Incredibly difficult logic problem.

Pan1cMode · Mar 28, 2014

A friend told me this and it took a solid day of pondering and thinking about it to finally get it. I thought the problem solvers among you guys might find it interesting;

You are walking down a path and come up to a fork in the road being guarded by 3 guards. A sign at the foot of the fork informs you of the following (and you are to assume the sign is factual):

- One of these paths leads to untold riches, the other to certain death.
- One of the guards here will always answer truthfully
- One of the guards here will always answer with a lie
- One of the guards here will answer either truthfully or falsely but which is random.
- The guards understand English but they will reply in their own native tongue.
- It is known that Ba and Da mean yes and no in the guard's native language but which means which is unknown. One means yes and the other no.
- Each guard will answer only one question. (You may pose up to three questions, one to each guard)
- The guards know which direction leads to where and the identities of the other guards.
- Further clarification; the guards may only answer Da or Ba nothing else. They cannot gesture or point. If presented with a paradox or something unknowable they will answer randomly.

What question(s) do you pose to the guards to find out which path to take?

EDIT:
Some clues. Answer will be posted in 24 hours.

You only need to ask one question.

You can solve the riddle without knowing the explicit meanings of Da and Ba or which guard is which.

Disregard the random as he will either act as a truth teller or a liar

You must ask a question to which all 3 guards would answer the same

EDIT 2:
Answer is below

You ask any one of the guards; "In your current mental state, would you answer Da to the question, does the left path lead to riches?" If the answer is Da take the left path. If the answer is Ba take the right path.
The scenarios are shown below. Note that it doesn't matter if you're talking to the random guard because he will essentially act as either a liar or a truth teller.

The scenarios are thus:

Da = Yes, Left = Riches
Truth answers: Da
Liar answers: Da
Take left path

Da=No, Left = Riches
Truth answers: Da
Liar answers: Da
Take left path

Da = Yes, Right = Riches
Truth answers: Ba
Liar answer: Ba
Take right path

Da = No, Right = Riches
Truth answers: Ba
Liar answers: Ba
Take right path

Rodrigue · Mar 28, 2014

I think I might know the answer but I won't post it. It's kinda early and I don't wanna ruin it for you pan1c

Classic riddle though

FrozenG3oX · Mar 28, 2014

Pan1cMode said:
A friend told me this and it took a solid day of pondering and thinking about it to finally get it. I thought the problem solvers among you guys might find it interesting;

You are walking down a path and come up to a fork in the road being guarded by 3 guards. A sign at the foot of the fork informs you of the following (and you are to assume the sign is factual):

- One of these paths leads to untold riches, the other to certain death.
- One of the guards here will always answer truthfully
- One of the guards here will always answer with a lie
- One of the guards here will answer either truthfully or falsely but which is random.
- The guards understand English but they will reply in their own native tongue.
- It is known that Ba and Da mean yes and no in the guard's native language but which means which is unknown. One means yes and the other no.
- Each guard will answer only one question. (You may pose up to three questions, one to each guard)

What question(s) do you pose to the guards to find out which path to take?

If you are interested in the solution I'll post it later, but think about it for a bit.

wait...there are 2 or 3 paths ? i dont understand...one leads to untold riches and the other to ceartin death...then there are 2 yet 3 guards ? or there is no nothing saidf ab the 3rd path ?

Pan1cMode · Mar 28, 2014

FrozenG3oX said:
wait...there are 2 or 3 paths ? i dont understand...one leads to untold riches and the other to ceartin death...then there are 2 yet 3 guards ? or there is no nothing saidf ab the 3rd path ?

There are only two paths but there are three guards standing at the foot of the fork in front of the sign. The guards serve no purpose other then to answer your questions.

TaffyMeat · Mar 28, 2014

Ask the guards to go down the path and get the money. One will get the money the other will lie and say there is no money.

Pan1cMode · Mar 28, 2014

TaffyMeat said:
Ask the guards to go down the path and get the money. One will get the money the other will lie and say there is no money.

No they won't.

And you won't understand what they're saying anyways.

Doombawkz · Mar 28, 2014

Ask two of the guards to point to the correct path.

If both point towards the same path, then ask the final one to point to the path thats on the left.
If both point in opposite directions, then ask the final one which path leads to the treasure if you asked the guard on the left.

Pan1cMode · Mar 28, 2014

Doombawkz said:
Ask two of the guards to point to the correct path.

If both point towards the same path, then ask the final one to point to the path thats on the left.
If both point in opposite directions, then ask the final one which path leads to the treasure if you asked the guard on the left.

