Three Gods
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.
- hamujemy
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.
- hamujemy
Labels: SharedPuzzle
posted by Rajesh Lal at
12:11 AM
74 Comments:
wow, can any1 think of any way???
im completely clueless!!!!
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I must apologise. I am hamujemy who posed the question.
I was given this puzzle many years ago and have been ripping my hair out trying to solve it.
I know that I should post the answer within a week, but I must confess that I don't know it.
Please excuse me and I hope that someone can put an end to my misery of not knowing.
Thank you
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LOL. Thank you for that. Even if no-one can solve it, it sounds like a wonderful problem. I'm glad you risked posting it. I take that risk myself sometimes and hope someone can save me from the shame of not knowing the answer.
As it looks quite tricky, can you say whether you believe all three questions must be to just one of the gods, or is it one question to each god? Thank you.
... I'm assuming that it can be three different questions.
Chris,
I believe that each God can be asked any yes/no question. The only stipulation is that each god is only asked one, making 3 in total.
This puzzle has been driving me mad for years. I periodically go back to it, but have never found anyone who can solve. I don't know the origin of it.
ps I used to be "anonymous" who had first post in your puzzle about 3 men in a hotel.
I have just spoken to someone about posting this puzzle who has told me that the solution is on wikipedia.
i dont want to look in case its too simple and I feel like a buffoon
I looked at the puzzle on wikipedia. I havent looked at the answer but the clarifications offered might help...
It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).
What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.
Random will answer 'da' or 'ja' when asked any yes-no question.
Hi Agrajag. I love the word "buffoon". Thanks for the info. I thought your answer to 3 men in a room, was very neatly stated.
Hi Thrym, Thank you for that info. That could be very helpful. Aren't I the optimist;) I don't want to look it up either - that's no fun.
Agrajag, ... and welcome aboard.
I think one of the questions might be along the lines, "Would both of the other gods answer my questions consistently?". I'm not sure if that can be the first question though. Also it seems pointless to knowingly ask the random god anything - so obvious you might miss it.
Think carefully about this statement...
Random will answer 'da' or 'ja' when asked any yes-no question
And you realize that any question posed to Truth, asking about Random's answers, will be unanswerable. Since Truth will never know how Random will answer.
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Hi again Thrym. I just beat you to it (by seconds) - how to deal with that problem.
i really think this is only possible if you are _allowed_ to put each question to more than one god!
if you are allowed i even have a solution ^^
I've thought of a few more questions to ask. But I'll hang onto them for a while.
One interesting question is "If I were to ask the random god any question whose answer is 'yes', what would he answer?" True and False would disappear in a metaphysical dichotomy, but Random might be able to respond (not sure about that last one as not sure if the poster may have been careless, or not, about how the random god works). :)
Looks like you are thinking from a different direction though. My point was that you could determine which was Truth with any question referring to the other gods responses. And that is also the answer....
Ask A: Will B and C tell me 'da' means 'yes'?
If unable to answer then A is truth. If A answers then move to B.
Ask B: Will A and C tell me 'da' means 'yes'?
Again if unable to answer then B is Truth. If B answers then move on to C.
If B answered then we know C is Truth.
Ask C: Will A tell me 'da' means 'yes'?
If unable to answer then A is Random. If C answers 'da' then 'da' means 'no' cause A will be false. If C answers 'ja' then 'ja' means 'no' cause A is still False.
I hope that reads the way I am thinking it.
Hi t:b:H. I think we've decided!!!! that you can ask a total of three questions. Whether they're the same or not is up to you. You can't e.g. ask each god three questions.
I just noticed your follow up - have we understood the rules correctly. Is the random god really answering questions but with a random answer, or is he simply saying "da" or "ja" just because he's been asked a question?
Give us a bone :)
Chris, wouldnt that end up the same? Random is random...and just giving an answer to a question would still be random.
Hi Thrym, Just a quick post to acknowledge yoour post. It made my head hurt.
I like the idea about asking about "da" and "ja" - I hadn't thought of that (yet).
Now I'm going to read your post properly. Especially as you seem to have got the answer. Greetz.
