Talk:The Hardest Logic Puzzle Ever

message: The idea is to use the effect of "iff" to design a question that will direct the True and False to have same answer about anything he include in the question. (As shown in the illustrated diagram)
   
Logicians have introduced the useful abbreviation "iff," short for "if, and only if." The way iff works in logic is this: when you insert iff between two statements that are either both true or both false, you get a statement that is true; but if you insert it between one true and one false statement, you get a false statement.
The key point is that he designed a question using iff so that the answer is directly tell the truth about anything he wanna know (the “X” in the question) from the True and False guys. 
So, he used this designed question to ask True and False about the location of the random guy, and so he was able to easily proceed with his solution in the other two questions (Q2 & Q3). Brilliant!
The idea is to use the effect of "iff" to design a question that will direct the True and False to have same answer about anything he include in the question. (As shown in the illustrated diagram)
 Actually, you can reach to the same thing, by a simpler question: (Q1: Ask A ‘’if you ask the none-random guy (from the other two) ‘is B=R’, then would you answer be ja?”), which is based on a similar idea, which is: (The golden rule applied here: T+F=F; that’s if you ask T (or F): if you ask  the other one, F (or T) about a truth (which they both know), then the truth is the opposite of the answer you got.)  — Preceding unsigned comment added by Essam.abdellatif (talk • contribs) 13:45, 17 April 2013 (UTC)
thread_title: Explanation of the question(s) used in Boolos Solution

message: This is a more rationale and simple solution of the hardest logic puzzle (invented by Raymond Smullyan and solved by G. Boloos, 1996). It is just has a different road-map (milestones) and a different set of questions that the original solution has. Its road-map of this solution is: (1) first 2 moves has one goal (goal1) which is to identify the “random” guy in 2 questions, and then, (2) goal2 is to identify who is the True/False by the 3rd question.
The first goal (goal1) has 2 milestones (one per each question: (1) identify one of the none-random guy by the 1st question, (2) identify the other none-random guy, and hence identify the random by the 2nd question
And it's based on the following 3 key concepts:
key#1: The golden rule applied here: T+F=F; that’s if you ask T (or F): if you ask  the other one, F (or T) about a truth (which they both know), then the truth is always the opposite of the answer you got from them. 
Key#2: If Q(something), ja? then answer(ja)=yes, and answer (da) =no. 
But, please notice that :the answer you get here is just yes or no; it does not mean they are True or False about the thing is asked about. The rule of this is working as follow: Any question about "something" (that you don't know, and wanna know actually) and you include the part " would you answer by ja?"(whatever ja=yes, or ja==no) in the question, then when you get the answer "ja", it means two things (not just one):
* ja, this thing is true, which is answered by a True person (which means this thing you are asking about is really the truth), or,
* ja, this thing is true, which is answered by a Lair (which means this thing you are asking about is really not the truth)
* 
:Indented line
Finally the 3rd key concept is that if I questions you about something that I already know it's truth and include "would you answer ja" (regardless ja=yes, or ja==no) ) in the question, then who answers "ja" he is True, and who answers "da" is False. So, Key#3: If Q(truth, that you already know), ja? then answer(ja)=True, and answer (da) =False.
The goal1 (first milestone) is achieved in 2 steps (using Q1 and Q2 and applying key1 and key2), while goal2 is achieved in the 3rd step (using Q3, and key3)
And, the questions set of the solution is as follow:
Q1: Ask A ‘’if you ask the none-random guy (from the other two) ‘is B=R’, then would you answer be ja?”  
''
So, if we got the answer ja, it means: 
*:either A is truly the one of the none-random guys, and hence the truth is the opposite of their answer (i.e., C=R)
*: or, A is the random guy and both B and C is not R. 
And in both cases, we are  definitely sure that B is not R.
Similarly, if we go the answer da, it means:
*:either A is truly the one of the none-random guys, and hence the truth is the opposite of their answer (i.e., B=R)
*: or, A is the random guy and both B and C is not R. 
And in both cases, we are  definitely sure that C is not R.
So, we are now, in both cases, identified one of the three who is a none-random (either B or C, in each of the ja and da answers) 
Now, we are going to direct the second question, to that none=random guy we knew from Q1 (i.e., either B or C), as shown in the illustrated diagram.  
Q2: ask the none-random guy identified in Q1 “if you ask the none-random guy (from the other two) ‘is  A=R’, then would you answer be ja?”  
And again, the answer we get is just the opposite of the truth we are looking for (and this time, in Q2, we already excluded the random guy, so we are having just one scenario per each answer (ja/da) in the 4 paths (cases) in Q1&Q2), and therefore we can easily identify the other none-random guy and hence, or of course the random guy.  
Q3: I hold a blue pen and ask any one of them (Q3): if I asked you is this pen blue, would you say "ja"? 
:* If the answer is "ja" then he is the True guy and the other one is the False. Or, 
:* if the answer is "da" then he is the False guy and other one is the true.
(And that what's required!)
The attached diagram illustrates the solution with it's logic-tree of the possibilities and conditions.  
I said this solution is more rational and simple because the original solution is a but complicated (and even I'm not sure if it's correct) and also some other solutions, such as the one which is based on the "embedded question lemma" I found it incorrect. 
What's the point of any of this? It appears to be Original Research and has nothing to do with improving the article. -- Jibal (talk) 11:47, 5 May 2017 (UTC)
thread_title: Another solution which is more rational and simple