They won't change the direction they are pointing. Two will point one direction and one will point another.

1man3letters · Mar 28, 2014

seems like a twist on the 4 heads 2 doors thing from labyrinth...

Doombawkz · Mar 28, 2014

Pan1cMode said:
They won't change the direction they are pointing. Two will point one direction and one will point another.

In the first one, if two guards point to the same path then you know they are either both honest or both lying, as the honest one would have no reason to point you to a false path, and the liar would have no reason to point you to the true path. In that case, asking the final guard to simply "point to the path on the left" would show that either he is a liar and the other two are honest, or he is honest and the other two are lying.

In the second example, each path is covered and the final guard is either a liar, honest, or a mix. Now the guard on the left is either honest or lying, but it can't be both. Same with the one on the right. So the final guard will either lie or be honest. This is where it gets interesting. If he is honest, then he would be incapable of "lying", and if he were a liar, he would be incapable of telling the "truth", so asking him to take the perspective of one of the guards (namely the left guard) will reap one of two results: Either a double truth where the guard on the left is honest and that's your result, or a double lie where its the opposite.
A being left guard, B being right guard, C being third guard, and 1 being honest, 2 being liar.

If A is 1, then B must be 2.
If C is 2, then he will point the opposite of A.
If C is 1, he will point the same way as A.
If C is 1 and A is 1, then answer is A's point.

If A is 2 then B must be 1.
If C is 1, he will not point.
If C is 2, then he will not point.
If C is 1/2 and A is 2, then C will not point and thus the answer is opposite of A.

If C is 1/2, then A is 1/2 and B is 1/2.
If C is 1, and A is 1 and B is 2, then C will point in the same.
If C is 2, and A is 1 and B is 2, then C will point in the opposite.

So basically, if we accept that C has a chance of being completely one or the other without changing, then the answer is simple. If he is honest, then him taking the persona of a "liar" would be impossible, even if the perspective of the left guard is that of a liar, because that in turn would still be the honest lying. Likewise, if he is a liar then him taking the persona of a "honest" would be impossible since, by pointing in that direction, he would be telling the truth. The only way for him to be able to point and maintain his honesty or lies would be if he doing so based on an honest person since that would allow him the proper alternatives. Then it comes down to the actual third guard. If he is honest, then he and A will have the same answer. However, if he is a liar, then him and A will have differing answers.

Thats only if you believe in true absolutes though.

If he doesn't point, then you know A is the liar. This is because if C is honest, then he won't be able to lie and point to the wrong path. Likewise, if C is a liar, then he will lie about A's lie and thus point to the right path, being honest.

So basically...

If A is honest:

C will either point the same way, or the opposite way (if C is honest, then its two up on A. However, if C is a liar, then he will point to the path A isn't pointing to.)

If A is a liar:

C will not point as both results will end up as the opposite of his persuasion.

Doing this as it is, you have the answer based on if C points or not. If he does, take path A. If he doesn't, take path B.

AK Black Preon · Mar 28, 2014

Doombawkz said:
In the first one, if two guards point to the same path then you know they are either both honest or both lying, as the honest one would have no reason to point you to a false path, and the liar would have no reason to point you to the true path. In that case, asking the final guard to simply "point to the path on the left" would show that either he is a liar and the other two are honest, or he is honest and the other two are lying.

In the second example, each path is covered and the final guard is either a liar, honest, or a mix. Now the guard on the left is either honest or lying, but it can't be both. Same with the one on the right. So the final guard will either lie or be honest. This is where it gets interesting. If he is honest, then he would be incapable of "lying", and if he were a liar, he would be incapable of telling the "truth", so asking him to take the perspective of one of the guards (namely the left guard) will reap one of two results: Either a double truth where the guard on the left is honest and that's your result, or a double lie where its the opposite.
A being left guard, B being right guard, C being third guard, and 1 being honest, 2 being liar.

If A is 1, then B must be 2.
If C is 2, then he will point the opposite of A.
If C is 1, he will point the same way as A.
If C is 1 and A is 1, then answer is A's point.

If A is 2 then B must be 1.
If C is 1, he will not point.
If C is 2, then he will not point.
If C is 1/2 and A is 2, then C will not point and thus the answer is opposite of A.

If C is 1/2, then A is 1/2 and B is 1/2.
If C is 1, and A is 1 and B is 2, then C will point in the same.
If C is 2, and A is 1 and B is 2, then C will point in the opposite.

