Hardest Logic Puzzle Ever

Three men 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 person.

The men understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which.

Edit: here is more clarification

• It could be that some man gets asked more than one question (and hence that some man is not asked any question at all).

• What the second question is, and to which man it is put, may depend on the answer to the first question. (And of course similarly for the third question.)

• 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

P.S. You're a person with impressive intellegence if you managed to solve this puzzle without help.

I've solved that one before, just not gonna ruin it so soon because its a very good puzzle.Jakesgotbeef

PM me the answer PLEASE

much appreciated 

[QUOTE="Jakesgotbeef"]I've solved that one before, just not gonna ruin it so soon because its a very good puzzle.comrade_sniperr

PM me the answer PLEASE

much appreciated 

look it up im lazy and tired

[QUOTE="comrade_sniperr"]

[QUOTE="Jakesgotbeef"]I've solved that one before, just not gonna ruin it so soon because its a very good puzzle.Jakesgotbeef

PM me the answer PLEASE

much appreciated

look it up im lazy and tired

where?  

[QUOTE="Jakesgotbeef"][QUOTE="comrade_sniperr"]

[QUOTE="Jakesgotbeef"]I've solved that one before, just not gonna ruin it so soon because its a very good puzzle.comrade_sniperr

PM me the answer PLEASE

much appreciated

look it up im lazy and tired

where?

here is more clarification

• It could be that some man gets asked more than one question (and hence that some man is not asked any question at all).

• What the second question is, and to which man it is put, may depend on the answer to the first question. (And of course similarly for the third question.)

• 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

[QUOTE="Jakesgotbeef"]I've solved that one before, just not gonna ruin it so soon because its a very good puzzle.comrade_sniperr

PM me the answer PLEASE

much appreciated 

CAn you please PM me the answer and the way to get there im so confused

I guess I'd ask each person "Are you dead?" repeatedly until a pattern arises.ExiledHero

Good one.  That should work. 

I guess I'd ask each person "Are you dead?" repeatedly until a pattern arises.ExiledHero

How would you know what "da" and "ja" mean though?  

This logic puzzle took me a whole day to solve, I used a lot of Boolean logic skills I picked up throughout my years of software development just to solve it.  It's without a doubt the hardest logic puzzle I have ever encountered.

Here is my solution (warning: wall of text)

I'd ask my 3 questions to any of the guys (regardless), because the way I'm gonna formulate my question should allow me (all in one shot) to: a) extract the truth out of any of them, regardless of being truthful, lying or random. b) solve the language barrier

Q1 (for any of the guys)
Answer yes with da and no with ja then tell me what would a truthful person (that knows whether or not you're going to tell the truth) say if I asked him to tell me what would your answer be to the following question? "is A TRUE?"

The first part of this question "Answer yes with da and no with ja" forces the person to use da for yes and ja for no (regardless of what they mean in his language).

So from the first part of the question, I already eliminated the language barrier.

The second part of the question is "what would a truthful person say about what you're going to say" forces him (even if he lies) to flip his lie to truth.

Here is an explanation to the lie flipping trick:

Assume A is FALSE and B is TRUE.
If you ask A "are you a liar?"
The correct answer is "YES", but since A is FALSE, he'll say "NO"

Now, if we ask B to tell us (from his perspective) what would A answer be to the question of "are you a liar?"
B knows that A would answer it with "NO", so B's answer would be "NO" (similar to A's answer).

Now if we ask A about what B's gonna say about A's answer (I know,  complicated :P), then we actually gonna get the truth out of A.
Reason for that is, A will now know that B will answer with "NO", and because he's FALSE, he'll flip it to "YES" when he answers us.

Which in this case our original question of "Are you a liar?" would be answered by the liar as "YES".

And the good thing about this logic is that if the person in which we're trying our tricky logic here is already truthful, no truth flipping will occur. (I know it's a bit complicated but try it out for yourself with examples if you want).

So now that we dissected how our first question is formulated (the other two will use the exact same lie flipping trick), we can proceed knowing that a) we don't have a language barrier, and b) whomever we'll ask (TRUE, FALSE, or RANDOM) we should receive a truthful answer.

