stuh505:
I identified a non-random person with one question.
I determined the meaning of ja/da with one question.
gravenewworld:
I'm quite familiar with iff. Iff is true when both are true or both are false. It is not false when both are false.
Seeing as it seems that no one has progressed any further on this puzzle, I will post 3 big hints that should help you to solve this one. Straight from the solution:
The Solution: Before solving The Hardest Logic Puzzle Ever, we will set out and solve three related, but much easier, puzzles. We shall then combine the ideas of their solutions to solve the Hardest Puzzle. The last two puzzles are of a type that may be quite familiar to the reader, but the first one is not well known (in fact the author made it up while thinking about the Hardest Puzzle). and, with Richard Jeffrey, Computability and Logic (Cambridge, 1974).
Puzzle 1: 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.
Puzzle 2: Suppose that, somehow, you have learned that you are speaking not to Random but to True or False ?- you don't know which ?- and that whichever god you're talking to has condescended to answer you in English. For some reason, you need to know whether Dushanbe is in Kirghizia or not. What one yes-no question can you ask the god from the answer to which you can determine whether or not Dushanbe is in Kirghizia?
Puzzle 3: You are now quite definitely talking to True, but he refuses to answer you in English and will only say da or ja. What one yes-no question can you ask True to determine whether or not Dushanbe is in Kirghizia?
H ERE'S ONE SOLUTION TO PUZZLE 1: POINT TO THE middle card and ask, "Is the left card an ace?" If I answer yes, choose the left card; if I answer no, choose the right card. Whether the middle card is an ace or not, you are certain to find an ace by choosing the left card if you hear me say yes and choosing the right card if you hear no. The reason is that if the middle card is an ace, my answer is truthful, and so the left card is an ace if I say yes, and the right card is an ace if I say no. But if the middle card is the Jack, then both of the other cards are aces, and so again the left card is an ace if I say yes (so is the right card but that is now irrelevant), and the right card is an ace if I say no (as is the left card, again irrelevantly).
To solve puzzles 2 and 3, we shall use iff.
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 statment, you get a false statement. Thus, for example, "The moon is made of Gorgonzola iff Rome is in Russia" is true, because "The moon is made of Gorgonzola" and "Rome is in Russia" are both false. But, "The moon is made of Gorgonzola iff Rome is in Italy" and "The moon lacks air iff Rome is in Russia" are false. However, "The moon lacks air iff Rome is in Italy" is true. ("Iff" has nothing to do with causes, explanations, or laws of nature.) To solve puzzle 2, ask the god not the simple question, "Is Dushanbe in Kirghizia?" but the more complex question, "Are you True iff Dushanbe is in Kirghizia?" Then (in the absence of any geographical information) there are four possibilities:
1) The god is True and D. is in K.: then you get the answer yes.
2) The god is True and D. is not in K.: this time you get no.
3) The god is False and D. is in K.: you get the answer yes, because only one statement is true, so the correct answer is no, and the god, who is False, falsely says yes.
4) The god is False and D. is not in K.: in this final case you get the answer no, because both statements are false, the correct answer is yes, and the god False falsely says no.
So you get a yes answer to that complex question if D. is in K. and a no answer if it is not, no matter to which of True and False you are speaking. By noting the answer to the complex question, you can find out whether D. is in K. or not.
The point to notice is that if you ask either True or False, "Are you True iff X?" and receive your answer in English, then you get the answer yes if X is true and no if X is false, regardless of which of the two you are speaking to.
The solution to puzzle 3 is quite similar: Ask True not, "Is Dushanbe in Kirghizia?" but, "Does da mean yes iff D. is in K.?" There are again four possibilities:
1) Da means yes and D. is in K.: then True says da.
2) Da means yes and D. is not in K.: then True says ja (meaning no). 3) Da means no and D. is in K.: then True says da (meaning no).