So basically, if we accept that C has a chance of being completely one or the other without changing, then the answer is simple. If he is honest, then him taking the persona of a "liar" would be impossible, even if the perspective of the left guard is that of a liar, because that in turn would still be the honest lying. Likewise, if he is a liar then him taking the persona of a "honest" would be impossible since, by pointing in that direction, he would be telling the truth. The only way for him to be able to point and maintain his honesty or lies would be if he doing so based on an honest person since that would allow him the proper alternatives. Then it comes down to the actual third guard. If he is honest, then he and A will have the same answer. However, if he is a liar, then him and A will have differing answers.

Thats only if you believe in true absolutes though.

If he doesn't point, then you know A is the liar. This is because if C is honest, then he won't be able to lie and point to the wrong path. Likewise, if C is a liar, then he will lie about A's lie and thus point to the right path, being honest.

So basically...

If A is honest:

C will either point the same way, or the opposite way (if C is honest, then its two up on A. However, if C is a liar, then he will point to the path A isn't pointing to.)

If A is a liar:

C will not point as both results will end up as the opposite of his persuasion.

Doing this as it is, you have the answer based on if C points or not. If he does, take path A. If he doesn't, take path B.

But pointing to the path to the left... isn't a question you can lie to. If I point right I disobeyed but I didn't lie. I mean if I told you to not pick Bane... and you picked him anyway... you didn't lie... you just didn't do it.

Doombawkz · Mar 28, 2014

AK Black Preon said:
But pointing to the path to the left... isn't a question you can lie to. If I point right I disobeyed but I didn't lie. I mean if I told you to not pick Bane... and you picked him anyway... you didn't lie... you just didn't do it.

Well phrasing it into a question such as "Which path is on the left from my view?" or the like is something you can lie about. If he points right, he lied because thats not the "path to the left". Disobedience of a question by giving the wrong answer isn't honest, so in this aspect of things if we trust they are completely absolute in their answers then thats essentially a lie. Theres no inbetween or disobedience, no hairs to be split. Either he is honest and points to the left, or he lies and doesn't point to the left. There is no third option.

Mikemetroid · Mar 28, 2014

Kill the three guards and use my gps to find which way is correct.

Pan1cMode · Mar 28, 2014

Doombawkz said:
Well phrasing it into a question such as "Which path is on the left from my view?" or the like is something you can lie about. If he points right, he lied because thats not the "path to the left". Disobedience of a question by giving the wrong answer isn't honest, so in this aspect of things if we trust they are completely absolute in their answers then thats essentially a lie. Theres no inbetween or disobedience, no hairs to be split. Either he is honest and points to the left, or he lies and doesn't point to the left. There is no third option.

It won't matter anyway because you have no idea which one is the random guard.

Temjiin · Mar 28, 2014

This question has its own wikipedia page... damn

Doombawkz · Mar 28, 2014

Pan1cMode said:
It won't matter anyway because you have no idea which one is the random guard.

I don't need to, because regardless of which is the random he is still either honest or dishonest. The answer is still right because no matter which one he is, if he is honest and by the left or dishonest and by the left, if he is on the right side being honest or dishonest, or if he is the third guard being honest or dishonest, the math still works out perfectly. As you said, he is either honest or dishonest, not both.

If he is not the third guard, then his honesty or dishonesty plays into either the first or second scenario depending on who is coupled with him.

If he is the third guard, the other two guards force the 2nd scenario.

Youphemism · Mar 28, 2014

Or, ORRRRRR, you could just go home and play NRS games until you feel like you're WORTH untold riches

AK Black Preon · Mar 28, 2014

Do you ask all 3 of them the EXACT same question?

Which path is on my left?

Liar Will point Right
Bat Girl Mixup guy will point left or right
Truth CAN'T lie.

So if you get two rights and a left. You know that two lied and one is doing the only option the truth man could.

If you get two lefts and a right you know the LIAR was forced to go the other way.

Doombawkz · Mar 28, 2014

AK Black Preon said:
Do you ask all 3 of them the EXACT same question?

Which path is on my left?

Liar Will point Right
Bat Girl Mixup guy will point left or right
Truth CAN'T lie.

So if you get two rights and a left. You know that two lied and one is doing the only option the truth man could.

You get to ask each one question.
You ask 2 which is the correct path (right/left path) and then depending on their answer, you ask the third a different question.

Pan1cMode said:
- Each guard will answer only one question. (You may pose up to three questions, one to each guard)

What question(s) do you pose to the guards to find out which path to take?

Pan1cMode · Mar 28, 2014

AK Black Preon said:
Do you ask all 3 of them the EXACT same question?

Which path is on my left?

Liar Will point Right
Bat Girl Mixup guy will point left or right
Truth CAN'T lie.