message: that flow chart is unhelpful and is explaining the trivialization no the real solution. i suggest it be deleted or one be made for the actual solution section, if people find them helpful.  —Preceding unsigned comment added by 71.196.245.150 (talk) 04:06, 6 January 2010 (UTC)
thread_title:  flow chart 

message: PhysicistQuery 09:08, 23 July 2007 (UTC)
thread_title:  Apparent Single-Question Solution to the Clarified (Boolos) Puzzle 

message: Anon: Everything below should be removed. This is not the puzzle. It is simply Fyz's unique re-interpretation of the puzzle. No academic articles published on the puzzle have supported Fyz's interpretation.  The Hardest Logic Puzzle Ever is the puzzle published by George Boolos (which can be found Here).  Any "controversy" over Conditions 1 and 3 below are settled in that article. Condition 2 (which would be better worded as "The gods will grant an answer to any yes-no question that they can answer") is nowhere to be found in the article.  The possibility of unanswerable yes-no questions by all knowing gods was probably just not considered.  But this possibility provides for very interesting solutions that have philosophical implications related to the Liar's paradox.  Furthermore, as lwr314 has proven, Fyz's added constraints in conjunction with the standard interpretation of the puzzle makes it unsolvable and thus uninteresting.  I leave it to others to fight with Fyz.  I have made the case against her already before but she seems stubbornly committed to a misinterpretation.  
Fyz 16Jul: It appears that you have taken it on yourself to remove the entire contribution. Please explain on what authority and expertise you do this.  Note that I am by no means alone in believing that the puzzle solved by Boolos is not the same as that posed by Smullyan - see for example http://www.uweb.ucsb.edu/~rabern/SSHardPuzzle.pdf, which is reference 4 of the main article.  What I have done is to elucidate why Smullyan's puzzle as written might be worth more attention than it has heretofore received. I now understand that everything in the encyclopaedic section needs to be referenced to other work, so you would be correct to remove my extension to the puzzle as written.
Anon the monkey: Look, man, there is no such thing as "Smullyan's puzzle as written". You have made this up.  There are Smullyan puzzles as written but none of these are The Hardest Logic Puzzle Ever. There is Boolos' puzzle, i.e. The Hardest Logic Puzzle Ever, which is inspired by (or Boolos' re-working of or Boolos' take on or Boolos' memory of) certain Smullyan puzzles. I don't know how else to convey this. It is getting silly.
The Hardest Logic Puzzle Ever is not equal to some puzzle x such that x was authored by Smullyan.
The Hardest Logic Puzzle Ever is equal to some puzzle x such that x was authored by Boolos and was based on some puzzle y such that y was authored by Smullyan.
PhysicistQuery 21:37, 18 July 2007 (UTC)
thread_title:  Anonymous assertion and discussion regarding "More rigorous interpretation of the puzzle?" 

