# Thread: The World's Hardest Logic Puzzle

1. So far, I believe that Kiddo has gotten the farthest. In fact, I am not sure if realized or not, but I am quite sure that Kiddo is near the solution.

2. Originally Posted by Dana
But how will you ever know you are talking to Truth? Random is the easiest to decipher.
But you can't rely on Random slipping up and contradicting himself because he might always tell the truth or he might always tell lies in the answers he gives you.

3. Originally Posted by Jennifer
Kill each one of them with The Subtle Knife, then check their IDs in their wallets. (See? Simple!)
We also would have accepted, "Invent a babelfish. Then all of the gods would disappear in a puff of logic."

4. If you ask the first God if Ja means yes, Truth will always answer Ja and False will always answer Da.

5. This really is a tough one. I'll be sure to sleep on it tonight. (I am working on a possible solution, but it may not be one that is workable at all. tit also seems that the pattern of the answers will be very important in working out how to solve it, but i may be completely wrong there.)

6. you have to ask the same question 3 times and you have to know the answer to the question that you're asking it also must be a true/false question.

7. OK. This was a lot of fun to think about (thanks for distracting me from my HW). I am not sure if this is a spoiler or not, but consider the following. (You can highlight to see)
I may be severely side-stepping the rules of the puzzle however, and I have one case to figure out.

From a cursory glance, it seems like you need to distinguish between 6 possible assignments of Gods A, B, and C to True, False or Random.
You also need to distinguish between "da" meaning yes, and "ja" meaning no. That makes for 12 possible configurations.

With three yes/no questions in a conventional sense, you can distinguish between 8 possible states. So we seem to run up against the bounds of information theory.
Granted, you need not find out the translations for yes and no, but in a conventional logic puzzle, with conventional questions you would (I think).

But if we ask undecidable questions to the Gods, they wont be able to answer, and thereby give us three possible outcomes for each question: "da," "ja," and no answer.
The only way I know of to do this is through self-referential questions. So I may be breaking the rules.

This gives us potentially 27 distinctions, and makes the problem tractable.

"Is it true that you are True and answering this question falsely?"
If God A is True, then it can't answer, because "you are True and answering this question falsely" is an undecidable statement for it.
If God A is False, then it answers yes, because "you are True and answering this question falsely" is false for it, and it will lie.
If God A is Random, and it flips to true mode, then it answers no, because "you are True and answering this question falsely" is false for it, and it will tell the truth.
If God A is Random, and it flips to false mode, then it answers yes because "you are True and answering this question falsely" is false for it, and it will lie.

"Is it true that you are True or Random and answering this question falsely?"
If God A is True or Random, then it can't answer, because "you are True or Random and answering this question falsely" is an undecidable statement for it.
If God A is False, then it answers yes, because "you are True or Random and answering this question falsely" is false for it, and it will lie.

Also note, that for your question to God B, you have only two possibilities: No answer, and yes (so if you get an answer, you know which of "da" and "ja" is yes)

If you get no answer from God A, and no answer God B, you know that God A is True, God B is Random, and God C is False.
If you get no answer from God A, and yes (which you know know the translation to) from God B, you know that God A is true, God B is false, and God C is Random.

The tricky part (where you have to use your last question) is if God A gives you an answer. In this case you know God A is either Random or False.
If God B does answer, then you know it is yes, and that God B is false.
3-1)You then ask God B, "Is God A Random?". If it answers no (remember you have the translations now), then you know God A is Random, and God C is True.
If it answers yes, then you know God C is Random, and God A is True.

This leaves the case when God A answers, and God B does not. This is the really tricky part.
Here you know God A is Random or False, and God B is Random or True.
3-2) Ask God C, "Is it true that you are Random and answering this question falsely?"
If God C Random, then it can't answer, because "you are Random and answering this question falsely" is an undecidable statement for it.
If God C is True, then it will answer no, because "you are Random and answering this question falsely" is a false statement for it.
If God C is False, then it answers yes, because "you are Random and answering this question falsely" is false for it, and it will lie.

So if God C doesn't answer, you know God A is False, God B is True, and God C is Random.

If God C does answer, unfortunately, you still won't know what yes and no mean, without some normal logic puzzle thought. You know God C is either True or False.