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As a side note...whenever you find Truth you can skip to the last question to determine False and Random.
Oh... and I promise I havent looked at the answer yet.
If random was sentient he'd disappear too (I think).
I dont think Random would disappear. But your thought about False disappearing might be right since he would have trouble lieing about Randoms answer.
I'm not sure if exterminating the gods is allowed. I think the questions posed to them should be answerable. Just a niggling doubt.
ANyway back to read your answer:)
I read nothing in the rules about making their brains implode. :)
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You distracted me again ;) If he were sentient. Random could not internally choose yes or no whether or not he's in honest or lie mode. The question is unanswerable. A thickie god wouldn't be bothered by that detail.
I'm starting to get too deeply into this aspect of the problem.
well, IF you're allowed to put one question to more than one god then do it like this:
1st Q(to all): -answer is truth-
e.g.: "Are you gods?"
--> Truth will answer yes, Lie answers no, Random yes or no (You still don't know whats what).
The point is, two will answer the same, lets say B and C and one will answer sth. else, lets say A.
=> A is either Lie or Truth NOT Random
2ndQ(to god A): -answer is no for Truth and Lie-
eg: "Are you Lie?"
-> both will answer no, look up 1stQ, and compare to know if you are talking to Lie or Truth.
3rdQ(to god A): point to B or C(doesn't matter), and ask if he is Random.
Based on 2ndQ, you know how it is meant(always true, or always lie) and you can deduce which of B and C is random, and logically also the third one.
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I don't think either works. But I'll recheck I'm not in error.
If you can ask all three the same question at once (and only counts as one question), I'd try "Do you tell the truth?"
T->y, F->y, R->?. Then you'd know if "da" or "ja" meant "yes".
If R said "no", then you'd know he was randaom. And the problem reduces to asking either of the others "If I asked the other god if he spoke the truth, what would he say?". Y->y, N->n.
That's as far as I got before impatience made me post. I'll tell you where I think you've gone wrong (if you have) in a few minutes.
Just re-checked the question. It seems clear that you can only speak to one god at a time.
So I'll ignore anything that doesn't comply with that (unless it's funny).
Thrym, If ask the question "will the other gods tell me that 'da' means 'yes'?".
T-> n, F->y, R-> n/a or y.
I'm assuming that R is already in lie or truth mode when you ask the question. I'm also assume that T really means "not always", which is nothing to do with what F would say or what "da" means. That's as far as I've got for now.
I pretty sure that any question has to be asking what the other god(s) would say. It's the only way to tap they're presumed knowledge of each other.
I've thought of a variation on this. I'll keep it to myself, for now, it could be quite a good puzzle - make this one look tame ^^
I have realised over time that we have to ask each god some kind of conditional question like " if I asked you if you were random, would you say ja". This would give more information, but I still can't get anywhere.
I hope you will all agree that we must find the god who is not random first, leaving it easier to find true and false.
Now you know why I have been going mad with this.
Also, your right Chris, you speak to one at a time.
The question states that each question must be put to exactly one god. I assume that means you could ask 1 god 2 questions and not ask any questions to another.
Ask one god "Will the other gods tell me that 'da' means 'yes'?"
If you pretend that you asked the inner question directly to a god,
then T->da, F->ja, R->random. Took ages to work out (shame on me).
It doesn't look useful by itself.
Now if ask the outer question, taking their answers to allow for
R's unreliable nature: T->no, F->yes, R->? Still not looking useful.
Hmmm. I thought we were getting somewhere, suddenly I'm plunged into
the deepest pits of despair. The god of Random is a pain. I can't
think of anything that isn't an unanswerable question ploy. Even
those don't seem too helpful.
Agrajag, just saw your post in time. It's a mighty fine question.
The only thing I'm assuming is that the gods know who each one is,
and that you probably ask a question about what another one would
say, or what another one would say about another one. Deeeeeeep:)
Definitely appreciate your frustration.
I agree, three questions total, and only to one god at a time. No other restrictions. e.g You could ask only one god all three questions.
You must not ask one god all the questions. If it was R you will learn nothing. He could lie three times straight for instance.
I think that you have to talk to at least two gods. Fat lot of help thtat is.
Sorry, I'm spelling out the obvious.
well, i know how the puzzle was placed, thats why i told:
"t.:b:H said...
i really think this is only possible if you are _allowed_ to put each question to more than one god!"
meaning not the same question to other gods, but EACH to more than one =)
Can anyone of you solve it even if you would know what "yes" and "no" means, with that strict "one-quest.-one-god" condition??
I'm sure that the 1 Q 1 G is right. And "no", I can't do it even knowing da and ja, or even when as was considering a multi-god question as one question, I didn't see how to do it. It's me beat so far.
---------
Just bringing a few possible questions and answers into one post for reference.
"Does 'da' mean 'yes'?" => T->da, F->ja, R->random.
If get back 'ja', then can't be T (so is F or R).
If get back 'da', then can't be F (so is T or R).
"Are you T?", T->y, F->y, R->random
If get back n, then must be R. If get back y, then no info.
Punch one. Then ask "Did I just hit you"
You can take it from there.
LOL to that, I think I prefer exterminating them.
It may be that at the end we still don't know what da and ja mean. We're not being asked to find that out. SO you don't HAVE to ask questions that try to find that out.
good point... but as we are asking yes/no questions, as soon as we know who is who, and who gave which answer, you also know the meaning.
So maybe you don't need to know the words to know the gods, but you know the words when you know the gods^^
Although my intuition tells me, that you will first know the words before you know all gods
I expect you're right tht will will also know what da and ja means.
Been ripping hair out trying to think of a question that both T and F will give the same answer to => R will as well, just realised that is useless too.
It may also be that all three questions may have to be asked before you can deduce anything. But again, not necessarily.
well, again i think its not possible, just wanna show why.
look at every question as one condition, so you have 3 conditions and 3 unknowns(our gods). but every time you ask Random, the condition won't give you any information. As the best you can do is to ask Random only once, i.e. 1q - 1god, you get only 2 conditions for 3 unknowns. just think of it as under-determined system of equations.
Or maybe thats just the way i see it, and i am forgetting sth important.. Dunno, gn8 folks maybe tomorrow again
maybe that can help those who aren't as desperate as me ^^
Propositional Logic Calculator
http://logik.phl.univie.ac.at/~chris/gateway/formular-uk-zentral.html
The fact that you only have 3 qs makes me think you can only get solve for 3 vars. But, as knowing T and F and da say, automatically means you know R and ja, maybe you can know all the info. gn8.
What is the sth? I first thought it was a typo. Just in case, I wan't trying to disagree with you in my last post, just throwing my 2c in :)
oh, i have at least 17ct hanging here around my desk ;)
sth. means something, and my talk about equations and stuff is only what i think might be, not proven or even directly related at all.
t:b:H this prob keeping u up?
I understand that we're all struggling and throwing in thoughts in case they help a penny drop somewhere. I'm only used to simultaneous equations in continuous variables, not sure how to talk about these discrete variables either. But I think the idea of reasoning in terms simultaneous equations is perfectly valid.
It's that pesky random that's giving me grief. I feel that it is necessary to ask questions about the consistency of the possible answers that the gods would give. Just can't think of the right question(s).
Answer can be found here: http://en.wikipedia.org/wiki/The_hardest_logic_puzzle_ever
Too much to put here and can become very confusing, you may have to read it slowly....
Random true is always sometimes speaking untruthfully and yet speaks that random true is always true in which random true is a randomly true thing
Sorry to drop out like that but I had some stuff to do. As far as a single question goes it could be along the lines of what I think Alice in Wonderland used....
If I were to ask you yesterday what would your answer be?
Not the exact question but I think you get the idea.
Truth would answer the same for both days, False would have to lie about a lie thereby giving the true answer and Random would still be random
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Ok, here my little contribution.
First, I don't think the problem has a solution. We have to classify 3 gods, for which we need log2(3)=1.58 bits of information, plus 1 bit for the da/ja classification, which means that in theory, three questions (3 bits) would be enough to solve it. But the problem is the random god which, I believe, adds a bit of randomness and though I'll need plus information to solve the problem: it will be bigger than 3 bits (although I can't quantify it), and three questions won't be enough. Please proove me wrong and solve it!
I thought about it for some time, and I think that, if there is a solution, it must be based on some premisses:
i) A, B and C are gods, and so they know EVERITHING, even what your questions will be, and what the answers will be. These guys know the past, the present and the future (by god's definition); and
ii) the universe where these gods live is logically coherent, in the sense that there can be no paradoxes. For example, if you choose a set of questions that would create a contradiction in the answers if you ask the first question to god True, then the god you ask the first question cannot be the god True.
Based on this, I tryied to solve a simpler problem, forgetting the da/ja stuff: normal gods that say yes and no. I got some interesting results.
I managed to find three questions, one for each god, that only two possible answer sequences did not lead to paradoxes, that is, only two anwers sequences are allowed in the universe. These sequences where yyn and nyn; yyn implied that god C was True, and the sequence nyn that god C was False. "Good!", I thought, "I solved it! I ask the first question, and based on that I know which is C!". But then I realised that the paradoxes were present only if I make the three questions, and so I coudn't change the questions once I started to make them (remember, gods know your questions and their answers in advance).
Thinking a little bit more, I found those two initial questions:
1) Is the answer of the next question a yes?
2) Is the answer of the previous question a yes?
if the first two answers is yy, then gods A and B are either T or R, which means that god C is F; yn means A and B are F or R, which makes god C the T one; same to ny and nn is the same of yy.
These result means that if by chance you ask first the mighty T and then the all powerfull F, you have a paradox! That is, in this universe, once you pick the questions, logical laws are a guarantee that the two first gods you ask are not F and T (kind of philosophical, isn't it?).
Once you know what the C god is (remember it cannot be the R once you choose the questions), the next question to solve the problem is easy.
I tried, without success, to include the da/ja in this approach. As I said before, I don't think it's possible, but I hope I had contributed for some extra-work to trickofmind addicts :)
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Hi Miguel (and eveyone). As we've got 3 binary response questions, I reckon we can get 2^3 = 8 combinations. If "no response" is allowed, we've got3^3 = 27 combinations. Not sure where to run with that though or even if that is the right way to do it.
I think it may be important that we aren't required to find out what da and ja actually mean. So I reckon there's more than enough data.
I always assume that a question like this can be answered. It would be very silly if it was a trick question.
I think that idea of the gods being able to transcend time is quite clever, but I'm not buying into it, yet:)
I've only glanced at your thesis ;) But definitely will study it when I get the time.
Wow, aren' we doing well - not ;) Greetz.
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I suspect that it may even be possible to prepare all three questions in advance - no conditionals required.
Chris, I though of that too, but I believe even if you don't need to know the meaning of da/ja, it is part of the problem and thus it must count as information.
As to the "no answer", that would do the trick. I'll think about it. Nevertheless, I continue to think that the approach based on paradoxes is the most promising one. Even more, I think that the characters are gods exactly because of tha "future knowing" ability, which is the source of them.
Hi All. I gave up and checked the link. I won't tell you how to do it. But will only try to stop you going in the wrong direction.
They are not real gods, that's just candy; they can't transcend time etc. In the original version of the problem Random either gives a true or false answer, not a random da/ja answer. There is a variation on the puzzle where Random is simply a random da/ja machine, it can be done but that takes a lot more care. The solution doesn't involve answering an unanswerable question. You do find out what da and ja mean. The full solution is quite nice.
THANK YOU ALL for your input to this puzzle. I too have now looked at the solution and agree, it is nice, although I have to question the sanity of anyone who can pose such a puzzle.
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Soz, I re-read the wiki, there is just about every variation you can think of for this puzzle, exploding gods included.
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Visit
http://en.wikipedia.org/wiki/The_hardest_logic_puzzle_ever
for those wanting the answer. See the flowchart, its clearer.
Another amendment. You don't find out what da/ja mean, I was too hasty before.
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