message: (which also has a solution)
Just add the following to the end of the question:
The gods will not answer any question until after all three have been posed, and will not answer any of the questions if the answers to any two imply the answer to the third.
: I have a more difficult version, too: You don't know the words 'da' or 'ja' - You only know that there exist translations of 'Yes' and 'No'. So the first question can not contain "...Does 'da' mean 'yes'..." but rather "...is in the ghosts alphabet the translation for 'Yes' before the translation for 'No'...". The difficulty is that in the end the outputs "da. da. da." and "ja. ja. ja." are the same cause you don't know the other word. :de:User:Träumer 17:32, 11 February 2008 (UTC)
replies: text:  That seems unsolvable given that you can only get 4 different sequences of answers: "111", "112", "121" and "122". But 4 is not enough to differentiate between the 6 possible god configurations. RedNifre (talk) 00:47, 22 March 2015 (UTC)

text: You can make that even harder by only allowing all three questions to be addressed to the same god. RedNifre (talk) 00:47, 22 March 2015 (UTC)
thread_title:  A more difficult version of the question 

message: Here's a generalized version of the famous Smullyan/Boolos Hardest Logic Puzzle [in its regular form]. I don't know of a solution yet, I even don't know if it is indeed a harder puzzle although it looks like (but I have a conjecture based on my work on the original one, using utterance operators). So here it is, for what it is worth:
Suppose we are confronted with n+1 GODs, name-numbered G0 ... Gn. G0 always tells the full truth, i.e. G0(p)=p all p. G1 deviates randomly from G0 on some statements and/or some occasions, i.e. G1(p)<>G0(p)= p for some p. G2 deviates still more from G0 but in such a manner that deviations by G1 are retained. Etc. Gn will deviate from G0 on all statements, so he is the real and only full liar. This can easily be formalized in terms of sets and implications.
So there will be a hierarchy of ever more untrustworthy Oracles in between one good God and one evil Devil (G-O-D). Of course, all G-O-D's know their own identity as well as the identity of the other G-O-D's (or at least their immediate precursors and/or successors in the hierarchy?) Is there a simple way to reveal each creature's identity by asking just n+1 regular questions (although there are clearly (n+1)! different possible orders)?
Note: If n=3, we have the original puzzle, which is indeed solvable in 3 regular questions by first eliminating the unreliable G-O-D and then asking two more questions. I guess we can do a similar thing for general n by focussing in on G0 and Gn by n-1 questions (eliminating on our way all unreliable G-O-D's), then asking again n-1 questions using the double negation technique, and finally deciding between G0 and Gn; so this results in 2(n-1)+1 questions (correct for n=3). Can we do better? Koyaanisqatsi II (talk) 12:24, 19 June 2008 (UTC)
thread_title:  A generalized version of the original puzzle ? 

message: Interestingly my friend used the same expression to refer to a different situation which is not clarified in this article: Assume that god A is True, and god B is Random (although of course we don't know this). Ask god A, "What would B say if...?" How does A answer? Does A impersonate B, providing a random answer? Or does his head asplode? This question must have been covered somewhere? Stevage 15:04, 23 May 2007 (UTC)
thread_title:  Exploding heads 

message: ----------
Fyz: Rather than "Clarify" the puzzle in so many ways that actually change its meaning, would it not be sensible to split the question into two completely different versions:
One would be exactly as posed, which has a relatively simple solution (see discussion) once the worst-case interpretations of the questions has been ascertained; and
One where the question itself is modified to fit Boolos' answer and the various clarifications?
Anon Reply: have you read the puzzle?
It clearly states that "...whether Random speaks truly or falsely is a completely random matter".  The modification is to change this to 'whether Random replies affirmatively or negatively is a completely random matter'. There is no conflict between Boolos' statement of the puzzle and his clarifications. There is only a conflict between the way Boolos intended to have Random work (evidence: look at his solution) and the way he must actually work (see this section).
Fyz Re-reply: There are two significant modifications to the puzzle - one by Boolos (specifying immediate answers) is a restriction that trivialises the original puzzle as written, and the other is the one required to repair Random to make Boolos' solutions appropriate (though his solution does actually work for the trivialised puzzle). The two puzzles are the original one (as stated and without Boolos clarifications), and the one with Boolos' "clarification" integrated and Random mended as described.  I believe that both belong here, because the first is as originally stated and is non-trivial, and the second is supported in ref 4 as well as in the above text.  (However, I don't believe that this discussion should stay in the encyclopedia).
Anon Reply continued: Also keep in mind that the clarifications are part of the damn puzzle!
Fyz Re-reply continued: Any clarification that changes the meaning (in common with blasphemy) is completely unnecessary, and had time permitted would in itself have caused any referees to require the original 'paper' to be amended for consistency.  We are not doing either the puzzle or Boolos' memory any favours by slavishly reproducing the original, which could be regarded as a "working document".
lwr314: Boolos' original paper was consistent.  His solution to the puzzle that he posed (with the clarifications, since those are part of the puzzle that he posed) was correct.  Apparently, he just did not realize that useful information could be acquired from Random as he defined him (surely, in his mind he had the assumption that Random gives no information as most commentators on the puzzle have assumed).  Here are the facts:
(1) The article concerns 'The Hardest Logic Puzzle Ever' which is the name Boolos' gave to a puzzle that he published a solution for (the puzzle containing his clarifications).  The article is about *that* puzzle.  
(2) Modified Random fits in with the article since Boolos' solution applies to that no-information-giving Random as well.
(3) Exploding heads fits in with the article since they give a method of solving Boolos' puzzle in two questions.
(4) Your modifications do not fit in with the article since Boolos' solution does not solve your puzzle.  You are discussing a *different* puzzle.  As i have shown on the discussion page, this different puzzle is not interesting.  One of your versions is a completely trivial modification which is uninteresting and for the other you have just added an arbitrary constraint to make the puzzle slightly harder.  As i showed you over there, i could make it even harder by adding more arbitrary constraints.  With the constraints we are discussing a different puzzle -- it does not belong in this article.
(5) i'll say this again since you don't seem to understand.  `The Hardest Logic Puzzle Ever' refers to a puzzle by Boolos' which includes his clarifications.
PhysicistQuery 21:29, 17 July 2007 (UTC)
thread_title: Moved from article 17 July 2007