Can we work out the cases?:

If God A said the same thing as God C, means they both said no or they both said yes. If they both said no, that would mean God A is Random, God B is True (Random already taken), and God C is also true? A contradiction. So in this case that means they both said yes, and God A is Random, God B is True, and God C is false.

If God A said a different thing from God C, means either God A said yes, and God C said no, or God A said no and God C said yes. If God A said no, and God C said yes, then God A is Random, God B is True (Random is taken), and God C is False. If on the other hand God A said yes, and God C said no, then God C is True, God B is Random, and God A is false.

So damn close!!! If God A and B answer the different things and God B does not answer, we are kind of screwed with my set of questions.
Damn God B, not answering our question, we should get another question in that case.
4*) If were allowed this (because we got no answer from a previous question), I would ask God A the same question I asked God C.
We know God A is not True, so we would either get no answer (meaning God A was Random, God B True, and God C false) or get yes(giving the translation for yes, and the fact that God A is false, God B Random, and God C true)

I need to get back to doing my HW. I am sure others, can work off of this.

8. I think I got the full solution (couldn't focus on what I needed to do).

If I correct what I said earlier with:

Make the second question contingent on whether or not you get an answer to the first. If you don't get an answer, continue as I posted earlier.

If you do get an answer you know that God A is either False or Random, so ask it another question.

2-2) Ask God B Question 3-2) from my earlier post:
Ask God B, "Is it true that you are Random and answering this question falsely?"
If God B is True, then it answers no, because "you are Random and answering this question falsely" is false for it, and it will tell the truth.
If God B is Random, then it can't answer, because "you are Random and answering this question falsely" is an undecidable statement for it.
If God B is False, then it answers yes, because "you are Random and answering this question falsely" is false for it, and it will lie.

If we get no answer, we know God B is Random, and therefore God A is false, and God C it True.

If we get an answer, and it is the same as what God A gave, then they both answered yes or both answered no. If they both answered yes, that would mean God A is Random, God B False, God C True. If they both answered no, that would mean God A is Random, God B is True, God C is False.

In either case where the answers to the first two questions is the same, we know God A is Random.

3-1 new) So now we ask God C, the same question as God A. If we get no answer, we know God C was True, and God B was false, and we're done. If we do get an answer, we know what yes translates to, and we know God C is False, and God B is True.

If the answers to the first two questions are different.
We have three possibilities:
God A answered no and is Random, and God B is False (God C is True).
God A answered yes and is Random, and God B is True (God C is False).
God A answered yes and is False, and God B is True (God C is Random).

3-2 new) We ask God B a question "Is it true that you are True and also true that God C is Random or you are answering this question falsely?".
If God B is True, and God C is Random, then God B will answer yes, because "God C is Random or you are answering this question falsely" is true for it.
If God B is True, and God C is False, then God B will answer no, because "God C is Random or you are answering this question falsely" is undecidable for it.
If God B is False (God C is True) then God B answers yes, because "You are true" is false for it, and it will lie.

You will get a yes answer or no answer. If you get no answer, you know that God C is Random, God B is True, and God A is False.

If you get an answer, it means yes.
If it is the same as what you received from your second question, then you know God B is False, God C is True, and God A is Random.
If it is different from what you got from your second question, then you know God B is true, God C is False, and God A is Random.

There is probably a more efficient/cleaner solution, but I think this one works.

9. Go for it.
Have been thinking for about 3 minutes (at the point started writing this post).

All I've got so far (only looking at OP):

If you ask all three: Does "ja" mean "yes"?

If "ja" does mean "yes": Truth will say "yes"---> "ja"
Liar will say "no"-----> "da"

If "da" means "yes": Truth will say "no" ---> "ja"
Liar will say "yes"-----> "da"

So- Truth will always say "ja", liar will always say "da". Don't know how to smoke out random yet. If can ask all three, then 2 will have one answer and 1 will have another answer... so maybe ask the one alone in answer if one of the others is the liar?

ja: Person X; while da: Persons Y and Z
Person X is the truth teller. But I don't know whether "ja" or "da" means "yes". Crap. Must require more thought.

10. Have put a little more thought into it:

Ask A and B each: Does "ja" mean "yes"?

