Three Gods

[mmiguel]

Three gods A , B , and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A , B , and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer in their own language, in which the words for yes and no are “da” and “ja”, in some order. You do not know which word means which.

[Rob_Gandy]

A. Is your answer to this question a lie? OR B. Is your answer to this question the truth? Anyone you ask A will answer No and anyone you ask B will answer Yes. This will let you know which word is yes and which is no.

I think this is where I would start. Still working on Q#2 and 3.

[Yoruichi-san]

Assuming if you ask a god a question they can't answer, they'll say nothing or something completely different that means, like, 'error'...

Ask two of them "If I ask you next 'Is the sky blue', will you answer da or ja?"

If one can't answer, he is the random answerer, otherwise both will answer which ever is yes and the third is the random.

Third question, ask one that answered yes to the first question, "Is the sky blue?" to discern if liar or truth teller.

[TheChad08]

Assuming if you ask a god a question they can't answer, they'll say nothing or something completely different that means, like, 'error'...

Ask two of them "If I ask you next 'Is the sky blue', will you answer da or ja?"

If one can't answer, he is the random answerer, otherwise both will answer which ever is yes and the third is the random.

Third question, ask one that answered yes to the first question, "Is the sky blue?" to discern if liar or truth teller.

One issue is that you don't which (da or ja) means yes and which means no.

[phaze]

How omniscient are the 3 Gods?

By this I mean

Can the three identify each other?

and

Can the truth and lying God reliably predict what the random God is going to say if asked?

Edit: can they reliably predict what the random God will say in future?

Is the random God capable of changing his mind one he has decided to go down the path of truth or the path of lies? i.e is is possible to ask him the same question twice and get different answers

Edited September 18, 2012 by phaze

[Rob_Gandy]

Assuming if you ask a god a question they can't answer, they'll say nothing or something completely different that means, like, 'error'...

Ask two of them "If I ask you next 'Is the sky blue', will you answer da or ja?"

If one can't answer, he is the random answerer, otherwise both will answer which ever is yes and the third is the random.

Third question, ask one that answered yes to the first question, "Is the sky blue?" to discern if liar or truth teller.

Will they try to be tricky and answer the question as "If I ask you a question will you answer with either da or ja?" True would say yes, False no and Random either. So assuming you can pose a question the Random can't answer, I would change the first question to "If I ask you next 'Is the sky blue', how will you respond?"

Now, I'm assuming that no matter what question you pose they will all be able to answer, so I'm still stumped for now.

[Yoruichi-san]

One issue is that you don't which (da or ja) means yes and which means no.

I meant whatever they answer will mean yes, since truth teller will truthfully answer 'yes' and liar would say 'no' to "is the sky blue", but he'd lie to this question and hence answer 'yes'.

Will they try to be tricky and answer the question as "If I ask you a question will you answer with either da or ja?" True would say yes, False no and Random either. So assuming you can pose a question the Random can't answer, I would change the first question to "If I ask you next 'Is the sky blue', how will you respond?"

Now, I'm assuming that no matter what question you pose they will all be able to answer, so I'm still stumped for now.

If it's truly random, there is no way they can answer every question...but if you want to assume they pre-agreed and memorized the lie/truth pattern of the Random teller...

...is you

. Ask: "If I knew which one of the three you were, then what would would I say you would answer to the question 'is the sky blue?'" to two of them, then follow up as above.

[Yoruichi-san]

If it's truly random, there is no way they can answer every question...but if you want to assume they pre-agreed and memorized the lie/truth pattern of the Random teller...

I.e, alternatively...

If I ask you n more questions and then for the (n+1)th question asked "is the sky blue?", would you say the ja or da equivalent of 'yes'? Or, "If I ask you an infinite number of questions and one of those questions is "Is the sky blue", would you say...etc.

Edited September 18, 2012 by Yoruichi-san

[phaze]

Can we assume that they know what questions I am about to ask before I ask them?

[mmiguel]

A. Is your answer to this question a lie? OR B. Is your answer to this question the truth? Anyone you ask A will answer No and anyone you ask B will answer Yes. This will let you know which word is yes and which is no.

I think this is where I would start. Still working on Q#2 and 3.

Not all will answer that way with certainty, just 2 of 3.

[mmiguel]

Assuming if you ask a god a question they can't answer, they'll say nothing or something completely different that means, like, 'error'...