So back to our first question above ("Is A TRUE?"), we should get either one of two answers YES or NO truthfully and without a language barrier (since we eliminated that with the explicit instruction of "answer YES with DA, and NO with JA")

So if Q1 ("Is A TRUE?") answer was YES (we'll get to the NO answer in a bit), then it means person A is TRUE, that leaves us with B and C being either FALSE or RANDOM

For that, here is my second question

Q2 (for any of the guys, in case Q1 answer was YES)
Answer yes with da and no with ja then tell me what would a truthful person (that knows whether or not you're going to tell the truth) say if I asked him to tell me what would your answer be to the following question? "is B FALSE?"

Notice that I'm using the same lie flipping logic as Q1 (i.e. we'll get a truthful answer no matter what, and we won't have a language barrier).

If the answer was 'da' which means yes (since I forced him to use da for yes), then A is TRUE, B is FALSE, and C is RANDOM
But if answered with no, then A is TRUE, B is RANDOM, and C is FALSE.

That solves the puzzle in 2 questions only.

However, if the answer to Q1 wasn't YES (i.e. it was NO), this means A is not TRUE, which leaves us with him being either FALSE or RANDOM

So my second question in that case (using the same logic as the first one) would be:

Q2 (for any of the guys) in case Q1 answer was NO
Answer yes with da and no with ja then tell me what would a truthful person (that knows whether or not you're going to tell the truth) say if I asked him to tell me what would your answer be to the following question? "is A FALSE?"

Notice that this question is also using the same logic as Q1 (i.e. we'll get a truthful answer no matter what, and we won't have a language barrier since I forced him to use da for yes).

From this, if the answer was yes, then A is FALSE, which leaves us with B and C as either TRUE or RANDOM. But if he answered NO, then A can only be RANDOM in this case (cause from Q1 we found out that A is not TRUE, and form Q2 we found out that he's not FALSE either).

For that my third question would be:

Q3 (for any of the guys) in case Q1 answer was NO
Answer yes with da and no with ja then tell me what would a truthful person (that knows whether or not you're going to tell the truth) say if I asked him to tell me what would your answer be to the following question? "is B TRUE?"

This answer along with Q2 & Q1 answers will give us the full picture.

Here are the 4 possible answers along with their meanings:
(1)
Q1 answer = NO, Q2 answer= NO, Q3 answer = YES
This means, A is RANDOM, B is TRUE and C is FALSE

(2)
Q1 answer = NO, Q2 answer= NO, Q3 answer = NO
This means A is RANDOM, B is FALSE, and C is TRUE

(3)
Q1 answer = NO, Q2 answer= YES, Q3 answer = YES
This means A is FALSE, B is TRUE, and C is RANDOM

(4)
Q1 answer = NO, Q2 answer= YES, Q3 answer = NO
This means A is FALSE, B is RANDOM, and C is TRUE

This logic puzzle took me a whole day to solve, I used a lot of Boolean logic skills I picked up throughout my years of software development just to solve it.  It's without a doubt the hardest logic puzzle I have ever encountered.

Here is my solution (warning: wall of text)

I'd ask my 3 questions to any of the guys (regardless), because the way I'm gonna formulate my question should allow me to extract the truth out of any of them without having to deal with the language barrier.

Q1 (for any of the guys)
Answer yes with da and no with ja then tell me what would a truthful person (that knows whether or not you're going to tell the truth) say if I asked him to tell me what would your answer be to the following question? "is A TRUE?"

The first part of this question "Answer yes with da and no with ja" forces the person to use da for yes and ja for no (regardless of what they mean in his language).

So from the first part of the question, I already eliminated the language barrier.

The second part of the question is "what would a truthful person say about what you're going to say" forces him (even if he lies) to flip his lie to truth.

And the good thing about this logic is that if he's truthful, no truth flipping will occur. (I know it's a bit complicated but try it out for yourself with examples if you want).

Now that we know we'll get correct answers no matter what. And we don't have a language barrier, the first question above would be answered with either yes or no.

If yes, then it means person A is TRUE, that leaves us with B and C being either TRUE or RANDOM

For that, here is my second question

Q2 (for any of the guys) in case Q1 answer was YES
Answer yes with da and no with ja then tell me what would a truthful person (that knows whether or not you're going to tell the truth) say if I asked him to tell me what would your answer be to the following question? "is B FALSE?"

