answer) is Da from both True and False. So you know either God B is not random, or you're speaking to the random god (but you're speaking to God A, so if he is the random god, then God B cannot be random). Either way God B cannot be random. So address your next question to him.

I hope that makes it clearer.

 

[Judgeneo]

No it doesn't.

You just want to avoid the random god with the second question. Not specifically to find out which god is definitely random.

Why don't you think it works? Your logic doesn't make sense to me.

When you ask the first question, they say ja or da. At this point you know nothing about whether ja is yes or no, and which god is what as there is no reference to compare it to. If God A is truthful, the answer is ja. If God A is the Liar, the answer is ja, if God A is random, the answer could be ja. There is no way of knowing, so you cannot guarantee that the second question is not asked to the random God.

You need to ask two questions before you can gain any information.