4) Da means no and D. is not in K.: then both statements are false, the statement "Da means yes iff D. is in K." is true, the correct answer (in English) to our question is yes, and therefore True says ja.
Thus you get the answer da if D. is in K. and the answer ja if not, regardless of which of da and ja means yes and which means no.
The point this time is that if you ask True, "Does da mean yes iff Y?" then you get the answer da if Y is true and you get the answer ja if Y is false, regardless of which means which. Combining the two points, we see that if you ask one of True and False (who we again suppose only answer da and ja), the very complex question, "Does da mean yes iff, you are True iff X?" then you will get the answer da if X is true and get the answer ja if X is false, regardless of whether you are addressing the god True or the god False, and regardless of the meanings of da and ja.
We can now solve The Hardest Logic Puzzle Ever....
I had a feeling I would not like the answer, or even the basis on which the answer is based. Take the first:
PUZZLE 1:
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.
SOLUTION TO PUZZLE 1:
POINT TO THE middle card and ask, "Is the left card an ace?" If I answer yes, choose the left card; if I answer no, choose the right card. Whether the middle card is an ace or not, you are certain to find an ace by choosing the left card if you hear me say yes and choosing the right card if you hear no. The reason is that if the middle card is an ace, my answer is truthful, and so the left card is an ace if I say yes, and the right card is an ace if I say no. But if the middle card is the Jack, then both of the other cards are aces, and so again the left card is an ace if I say yes (so is the right card but that is now irrelevant), and the right card is an ace if I say no (as is the left card, again irrelevantly).
Now, put it into the context of T/L/R + Da/Ja and come up with a single question to produce the required result. In my humble opinion, a total impossibility.
I wait to be amazed.
Whilst waiting:
The negative of a negative is always a positive
In other words, you must embed a question within a question (so that they will all answer the same way). For the moment I discuss possible ways of solving this in English.
Question 1:
If I asked you if this God is always truthful, would you say yes?
(Points to T).
L, who always lies, will say "yes" (he would say "no" if asked if this was the T (a lie), so lying here he says he would not say "yes". (Because if he agreed it was No, he would be telling the truth)
Likewise, R as a L would say; yes. R as a T would say; yes
Therefore any positive answer has identified T with one question. He can then be asked another question to identify the other two. Problem solved with just two questions.
However, what would happen if you asking the same question:
But were pointing to the L?
In that case the answers would be reversed, and be all No's.
And the same again for R, as I hope this table shows:
?'If I asked you if this God is always truthful, would you say yes?'
(Point to L)
T=N
R/L=N
R/T=N
(R/T. R/N) Random Truth/Lies
(Point to R)
T=N
L=N
As there is no Yes, we know that the God pointed at is not the T.
This is as far as I have gone. If anyone can see a flaw in the reasoning thus far please make yourself known before I move to question two.
there is another way to do it.
ask a simple question to god a such as, "is 2+2=5?" let's say he answers "ja". go to god b and ask him " does ja mean ja or da?" if he says ja then you no god b must be the one that tell the truth or the one that some times tells the truth. or if he said da then you know he is the one that lies or some times lies. based on the answer he gives you would be able to determine wuther it ja means yes or no and if da means yes or no.considering that it is obvious that that if the first one says ja then it would mean no because the first one is false. any way the question you would have to ask the last one is " are you the one that tells lies sometimes?" if he says yes then he would be telling the truth. so it would not be the one lies and infact the one who lies sometimes. there your problem is solved.
bye bye
only some of what you wrote makes sense to me. I still don't see how you can determine da/ja to be yes/no from the questions you ask. from the first two questions you are proposing to ask, i see no way how you can determine da/ja to be yes or no
Well here is what you all have been waiting for, the solution to the hardest logic puzzle of all time-
http://people.ucsc.edu/~jburke/three_gods.pdf
When I said the puzzle was hard I wasn't kidding.
Looks like I was on the right track with the first two questions. I guess I should have stuck with it.