Notice that I'm using the same logic as Q1 (i.e. we'll get a truthful answer no matter what, and we won't have a language barrier).

If the answer was 'da' which means yes (since I forced him to use da for yes), then A is TRUE, B is FALSE, and C is RANDOM
But if answered with no, then A is TRUE, B is RANDOM, and C is FALSE.

That solves the puzzle in 2 questions only.

However, if the answer to Q1 wasn't YES (i.e. it was NO), this means the first is not TRUE, which leaves us with him being either FALSE or RANDOM

So my second question in that case (using the same logic as the first one) would be:

Q2 (for any of the guys) in case Q1 answer was NO
Answer yes with da and no with ja then tell me what would a truthful person (that knows whether or not you're going to tell the truth) say if I asked him to tell me what would your answer be to the following question? "is A FALSE?"

Notice that this question is also using the same logic as Q1 (i.e. we'll get a truthful answer no matter what, and we won't have a language barrier since I forced him to use da for yes).

From this, if the answer was yes, then A is FALSE, which leaves us with B and C as either TRUE or RANDOM. But if he answered NO, then A can only be RANDOM in this case (cause from Q1 we found out that A is not TRUE, and form Q2 we found out that he's not FALSE either).

For that my third question would be

Q3 (for any of the guys) in case Q1 answer was NO
Answer yes with da and no with ja then tell me what would a truthful person (that knows whether or not you're going to tell the truth) say if I asked him to tell me what would your answer be to the following question? "is B TRUE?"

This answer along with Q2 & Q1 answers will give us the full picture.

We have these 4 answer possibilities along with what they mean:
(1)
Q1 answer = NO, Q2 answer= NO, Q3 answer = YES
This means, A is RANDOM, B is TRUE and C is FALSE

(2)
Q1 answer = NO, Q2 answer= NO, Q3 answer = NO
This means A is RANDOM, B is FALSE, and C is TRUE

(3)
Q1 answer = NO, Q2 answer= YES, Q3 answer = YES
This means A is FALSE, B is TRUE, and C is RANDOM

(4)
Q1 answer = NO, Q2 answer= YES, Q3 answer = NO
This means A is FALSE, B is RANDOM, and C is TRUE

Hussein

I got confused halfway

[QUOTE="Hussein"]

This logic puzzle took me a whole day to solve, I used a lot of Boolean logic skills I picked up throughout my years of software development just to solve it.  It's without a doubt the hardest logic puzzle I have ever encountered.

Here is my solution (warning: wall of text)

I'd ask my 3 questions to any of the guys (regardless), because the way I'm gonna formulate my question should allow me to extract the truth out of any of them without having to deal with the language barrier.

Q1 (for any of the guys)
Answer yes with da and no with ja then tell me what would a truthful person (that knows whether or not you're going to tell the truth) say if I asked him to tell me what would your answer be to the following question? "is A TRUE?"

The first part of this question "Answer yes with da and no with ja" forces the person to use da for yes and ja for no (regardless of what they mean in his language).

So from the first part of the question, I already eliminated the language barrier.

The second part of the question is "what would a truthful person say about what you're going to say" forces him (even if he lies) to flip his lie to truth.

And the good thing about this logic is that if he's truthful, no truth flipping will occur. (I know it's a bit complicated but try it out for yourself with examples if you want).

Now that we know we'll get correct answers no matter what. And we don't have a language barrier, the first question above would be answered with either yes or no.

If yes, then it means person A is TRUE, that leaves us with B and C being either TRUE or RANDOM

For that, here is my second question

Q2 (for any of the guys) in case Q1 answer was YES
Answer yes with da and no with ja then tell me what would a truthful person (that knows whether or not you're going to tell the truth) say if I asked him to tell me what would your answer be to the following question? "is B FALSE?"

Notice that I'm using the same logic as Q1 (i.e. we'll get a truthful answer no matter what, and we won't have a language barrier).

If the answer was 'da' which means yes (since I forced him to use da for yes), then A is TRUE, B is FALSE, and C is RANDOM
But if answered with no, then A is TRUE, B is RANDOM, and C is FALSE.

That solves the puzzle in 2 questions only.