message: Why is there a tapestry of Odin, Thor, and Freyr, incorrectly labeled "True, False, and Random", in this article?  I can't imagine what purpose this illustration hopes to accomplish. Xezlec (talk) 02:58, 18 March 2008 (UTC)
replies: text: OK then, removing it. Xezlec (talk) 01:49, 15 May 2008 (UTC)
thread_title:  Weird picture 

message: Is this a valid solution? 
Ask god A "If I asked you 'does 2+2=4' twice in a row, would you answer both questions with a lie?"
If he is True or False, he will respond with whichever word means no and you will know that the other word means yes.  
Then ask him "does 2+2=4?"
From the answer you can determine whether he is True or False 
Then ask "If I asked god B 'does 2+2=4' would his answer be a lie?"
If god B is Random, god A will not be able to answer because he cannot read Random's mind and does not know whether Random will provide true or false information in response to that question. 
If god B is True or False, god A will answer the question. 
If you know the identities of two gods, you know the identity of the third 
If god A is Random, he will not be able to answer the first question because he does not know what the "coin in his brain" will land on one or two questions from now.  He will not have enough information to either lie or tell the truth.  
Then, you ask god B, who must be either True or False, the same question and based on his answer you will know what "da" or "ja" means. 
Finally, ask god B "does 2+2=4?"
You will know from his answer whether he is True or False
Unfortunately, this approach is less rigorous than the original solution by Boolos because it does not include a mechanism to guarantee an answer.  There is no way to know if the god is simply taking a long time to answer or not answering.  While it is certainly true that the god must answer after a finite amount of time, so that if you wait long enough you can solve the puzzle, this solution does not provide a way to ever know when the god will speak.
If you know the identities of two gods, you know the identity of the third  —Preceding unsigned comment added by 166.61.238.40 (talk) 00:45, 1 July 2009 (UTC)
thread_title:  new solution? 

message: In "The Solution" section following thing is written towards the end -
Ask god B, "If I asked you 'Is A Random?', would you say 'ja'?". If B answers 'ja', then either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is indeed Random. Either way, C is not Random. 
Suppose A always tells the truth, B always lies and C is random. Further suppose, 'ja' means 'Yes'. In that case if B is asked the question "If I asked you 'Is A Random?', would you say 'ja' ('Yes')?" B being a liar (s)he would say 'ja' ('Yes'). But still C is random. This contradicts the conclusion of the last line in the paragraph above. In fact even if 'ja' means 'No' the conclusion is still wrong.
Pranab.Chakraborty (talk) 17:45, 9 November 2010 (UTC)
thread_title:  Error in "The Solution?" 