So if you get two rights and a left. You know that two lied and one is doing the only option the truth man could.

If you get two lefts and a right you know the LIAR was forced to go the other way.

But that doesn't tell you which path to go down. You just know which one is the truth teller.

Juggs · Mar 28, 2014

You ask Guard #1 which path Guard #2 will point to if you ask him which is the correct path for the untold riches.
You ask Guard #2 which path Guard #3 will point to if you ask him which is the correct path for the untold riches.
You ask Guard #3 which path Guard #1 will point to if you ask him which is the correct path for the untold riches.

Let's say that left is the correct path.

If Guard #1 is the truth teller, he will tell you that Guard #2 will tell you to go the wrong way, thus the right path.

If Guard #1 is the liar, he will tell you that Guard #2 will tell you to go to the right path (if Guard #2 is the truth teller), and if he's the random one, he will not be able to point in either direction because he will not know which way Guard #2 will point.

If Guard #1 is the random one, Guard #3 will not be able to point in either direction because he will not know which way Guard #1 will point.

So no matter what, you'll be able to find the random one, and then go the opposite way the other two point.

EDIT: To clarify, you don't ask him to tell you which path the other guard would tell you to take, you make him point.

Pan1cMode · Mar 28, 2014

Doombawkz said:
I don't need to, because regardless of which is the random he is still either honest or dishonest. The answer is still right because no matter which one he is, if he is honest and by the left or dishonest and by the left, if he is on the right side being honest or dishonest, or if he is the third guard being honest or dishonest, the math still works out perfectly. As you said, he is either honest or dishonest, not both.

If he is not the third guard, then his honesty or dishonesty plays into either the first or second scenario depending on who is coupled with him.

If he is the third guard, the other two guards force the 2nd scenario.

Maybe I should rephrase the question. The guards may only answer your question with da or ba. They cannot do anything else.

AK Juggs said:
You ask Guard #1 which path Guard #2 will point to if you ask him which is the correct path for the untold riches.
You ask Guard #2 which path Guard #3 will point to if you ask him which is the correct path for the untold riches.
You ask Guard #3 which path Guard #1 will point to if you ask him which is the correct path for the untold riches.

Let's say that left is the correct path.

If Guard #1 is the truth teller, he will tell you that Guard #2 will tell you to go the wrong way, thus the right path.

If Guard #1 is the liar, he will tell you that Guard #2 will tell you to go to the right path (if Guard #2 is the truth teller), and if he's the random one, he will not be able to point in either direction because he will not know which way Guard #2 will point.

If Guard #1 is the random one, Guard #3 will not be able to point in either direction because he will not know which way Guard #1 will point.

So no matter what, you'll be able to find the random one, and then go the opposite way the other two point.

You don't understand what they are saying.

Doombawkz · Mar 28, 2014

AK Juggs said:
You ask Guard #1 which path Guard #2 will point to if you ask him which is the correct path for the untold riches.
You ask Guard #2 which path Guard #3 will point to if you ask him which is the correct path for the untold riches.
You ask Guard #3 which path Guard #1 will point to if you ask him which is the correct path for the untold riches.

Let's say that left is the correct path.

If Guard #1 is the truth teller, he will tell you that Guard #2 will tell you to go the wrong way, thus the right path.

If Guard #1 is the liar, he will tell you that Guard #2 will tell you to go to the right path (if Guard #2 is the truth teller), and if he's the random one, he will not be able to point in either direction because he will not know which way Guard #2 will point.

If Guard #1 is the random one, Guard #3 will not be able to point in either direction because he will not know which way Guard #1 will point.

So no matter what, you'll be able to find the random one, and then go the opposite way the other two point.

So if Guard 1 tells you to go right, Guard 2 tells you to go left, and Guard 3 says he doesn't know, you go which way?

Because in the case that Guard 1 is random but a liar, and guard 2 is a liar, and guard 3 is honest...

Doombawkz · Mar 28, 2014

Pan1cMode said:
Maybe I should rephrase the question. The guards may only answer your question with da or ba. They cannot do anything else.

You don't understand what they are saying.

Let me re-edit my scenario to end up as the same result, uno momento.
(Also you said they could point in your rebuttal, so I'm guessing its out the window?)

Pan1cMode · Mar 28, 2014

Doombawkz said:
Let me re-edit my scenario to end up as the same result, uno momento.
(Also you said they could point in your rebuttal, so I'm guessing its out the window?)

No pointing, nor gesturing. Only saying Da or Ba.

Incredibly difficult logic problem.

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