However, if the answer to Q1 wasn't YES (i.e. it was NO), this means the first is not TRUE, which leaves us with him being either FALSE or RANDOM

So my second question in that case (using the same logic as the first one) would be:

Q2 (for any of the guys) in case Q1 answer was NO
Answer yes with da and no with ja then tell me what would a truthful person (that knows whether or not you're going to tell the truth) say if I asked him to tell me what would your answer be to the following question? "is A FALSE?"

Notice that this question is also using the same logic as Q1 (i.e. we'll get a truthful answer no matter what, and we won't have a language barrier since I forced him to use da for yes).

From this, if the answer was yes, then A is FALSE, which leaves us with B and C as either TRUE or RANDOM. But if he answered NO, then A can only be RANDOM in this case (cause from Q1 we found out that A is not TRUE, and form Q2 we found out that he's not FALSE either).

For that my third question would be

Q3 (for any of the guys) in case Q1 answer was NO
Answer yes with da and no with ja then tell me what would a truthful person (that knows whether or not you're going to tell the truth) say if I asked him to tell me what would your answer be to the following question? "is B TRUE?"

This answer along with Q2 & Q1 answers will give us the full picture.

We have these 4 answer possibilities along with what they mean:
(1)
Q1 answer = NO, Q2 answer= NO, Q3 answer = YES
This means, A is RANDOM, B is TRUE and C is FALSE

(2)
Q1 answer = NO, Q2 answer= NO, Q3 answer = NO
This means A is RANDOM, B is FALSE, and C is TRUE

(3)
Q1 answer = NO, Q2 answer= YES, Q3 answer = YES
This means A is FALSE, B is TRUE, and C is RANDOM

(4)
Q1 answer = NO, Q2 answer= YES, Q3 answer = NO
This means A is FALSE, B is RANDOM, and C is TRUE

fathertroy

I got confused halfway

lol :P, don't worry man, I most probably wouldn't have solved it myself (or even understood a solution if it's written right in front of me) if I wasn't doing software development (lots of complicated logic) my whole life.

Hussein

[QUOTE="Hussein"]blackleech

the condition is; the outcome should always be either yes or no in their language, i.e. the outcome should only be 'da' or 'ja'

It's like me asking you, assume yes means no, and no means yes, and tell me if your tag name in GS is "blackleech"?

BTW, it's called Labyrinth puzzle and here is a geeky joke about it

Here is an example that explains the concept of flipping the lie to truth.

Assume A is FALSE and B is TRUE.
If you ask A "are you a lair?"
The correct answer is "YES", but since A is FALSE, he'll say "NO"

Now, if we ask B to tell us (from his perspective) what would A answer be to the question of "are you a lair?"
B knows that A would answer it with "NO", so B's answer would be "NO" (similar to A's answer).

Now if we ask A about what B's gonna say about A's answer (I know complicated), then we actually gonna get the truth out of A.
Reason for that is, A will know that B will answer with "NO", so, he'll flip it to "YES".
Which in this case our original question of "Are you a lair?" would be answered by the lair as "YES"

I point a gun at them and ask if they want to die.forgot_it

BAM! they said 'da'. I assumed that meant Yes!

Something that has been bothering me about this:

What happens if you ask one of them a yes / no question that they don't know the answer to?

Answer yes with da and no with ja then tell me what would a truthful person (that knows whether or not you're going to tell the truth) say if I asked him to tell me what would your answer be to the following question? "is A TRUE?"

 Hussein

You don't get to specifiy how they answer. You only get to ask questions, not give instructions. 

Here is an example that explains the concept of flipping the lie to truth.

Assume A is FALSE and B is TRUE.
If you ask A "are you a lair?"
The correct answer is "YES", but since A is FALSE, he'll say "NO"

Now, if we ask B to tell us (from his perspective) what would A answer be to the question of "are you a lair?"
B knows that A would answer it with "NO", so B's answer would be "NO" (similar to A's answer).

Now if we ask A about what B's gonna say about A's answer (I know complicated), then we actually gonna get the truth out of A.
Reason for that is, A will know that B will answer with "NO", so, he'll flip it to "YES".
Which in this case our original question of "Are you a lair?" would be answered by the lair as "YES"

Hussein

Wasnt that on an episode of smauri jack 

I guess I'd ask each person "Are you dead?" repeatedly until a pattern arises.ExiledHero

LMFAO!!!!!!! thats a good one dude:lol: