# Thread: The World's Hardest Logic Puzzle

1. Originally Posted by EsoteriEccentri
Far too complicated for me ^^
I have a problem though.
Suppose you asked what they would say to you?
Because I was thinking that if you asked whether, say, ja meant yes then the truth God would say yes and that was my sort of attempt to think about it! ^^ And if you said "will you say ja presuming ja means YES," the truth God would say Ja. But suppose ja was NO?
Erm, but if you said something like "are you going to say yes to me?" or I suppose it should be "are you going to say ja?"
Then if Ja DID mean yes what would the FALSE God say, supposing the God you asked was that God? If ja meant yes the false god could say yes or no - or ja or da but whatever he said he'd still be saying the truth. Because he would or wouldn't be saying yes. If that makes any sense at all.
E.G if he said ja(yes) then he would be telling the truth about saying ja because he would have just said it.
If he said da(no) then he would have been telling the truth about NOT saying ja.

But I suppose at the same time if you ask the TRUTH God and ja means NO, what would the truth God say?
He could say ja=no but then he would have lied.
He could say da=yes but then he would have lied.

Erm. Can someone sort this out for me?
Then maybe I'll try again. Lol. As if. These puzzles confuse me!!
Actually this makes a lot of sense, if I'm understanding it correctly. And if I understand paradox.

If "ja" means "yes":
True: "Yes" OR "No"
Random: "Yes" OR "No"

And it's quite possible the inverse works as well:
False: "Yes"
Random: "Yes"

Originally Posted by Merkw
* 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

Possible diagram for EsoteriEccentri's method.
God A: Question 1: Will your answer to this question mean "no"?
*If no answer to #1: God A = True
--------> If no answer: God A = True. God B = False. God C = Random.
--------> If answer: God A = True. God B = Random. God C = False.

*If answer #1, answer means "yes". (presumably) And God A is either False or Random.
--------> If no answer to #2: God A = False.
-------------------> Ask God B: Will you answer to this question mean "no"?
------------------------> If no answer: God A = False. God B = True. God C = Random.
--------> If answer to #2: God A = Random.
-------------------> Ask God B: Does "ja" mean "yes"?
------------------------> If answer "ja": God A = Random. God B = True. God C = False.
------------------------> If answer "da": God A = Random. God B = False. God C = True.

2. Someone solve this! Group think! Individual think! Anything!

3. Hm... I've forgotten most of my Logic 101. Is it allowed to use more than one "if and only if" in a sentence, or is that nonsense? I think I might see the beginnings of a solution if I could ask "x if and only if y if and only if z", or rather, I don't see how it could be avoided. If it's allowed, the truth/false values of such a sentence could be tailored to create predictable answers which would solve the "what's yes, what's no" question. x should be something connected with what kind of god one of them is, y a question with a known answer (like 1+1=2?) and z be about whether da/ja means yes/no. I'll think more on it, unless that helps someone else solve it before me.

I'll need to read up on basic logic operants first in any case (unless someone can answer me what if and only if is called in English and whether or not it makes sense to use more than one in a sentence.)

4. Ok, found it. The term I was looking for was "iff", though if and only if works as well. And I've found nothing to suggest that you can't have who iffs in a sentence.

(Eg. I am cool iff wearing sunglasses is cool iff I'm in Norway.

Where the sentence is true if all three are true or all three are false and false if some are true and some are not.)

I think this could get both true god and false god to answer the same.

Hm... I'll ahve to write this out to see if it makes sense.

Say I ask god A: Does ja mean yes iff god B is the random god iff 1+1 is 2?

Hm... what would happen then? Let's say the gods answer each part of their question in their heads first, truthfully, randomly or falsely, then adds up the values to the entire question and answers that one truthfully, randomly or falsely. If A is truth... ok, let's use T, R and F about the gods.

Let's see. Ok, let's pretend B is R and ja means yes. If A is T he'd get true for the question and answer true. If A is F he'd... bah, he'd get false for all three, true for the entire sentence and answer false. Bah, I wanted to force T and F to answer the same.

It has to be something like this, though!

5. Ah, but what if I the question to A is this instead:

Does ja mean yes iff you are true iff 1+1=2?

If A is T and ja means yes, he'd answer ja (yes) because it's true, true, true = true.
If A is T and ja means no, he'd answer ja (no) because it's false, true, true = false.
If A is F and ja means yes, he should have answered da (no), because the components become false, true, false in his head = false, but he lies and answers ja (yes).
If A is F and ja means no, he should have answered (yes), because the components become true, true, true in his head = true, but he lies and answers ja (no).

So now I've gotten both T and F to answer "ja" no matter what ja means... but that still leaves R and what the meaning of ja is. Bah... I think this is a part of the puzzle however... getting T and F to answer the same no matter what you ask them with the first question... but I'm far from the solution yet, and falling asleep, so I'll have to think more on this later.

Kiddo or Merkw, am I on the right path, or have I misunderstood everything?

6. Hm... what if I ask are you R instead of asking are you T? Bah, I'll figure out the implications later. ZZz

7. Okay here it goes (this is going to be lengthy). I'd attach my excel spreadsheet if I knew how:

There are 6 permutations:
TFR, TRF, FTR, FRT, RTF, RFT

Question 1:
Is an odd number of these statements true?
Ja=yes
A=T
B=R

By asking if Ja is yes you are essentially setting a value for Ja and Da.

If you ask the question: "Is Ja yes?" you will get an interesting response. If it is, the answer is Ja. If it isn’t, the answer is still ja. Therefore, by asking Question 1, you are making Da mean that

So if the god who is telling the truth says Ja, either A is true and B is random, or A is not true and B is not random (that can't be right anyway, since we are assumining he is True). Da means one of the two is true.

Now if A=R, then he could answer either way, so you can’t narrow them out. But if he is T, answering Da would eliminate TRF. If he is False and says Da, it would eliminate FRT, as he would lie. The same logic can be used to eliminate choices with the Ja answer.

If A=Da, then it going to one of the following permutations:

TFR, FTR, RTF, RFT

If A=Ja, then it would be either:

TRF, FRT, RTF, RFT

The next question would be directed at the one that you know is not Random.

In the first case, that is God B. In the second case, that would be C

You would ask him: Is ja yes?

As stated above, that question will be answered the same way no matter what ja means. If ja is yes, then the answer will be yes (ja). If ja is no, then the answer will be no (again, ja).

If he answers Da, then he cannot be the truthful god. And since we know he isn't random, that makes him the liar. If he answers Ja, then he is the truthful one.

Now that we know who he is, we can simply ask him a third question:

Is either ja yes or is A=Random?

If we know he is the liar, and he says Da, then A=T. If he is the one who tells the truth, and says Da, then A=R. That would make the third god whatever is left.

Da/Da/Da: RFT
Da/Da/Ja: TFR
Da/Ja/Da: FTR
Da/Ja/Ja: RTF
Ja/Da/Da: RTF
Ja/Da/Ja: TRF
Ja/Ja/Da: FRT
Ja/Ja/Ja: RFT

8. The problem with the paradox is that, the random god speaks truly or falsely. He doesn't just say yes or no randomly. He in fact, takes on the true or false identity randomly. Therefore, he would also falter half the time during that paradox.

The third clarification states: "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." It doesn't just say he says yes or no.

So if you ask if the answer will mean no, the truthful god would not answer, but the random god may not as well. It wouldn't really distinguish between the two.

9. ## Clarification

For my third question, when I say Either... or, I mean that either one is right or the other. If they are both right, then the answer would be no.

10. One year too late..