Hardest logical puzzle.

[Niveus Draco]

According to the philosopher and logician George Boolos, this is the hardest logical puzzle there is. I personally couldn't figure it outt, but I know the answer. Can any of you get it?


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 “daâ€￾ and “jaâ€￾, in some order. You do not know which word means which.

[White Dragon Alorith]

I've sat here and thought about this for half an hour (okay okay, so five minuets, I always exaggerate) and all I can think of for the questions is asking some question regarding the words, such as 'does ja me yes?' to God whatever. If I asked all of them and got the answers 'ja, ja and da' then I'm stuck. Same had I got 'Ja, da, and da.'

So how about I ask a question regarding the puzzle. Is the question asked directed towards the da/ja or something else entirely to figure out which means which.

Or can I assume they speak German and 'Ja' means yes?

Now watch as Tempest will step in and hand us all our asses when he tells us the answer in one short, simple sentance, claiming he invented this puzzle and has a harder one.

[Zoanrevived]

Ok, there are of 3 questions to be asked...

Are you the one that lies?

Are you the one that says the truth?

Is God (A,B,C) the one that lies?

Or atleast, that's what I think the questions should be.

2 of the gods would answer the same.

I think that may help some.

[White Dragon Alorith]

*Cough cough*

Niveus, response please.

[Niveus Draco]

Sorry about that. I just kind of forgot. How stupid of me. Here's the answer.


Turn to A and ask

Question 1: Does da mean yes iff(*), you are True iff B is Random?

If A is True or False and you get the answer da, then as we have seen, B is Random, and therefore C is either True or False; but if A is True or False and you get the answer ja, then B is not Random, therefore B is either True or False.

But what if A is Random? If A is Random, then neither B nor C is Random! So if A is Random and you get the answer da, C is not Random (neither is B, but that’s irrelevant), and therefore C is either True or False; and if A is Random and you get the answer ja, B is not random (neither is C, irrelevantly), and therefore B is either True or False.
Thus, no matter whether A is True, False, or Random, if you get the answer da to Question 1, C is either True or False, and if you get the answer ja, B is either True or False!

Now turn to whichever of B and C you have just discovered is either True or False — let us suppose that it is B (if it is C, just interchange the names B and C in what follows) — and ask:

Question 2: Does da mean yes?

True will answer da, and False will answer ja. Thus, with two questions, you have either identified B as True or identified B as False.
For our third and last question, turn again to B, whom you have now either identified as True or identified as False, and ask:

Question 3: Does da mean yes iff A is Random?

Suppose B is True. Then if you get the answer da, then A is Random, and therefore A is Random, B is True, C is False, and you are done; but if you get the answer ja, then A is not Random, so A is False, B is true, C is Random, and you are again done.
Suppose B is False. Then if you get the answer da, then since B speaks falsely, A is not Random, and therefore A is True, B is False, C is Random, and you are done; but if we get ja, then A is Random, and thus B is False, and C is True, and you are again done.


(*) iff = if and only if, biconditional, logic table as below:
T iff T = T
T iff F = F
F iff T = F
F iff F = T

[White Dragon Alorith]

Oh god. You have a simpler version for morons like me? Glad you got back to this.

[zoan.revivec]

Ok, yeah, that makes perfect sense now...not really, I'll try to simplify it.

Turn to A and ask

Question 1: Does da mean yes if and only if A is True and B is Random?

If A says Da, we know that A can be either True or False, but we know for sure that B is random. And C would be True or False

If A says Ja, then B is not random. Instead, B is True or False. We don't know.

If A is Random, then we know that B and C can't be Random.
So if you get Da as an answer, C isn't Random.
If you get Ja, B isn't random.
And B and C can be True or False.
So, Answer Da, means that C is True or False,
and Answer Ja means that B is true or false.

Have I lost you? I've lost myself, so yeah. I'm just trying to simplify it.

Next turn to B or C, it doesn't matter which one. But lets just say that you turn to B.

Question 2: Does da mean yes?

If B is True, he will answer Da. If B is False, he will say Ja. So with this question and the last one, you have Identified as B being True or False. b/c A can't be random, and B be random as well.

For our third and last question, turn again to B, who is either True or False.

Question 3: Does da mean yes iff A is Random?

Now, if B is True, you get Da, and A is random, and C is False.
If B is False, then A isn't random, he would need to be True, and C would be random.
B can't be Random, b/c of the last question and the one before it.

So there ya go, is that any easier to understand?

[Silentiea]

Almost... My brain itches.

[Niveus Draco]

I think this one will be better.

Ask A: Is da yes if you are true and b is random?