message: has a good post about this puzzle, including a version with a hierarchy of gods controlling the head explosions of the lower level gods.  Best quote: 
:Similarly, if we suppose that SuperGod is in charge of deciding whether or not God’s head blows up, SuperGod’s head is in danger of blowing up due to a clever self-referential question, and so forth. So we may actually extract an unbounded amount of information from a single yes-or-no question by choosing the question carefully and then observing how much of the universe is destroyed by our asking it.
link: http://xorshammer.com/2008/08/18/hardest-logic-puzzle-ever/
67.122.209.190 (talk) 07:00, 17 January 2011 (UTC)
thread_title:  Xor's hammer (blog) 

message: This puzzle is simple do to the fact of if a person said "True, is the god to your left false?" or "False, is the god to your left Random?" or even "True, is the god to the far left Random?" after finding out which god is wich you need only ask any two random questions you would like to ask. If anything you can even figure out what "Da" and "Ja" mean.
If anyone is wondering my name is Cody Joseph Heisel. I have a facebook account.  —Preceding unsigned comment added by 75.60.88.115 (talk) 06:21, 31 January 2011 (UTC)
replies: text: You can't direct your first question specifically at True, False or Random, because before asking any questions you don't know which of them is which. Equinox ◑ 11:19, 11 June 2017 (UTC)
thread_title:  Not the Hardest Logic Puzzle in the World 

message: The history section says that the puzzle Knights and Knaves was popularised in a film of 1986. I want to point out that it featured in the Doctor Who story Pyramids of Mars broadcast in November 1975. Perhaps the section should be edited to state this. Custardslice7 (talk) 21:10, 16 September 2011 (UTC)
thread_title:  History date change (Doctor Who) 

message: In the exploding heads section, the following is suggested:
"Would you answer ja to the question of whether you would answer da to this question?"
But it is stated that this would work only in the modified puzzle, where Random's answers are truly random.
This seems false to me, given Boolos's axiom that
"Random will answer da or ja when asked any yes-no question."
Since neither True nor False can answer this question at all, this is enough for the solution to work in the original puzzle.
--76.121.187.193 (talk) 06:57, 6 December 2011 (UTC)
thread_title:  Seeming unnecessary requirement 

message: The conclusion to the subsection "Random's behaviour" is to look to the end of the section "the solution". But the subsection "Random's behaviour" is technically the end of the section "the solution", so this is self-referential and incorrect. The best solution would appear to be to bump "Random's behaviour" up to a full section, but that seems out of place. Thoughts?  — Preceding unsigned comment added by Aannoonn (talk • contribs) 22:24, 7 December 2011 (UTC)
thread_title:  Page structure problem 

message: Just ask "Is a truth true?" to all three of them repeatedly until one of them answers differently to how they answered before. The god who answered differently is Random. This assumes that Random behaves in the "internal coinflip" way and not pseudorandomly seeded by the question. To determine which of the remaining gods is True, you need only to determine which word means "yes". To do this you can ask either of the remaining gods "Would your response to a question be the truth?". Whatever they answer is the word for "yes" and whoever gave that response to the original question is "True" and the other is "False".  — Preceding unsigned comment added by Nbrader (talk • contribs) 12:25, 13 February 2016 (UTC)
thread_title: Simple Solution

message: Surely the article is missing the Bush/Rumsfeld solution: waterboard everyone. — Preceding unsigned comment added by 95.150.63.49 (talk • contribs) 12:00, 26 February 2017 (UTC)
thread_title:  Missing? 

message: "If, however, the god is answering randomly." This sentence stands alone. What does it mean? Equinox ◑ 11:17, 11 June 2017 (UTC)
replies: text: It looks like this sentence is setting up for the Rabern and Rabern variant: if the god is answering randomly, as opposed to just randomly deciding whether to answer truthfully or liefully (as in Boolos' clarification), then this lemma doesn't work.
If I'm right, then the point this sentence was setting up for is explained in detail in a separate section, and isn't relevant to this section. I suspect the author was originally writing it with the variant embedded throughout, then later decided to separate the two out, and just left a fragment behind while rewriting. So I'm going to remove it. If I'm wrong, obviously revert and flesh out the sentence with whatever it was supposed to be. --157.131.168.209 (talk) 21:12, 27 February 2018 (UTC)
thread_title:  Ungrammatical sentence 