Ask two of them "If I ask you next 'Is the sky blue', will you answer da or ja?"

If one can't answer, he is the random answerer, otherwise both will answer which ever is yes and the third is the random.

Third question, ask one that answered yes to the first question, "Is the sky blue?" to discern if liar or truth teller.

A question that cannot be answered --- sounds like a paradox.

Likely not to get much useful info out of a paradox.

Random can always answer, since he doesn't even need to listen to your question, he can ignore you, flip a coin or roll a die and give you whatever answer he chooses.

[mmiguel]

How omniscient are the 3 Gods?

By this I mean

Can the three identify each other?

and

Can the truth and lying God reliably predict what the random God is going to say if asked?

Edit: can they reliably predict what the random God will say in future?

Is the random God capable of changing his mind one he has decided to go down the path of truth or the path of lies? i.e is is possible to ask him the same question twice and get different answers

They are omniscient.

They each know which God is which.

Random can provide different answers to the same question.

I guess I don't see any harm in them knowing what Random will say if for example you were to use question 1 to ask what Random would say question 2 or on question 3.

Edited September 18, 2012 by mmiguel

[mmiguel]

Can we assume that they know what questions I am about to ask before I ask them?

Hmm....

That could make things complicated because we can get into a circular: "but he knows that I know that he knows that I know that ....", which I would prefer to avoid.

The correct answer allows you to identify which Gods are which regardless of what they think you are thinking.

Edited September 18, 2012 by mmiguel

[phaze]

I can determine which one the lier is by asking "What answer will the Random God give when answering this question?" Lier is the one who answers differently (don't need to know what "da" or "ya" means)

[mmiguel]

Three gods A , B , and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A , B , and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer in their own language, in which the words for yes and no are “da” and “ja”, in some order. You do not know which word means which.

There are 3 smaller, easier puzzles that may serve as hints to building up the answer to this one.

I will post the first one below. Those with pride, feel free to not look.

Noting their locations, I place two aces and a jack face down on a table, in a row; you do not see which card is placed where. Your problem is to point to one of the three cards and then ask me a single yes-no question, from the answer to which you can, with certainty, identify one of the three cards as an ace. If you have pointed to one of the aces, I will answer your question truthfully. However, if you have pointed to the jack, I will answer your question yes or no, completely at random.

Edited September 18, 2012 by mmiguel

[mmiguel]

I can determine which one the lier is by asking "What answer will the Random God give when answering this question?" Lier is the one who answers differently (don't need to know what "da" or "ya" means)

i believe your question as it is, is not answerable in general, since the random god can change his answer if you ask him multiple times (a truthful or lying god, would need to know *which* occurrence of you asking the random god you are talking about in order to give a meaningful answer.

i think there is no way to guarantee that the random god will answer differently from the liar, hence you cannot say that the liar will provide a different answer, because the random god can answer however he pleases in his own unfathomable way.

Edited September 18, 2012 by mmiguel

[kbrdsk]

What happens when you ask the truth teller or the liar a question they can't answer?

[superprismatic]

If I happen to point to the jack, then your response will convey no information to me since that response depends only on a process (the random yes-no generator) which is completely hidden from me. This is, therefore, a case where I could not learn anything about where an ace may be. I conclude, then, that any answer to this puzzle must depend on trick wording or some such chicanery.

[Yoruichi-san]

Okay, let me get this straight. We're assuming:

1) Random means the god will randomly answer YES or NO regardless of the question, not will randomly answer truthfully or not.

2) The gods all know what random's YES/NO pattern will be.

Ask two of them: "If I ask the random god a random number of questions, then ask him 'Is the sky blue', will he answer the ja/da equivalent of YES?

This will tell you who the random god is since only the random god will be able to answer. Ask the one (or one of them if both couldn't answer): "Does da mean YES?" If he answers da, it's the truthteller, if he answers ja, he's the liar.

This is not a paradox, it is a strategy that utilizes the fact that random is random .

[TheChad08]

Okay, let me get this straight. We're assuming:

1) Random means the god will randomly answer YES or NO regardless of the question, not will randomly answer truthfully or not.

2) The gods all know what random's YES/NO pattern will be.

Ask two of them: "If I ask the random god a random number of questions, then ask him 'Is the sky blue', will he answer the ja/da equivalent of YES?