If A is True or False and you get the answer da, then B is Random, and C is true or false. But if you get the answer ja, then B is not Random it is tru or false.

If A is Random and you get the answer da, then B or C is true or false.

If you get da, C is true or false. If you get ja, B is true or false.


Ask either B or C, Does da mean yes?

True will answer da, and False will answer ja.


Ask B or C (the other one), Does da mean yes if A is random?

Suppose B is true.

-If you get da, then A is Random, B is True, and C is False.

-If you get ja, A is False, B is true, and C is Random.

Suppose B is False.

-If you get da, A is True, B is False, and C is Random.

-If you get ja, then A is Random, B is False, and C is True.

[Pandora]

Meeeess confuseded!


No really,I must be really stupid cause I really don't get it.

What IS the answer,if you yourself doesn't truely know, then how do you answer and how do you and I both know that yur correct?

Oh! my head!

[Draches]

If i ate an apple in the third parrallel dimension of JAKKA JAKKA WOO! (the universe inside my head) would i still be the same person that was me in the alternate other dimension in the fourth parrel to the sixth power?

i must say... i highly doubt it...

[Niveus Draco]

All I did was eliminate some of the words that didn't need to be there, and some phrases that were repeated. It's still the same answer. It worked when I tried it. Working it out on paper helps.

[Tempest]

All I have to say is: clever

I was on the right track but I didn't found the answer

[vampirehunter42]

I think I see a problem in the answer, but I need to run through it a couple of times to see. I will try to post it later.

[vampirehunter42]

I found the problem with it.

Here is what you posted and how it works.

Assuming da = yes and ja = no.

Question 1: Does da mean yes iff(*), you are True iff B is Random?

Asked to A.
1. If A is true and B is random and C is false: (T, {T, T}) so it is true, and will answer da.(yes)
2. If A is true and B is false and C is random: (T, {T, F}) so it is false, and will answer ja. (no)
3. If A is false and B is random and C is true: (T, {F, T}) so it is false, and will answer da. (yes)
4. If A is false and B is true and C is random: (T, {F, F}) so it is true, and will answer ja (no)
5. If A is random and B is true and C is false: (T, {F, F}) so it is true, but will answer either da (yes) or ja (no)
6. If A is random and B is false and C is true: (T, {F, F}) so it is false, but will answer either da (yes) or ja (no)

Ok looking at it the answer da will mean C is the other true or false, and the answer ja will mean B is the other true of false. And taking for thought if A were random using the above thought will still work.

Question 2: Does da mean yes?

Asking B.
2. If A is true and B is false and C is random: (T) so it is true, and will answer ja (no)
4. If A is false and B is true and C is random: (T) so it is true, and will answer da (yes)
Getting ja for the first question you will ask B. You will get ja if B is false (assuming da means yes), and da if B is true (assuming da means yes)

Asking C
1. If A is true and B is random and C is false: (T) so it is true, and will answer ja (no)
3. If A is false and B is random and C is true: (T) so it is true, and will answer da (yes)
Getting da for the first question you will ask C. You will get ja if C is false (assuming da means yes), and da if C is true (assuming da means yes)

Question 3: Does da mean yes iff A is Random?

Asking B.
2. If A is true and B is false and C is random: (T, F) so it is false, and will answer da (yes)
4. If A is false and B is true and C is random: (T, F) so it is false, and will answer ja (no)
5. If A is random and B is true and C is false: (T, T) so it is true, and will answer da (yes)
6. If A is random and B is false and C is true: (T, T) so it is true, and will answer ja (no)
Asking B again. Using what you get from question of B being true or false.
B is true.
If you get da: A is random, B is true and C is false.
If you get ja: A if false, B is true and C is random.
B is false.
If you get da: A is random, B is false and C is true.
If you get ja: A is true, B is false and C is random.

Asking C
1. If A is true and B is random and C is false: (T, F) so it is false, and will answer da (yes)
3. If A is false and B is random and C is true: (T, F) so it is false, and will answer ja (no)
5. If A is random and B is true and C is false: (T, T) so it is true, and will answer ja (no)
6. If A is random and B is false and C is true: (T, T) so it is true, and will answer da (yes)
Asking C again, Using what you get from question #2 of C being true or false.
C is true.
If you get da: A is random, B is false and C is true.
If you get ja: A is false, B is random and C is true.
C is false.
If you get da: A is random. B is true, and C is false.
If you get ja: A is true, B is random and C is false.

It looks like it works, but one little problem. This only works if da does mean yes and the asker has assumed it does. Remember you posted the asker does not know what means what. I am working on the other way but so far the questions do not seem to work.