message: Wouldn't a potential answer also be the following:
Ask the three gods if they are the random god. Since we know that in this question the answers of the 'True God' and the 'False God' will be the different and that the 'Random God' will either say "da" or "ja", we can claim with certainty that 2 gods will give the same answer and that one of those 2 gods will be the random one. Ergo, the god that answers differently will either be the truthful one or the liar(By no means can it be the random god).
Let's assume that the god that answers differently is god "B"(doesn't make a difference if it is A, B or C). Let's ask only god "B" if it is the Truthful God. Depending on the answer there are 2 solutions:
A1: If god "B" gives the same answer as it did to the previous question(which is "Are you the random god?") then that means that he either answered "Yes, I am the Random god." and "Yes, I am truthful god." respectively which would make him the Lying god since he lied, or he answered "No, I am not the Random god." and "No, I am not truthful god." which creates a contradiction indicating that he answered both questions with a 'Yes' instead of a 'No' making god "B" the lying god.
After that, we ask god "B" if god "A" is the random god. And if he gives the same answer as he gave to the previous two questions( a yes) then that would mean that he said a "yes, A is the random god", but since he is lying in reality A = 'Truthful God' and C = 'Random God'. However, if he gives a different answer to the previous two(No instead of a yes), then A = 'Random God' and C = 'Truthful God'
A2: If it gives a DIFFERENT answer as it did to the previous question(which is "Are you the random god?") then that means that he either answered "No, I am not the Random god." and "Yes, I am truthful god." respectively which would make him the Truthful god since he told the truth, or he answered "Yes, I am the Random god." and "No, I am not truthful god." which doesn't fit the descriptions of either of the gods which means that B answered 'No' and 'Yes' instead of 'Yes' and 'No' making B the Truthful God.
After that, we ask B if A is the random god and if he gives the same answer as he gave to the previous question(which is a 'yes') then that would mean that he is saying that "Yes, A is the random god" which is the truth and therefore A = 'Random God' and C = 'Truthful God'. However, if he gives a different answer to the previous question(or the same answer as first one), then A = 'Truthful God' and C = 'Random God'.
If there are any glaringly obvious mistakes please point them out to me so that they may be corrected
GAPITG (talk) 18:50, 12 September 2017 (UTC)
thread_title:  Wouldn't this be another simple solution [Edit: ISSUE SOLVED] 

message: Unlike the rest of the article, which is reasonably sourced, the section on "Enslaving gods and and making wishes" has no sources.
I'd normally just add citation tags, but in this case, I'm willing to bet that it can't be sourced, and is pure OR, so I'm going to be bold and delete it. Here's why:
* It's written as an argument that this solution is correct, rather than reporting on the solution.
* It's chock full of LessWrong-style jargon, which makes it unlikely that it's sourced to anything Wikipedia would consider a reliable source.
* It was added by User:Florian Dietz, whose only actions ever were to add this, re-add it after ClueBot reverted it as potential vandalism, and clear the ClueBot warning from his talk page. So, it's plausible that Florian wouldn't know the Wikipedia standards (most importantly: Wikipedia isn't about what's true, only what's verifiable, via reliable sources), and could add OR in purely good faith.
Of course I could be completely wrong about that bet. In which case, please revert the delete and add the citations. 
And either way, it's an interesting idea, so if it really is OR, the author really should create at least a blog post or something about it. --157.131.168.209 (talk) 20:58, 27 February 2018 (UTC)
replies: text: I have no external sources for what I just wrote because I came up with this myself and posted it here directly. I hope this is allowed? Is there a way to mention myself (Florian Dietz) as the author without referring to an external source?
So, all the guesswork above is unnecessary. It is original research, made in good faith by someone who didn't realize that OR is not allowed on Wikipedia. --157.131.168.209 (talk) 21:18, 27 February 2018 (UTC)
thread_title:  Enslaving gods and making wishes seems like OR 

message: (Warning: contains a hint towards solving the puzzle)
One obvious approach someone might take to this puzzle would be to first try to learn the meanings of 'da' and 'ja', and then use that knowledge in their remaining questions.  I think it's interesting to note that it's actually impossible to (reliably) obtain BOTH the solution AND the meanings of da/ja in the same 3 questions; correct solutions will identify the gods but will NOT determine the meanings of da/ja, even in retrospect.
This is easily provable, but I do not have a reputable citation for it, so Wikipedia rules on original research prevent me from adding it to the article.
(Proof:  There are 6 possible ways to label the gods, and 2 possible ways to label da/ja, producing 6*2 = 12 possible worlds.  But a binary question yields at most 1 bit of information (possibly less, because of Random, but definitely not more than 1 bit).  3 bits from 3 questions can distinguish between at most 2^3 = 8 possible worlds, which is not enough to solve the puzzle AND learn the meanings of 'da' and 'ja' at the same time.)  – Antistone (talk) 22:58, 11 May 2021 (UTC)
thread_title:  I think it would be interesting to note...