This will tell you who the random god is since only the random god will be able to answer. Ask the one (or one of them if both couldn't answer): "Does da mean YES?" If he answers da, it's the truthteller, if he answers ja, he's the liar.

This is not a paradox, it is a strategy that utilizes the fact that random is random .

But we claimed that the other God's know his answer, so therefore with that question you could get the two you ask saying yes , or the two you ask saying no, or different answers for each.

[Rob_Gandy]

There are 3 smaller, easier puzzles that may serve as hints to building up the answer to this one.

I will post the first one below. Those with pride, feel free to not look.

Noting their locations, I place two aces and a jack face down on a table, in a row; you do not see which card is placed where. Your problem is to point to one of the three cards and then ask me a single yes-no question, from the answer to which you can, with certainty, identify one of the three cards as an ace. If you have pointed to one of the aces, I will answer your question truthfully. However, if you have pointed to the jack, I will answer your question yes or no, completely at random.

I would ask, "Is the card to the right/left an ace?" If yes pick that one if no pick the other one. Still trying to apply that to the OP though.

[Yoruichi-san]

But we claimed that the other God's know his answer, so therefore with that question you could get the two you ask saying yes , or the two you ask saying no, or different answers for each.

They know his pattern, but since I specify it is random at which point in the pattern I'd ask the question, they cannot know which his answer will be.

[phaze]

They know his pattern, but since I specify it is random at which point in the pattern I'd ask the question, they cannot know which his answer will be.

The way I understand it is they are God's, they know everything, they know both the Random Gods pattern and where he is in that pattern. They know what the Random God will answer even though it be random as if the random God had prepared beforehand a sheet of paper that says the first time I will answer it Da, the second time Da, the third time Ya. Of course the values on the paper are random in every sense that the word "random" is random

[Yoruichi-san]

The way I understand it is they are God's, they know everything, they know both the Random Gods pattern and where he is in that pattern. They know what the Random God will answer even though it be random as if the random God had prepared beforehand a sheet of paper that says the first time I will answer it Da, the second time Da, the third time Ya. Of course the values on the paper are random in every sense that the word "random" is random

Right, but I'm adding an extra hypothetical random, i.e., one that is not on the sheet of paper, that is hypothetically at some point which is randomly determined (and independent of the random god's 'random') if I ask that question what will he say. I.e. if I randomly pick a point on that paper...

And I don't care how omniscient these gods supposedly are...there are some things that are just unknowable...or do I need herr Heisenberg to let loose the hounds? ;P

However, if you want to specify that questions are could be unanswerable are disallowed, fine...

Ask A, "If I ask you if B is the random god, would you say ja?" If he says ja, then either A or B is the random god. If he says da, either A or C.

Ask the one you know is not the random god, "If I ask you if A is the random god, would you say ja?", if he says ja A is the random god, if da, the other one.

Finally ask one of the non-random gods: "Does ja mean yes?" If ja, he's the truth teller, if da he's the liar.

[mmiguel]

If I happen to point to the jack, then your response will convey no information to me since that response depends only on a process (the random yes-no generator) which is completely hidden from me. This is, therefore, a case where I could not learn anything about where an ace may be. I conclude, then, that any answer to this puzzle must depend on trick wording or some such chicanery.

There is a logical solution.

[mmiguel]

Okay, let me get this straight. We're assuming:

1) Random means the god will randomly answer YES or NO regardless of the question, not will randomly answer truthfully or not.

2) The gods all know what random's YES/NO pattern will be.

Ask two of them: "If I ask the random god a random number of questions, then ask him 'Is the sky blue', will he answer the ja/da equivalent of YES?

This will tell you who the random god is since only the random god will be able to answer. Ask the one (or one of them if both couldn't answer): "Does da mean YES?" If he answers da, it's the truthteller, if he answers ja, he's the liar.

This is not a paradox, it is a strategy that utilizes the fact that random is random .

Could we really distinguish between someone whose policy is to randomly select yes or no to each yes-no question against someone whose policy is to randomly select to be truthful or false, and then correspondingly select yes or no to each yes-no question?

I don't really see how the other two gods would be unable to answer.

The only possibilities that I can think of where they might not be able to answer is if the question is bad -> if the question doesn't make sense, if it has no answer, if it has multiple different answers depending on some ambiguous context, or if it is a paradox.

The solution I have in mind does not require asking questions that any god may not be able to answer.