If both A and B say "ja", C is False.
If both A and B say "da", C is True.
In both these cases, you can ask C: Will A answer "da" if I ask A again? If A is Random, C cannot say for sure, and cannot answer (because C is True/False and must answer definitely). If A is True or False, C will answer ("ja" or "da")(Since if C is Random, C has to answer yes or no. And if C is True/False and knows A's identity, then C has an answer).
This method only works assumming A, B, and C know each other's identities. But I'm going to assume they do, since they cannot tell a lie/ cannot tell a truth. And cannot tell the future.

Does not work so well if A and B give split answers. More thought.

_________
*40 mins later*
I might have gotten it this time?

Ask A: Does "ja" mean "yes"?
A answers: Ja (A is True or Random) A answers: Da (A is False or Random)

Given A = True
*If B = False---> Ja/Da
*If B = Random ---> Ja/Da
Given A = False
*If B = True ---> Ja/Da
*If B = Random ---> Ja/Da
Given A = Random
*If B = True ---> No answer
*If B = False ---> No answer

---> So if B cannot give an answer to question 2, A is Random
Question 3: Ask B 1st question: Does "ja" mean "yes"?
*If B answers "ja": A=Random, B=True, C=False
*If B answers "da": A=Random, B=False, C=True

---> If A answered "ja" to Question #1, and B answered "ja/da" for Question 2: A=True
*If B answers "ja/da": A=True, B=Random, C=False
*If B has no answer: A=True, B=Flase, C=Random

---> (Similar to above) If A answered "da" to Question #1 , and B answered "ja/da" for Question 2: A=False
*If B answers "ja/da": A=False, B=Random, C=True
*If B has no answer: A=False, B=True, C=Random

Will now go check my reasoning against others' answers.

_______________
Trying to wrap my puny mind around ygolo's explanation.
Originally Posted by ygolo
"Is it true that you are True and answering this question falsely?"
If God A is True, then it can't answer, because "you are True and answering this question falsely" is an undecidable statement for it.
If God A is False, then it answers yes, because "you are True and answering this question falsely" is false for it, and it will lie.
If God A is Random, and it flips to true mode, then it answers no, because "you are True and answering this question falsely" is false for it, and it will tell the truth.
If God A is Random, and it flips to false mode, then it answers yes because "you are True and answering this question falsely" is false for it, and it will lie.
I'm not quite sure I understand. If God A is True, couldn't God A answer "no", given the "and" statement? While God A is True, God A is not answering falsely- making the whole statement "you are Ture and answering this question falsely" false, right? (Because not both "you are True" and "you are answering this question falsely" are true statements.) So God A can feel free to answer "no".

____________
It took more diagrams, but I'm not quite sure I understand your second question.
You said to use to following second question if in the first question, A gave no answer and we therefore sussed out that A was True.
Originally Posted by ygolo
"Is it true that you are True or Random and answering this question falsely?"
If God A is True or Random, then it can't answer, because "you are True or Random and answering this question falsely" is an undecidable statement for it.
If God A is False, then it answers yes, because "you are True or Random and answering this question falsely" is false for it, and it will lie.

Also note, that for your question to God B, you have only two possibilities: No answer, and yes (so if you get an answer, you know which of "da" and "ja" is yes)

If you get no answer from God A, and no answer God B, you know that God A is True, God B is Random, and God C is False.
If you get no answer from God A, and yes (which you know know the translation to) from God B, you know that God A is true, God B is false, and God C is Random.
I always thought the following:
Question: Are M and N true?
If M is true and N is true, the answer is yes.
If M is true and N is false, the answer is no.
If M is false and N is true, the answer is no.
If M is false and N is false, the answer is no.
I suppose this could only apply to questions stated : Are A and B *both* true?
But all my following reasoning is based off this principle. So if I'm wrong, please correct me.

Since we know A is True, B is either Random or False.
So there are the following possibilities:
Given statement M="you are True or Random" and statement N="you are answering this question falsely".
1. B is Random and has flipped to answer truthfully. M is true and N is false, therefore the truthful answer is "no". B is telling the truth, so the given answer is also "no".
2. B is Random and has flipped to answer untruthfully. M is true and N is true, therefore the truthful answer is "yes". But B is telling a lie, so the given answer is also "no".
3. B is False. M is false and N is true (because False will always answer untruthfully), therefore the truthful answer is "no". But B will always lie, so the given answer is "yes".

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