Navigating the Path of Life: One Question to Find the Way

[Remnant]

Let us say, when a person dies. He comes to a path (purgitory) or so. He walks down this path and gets to a fork in the road like a "Y". One gnome guards each path, one gnome tells falsehoods, the other tells the truth. One of the paths leads to heaven and one of the paths leads to hell.
*You do not know which path is which, or which gnome is which*

&You only have 1 question to ask both gnomes, and if you ask one know a question, you have to ask the other gnome the exact same question- in turn that will use up your one question!

What is the answer(let us say there are no flaws).

 

[Remnant]

a rivision of the above post..
*what would be one question you could ask, that would alow you to know what path leads to heaven and what path leads to hell?***

 

[Jimmy Snyder]

Answer 1:

While pointing to one of the paths, Ask one gnome "If I asked you if this is the road to hell, would you say yes?"
In this case, you don't need the second gnome. It's a double question and the liar must lie twice to answer it, and the two lies cancel each other out.


Answer 2:

Point back to the road from which you came and ask one of the gnomes "Is this the road to hell?". Then you will know if the gnome is a liar and so you will know if the other gnome is a liar. Then point to one of the paths and ask the other gnome the same question.

eom

 

[Remnant]

sorry if i did not specify but you can only ask the gnomes one question and the question has to be asked to both of the gnomes.. so i have to discard your Answer 2, which was probably my fault from lack of explination. i came up with ask "what would the other gnome say is the path he guarding" and like your answer one. the gnomes would lie twice and that would cancel out. If one answered "hell" you would know the path he is on would be "heaven" vice-versa.

 

[Jimmy Snyder]

i came up with ask "what would the other gnome say is the path he guarding" and like your answer one. the gnomes would lie twice and that would cancel out. If one answered "hell" you would know the path he is on would be "heaven" vice-versa.

No, in your case there would be exactly one lie in the answer no matter which road and which gnome. That is why the road is to hell when the answer is heaven, and vice versa.

 

[Remnant]

oh yeah your right.. i apologize.. yeah so the gnome would have to tell the truth about lying and the other would have to lie about telling the truth.. .therefore not llie twice.. but yeah.. but would my answer be valid? or just disreguarded.. when i was in high school.. we got half the school trying to figure that out.. it took me 2 days and my friend 3 days to figure it out.. i just want to verify if there are any other possible answers. which in your case yes, for your answer 1

 

[Proggle]

How about...

If honest gnomes go to heaven and lying ones go to hell, which way do you deserve to go?
[/color]

And you only need one gnome!

 

[billiards]

"Are you a liar?"

 

[Evo]

"Are you a liar?"

They would both answer no.

How about...

If honest gnomes go to heaven and lying ones go to hell, which way do you deserve to go?
[/color]

And you only need one gnome!

They would both respond Heaven.

i came up with ask "what would the other gnome say is the path he guarding" and like your answer one. the gnomes would lie twice and that would cancel out. If one answered "hell" you would know the path he is on would be "heaven" vice-versa.

If you ask the lier what path the truthful one was on he'd say "hell" if he was in fact on the path to heaven or "heaven" if he was on the path to hell. Then when you asked the truthful one which path the lier is on he'd tell the truth and say either heaven or hell, depending on which ever was true, I don't see how this solves anything.

 

[Jimmy Snyder]

They would both respond Heaven.

No, they would respond by saying which way they would go, not by where their destination was. I.e. each would say "I would go this way" and point to the road to heaven.

If you ask the lier what path the truthful one was on he'd say "hell" if he was in fact on the path to heaven or "heaven" if he was on the path to hell. Then when you asked the truthful one which path the lier is on he'd tell the truth and say either heaven or hell, depending on which ever was true, I don't see how this solves anything.

I'm pretty sure that if you go through the cases, you will find that Remnant's solution works as well. Because of the nature of the answerers, you can be sure that the answer will contain one lie and one truth. I.e. exactly one lie. Put another way, the Truther will truthfully report the liar's lie and the liar will lie about the truther's truth.

 

[Proggle]

They would both respond Heaven.

The question was "which way" not "to where", so either one of them would point towards the way to heaven.

 

[Evo]

No, they would respond by saying which way they would go, not by where their destination was. I.e. each would say "I would go this way" and point to the road to heaven.

I'm pretty sure that if you go through the cases, you will find that Remnant's solution works as well. Because of the nature of the answerers, you can be sure that the answer will contain one lie and one truth. I.e. exactly one lie. Put another way, the Truther will truthfully report the liar's lie and the liar will lie about the truther's truth.

If honest gnomes go to heaven and lying ones go to hell, which way do you deserve to go?

This question is asking them to respond with an answer, not point in any direction.

I don't see anyone asking them to point.

 

[Proggle]

This question is asking them to respond with an answer, not point in any direction.

I don't see anyone asking them to point.

The question is still asking them to identify the way, not the final destination.

It's irrelevant if the answer is "I would take the right way", or a pointing finger in that direction.

 

[Jimmy Snyder]

This question is asking them to respond with an answer, not point in any direction.

I don't see anyone asking them to point.

True, but irrelevant. They still have to answer the question that was asked, either by pointing or by some other means. Perhaps I should have said they would point out the road to heaven.

 

[Jimmy Snyder]

I like the logic of Proggle's solution, and after all, it is a logic puzzle. But it does have a minor flaw. The danger is that the answer will be "I deserve to take the road to heaven.". This would not be helpful. It is easily fixed though, the logic can be preserved with a question like:

If honest gnomes go to heaven and lying ones go to hell, do you deserve to go to the left or to the right?

-or-

You could point to one of the roads and ask:
If honest gnomes go to heaven and lying ones go to hell, do you deserve to go this way?

-or-

If honest gnomes go to heaven and lying ones go to hell, do you deserve to take the road that you guard?

eom

 

[Rogerio]

One gnome guards each path, one gnome tells falsehoods, the other tells the truth. One of the paths leads to heaven and one of the paths leads to hell.

I would just say:

"If someone asked you whether your path leads to heaven, would you answer yes?"

And the answer would be true.

 

[Evo]

True, but irrelevant. They still have to answer the question that was asked, either by pointing or by some other means. Perhaps I should have said they would point out the road to heaven.

Since this is supposed to use logic, it would be illogical to assume that if you asked them a question that instead of answering they would merely point. If Spoc was here you would have gotten that Vulcan pinch thing he does.

Pointing works for me.

 

[Evo]

I would just say:

"If someone asked you whether your path leads to heaven, would you answer yes?"

And the answer would be true.

No, for example, if the lier is on the path to heaven, he would say no, so the truthful one would be on the path to hell and also say no. You've got 2 gnomes both saying no, so you have no idea which path they are on. Same if they were on opposite paths, they'd both say yes.

 

[Jimmy Snyder]

Pointing works for me.

Good, because now that I think about it, I don't see that they would answer any other way. Human (and gnoman?) communication travels down many roads too. But for the gnome to describe which road in words and not gestures seems to me an unusual response. Indeed, he may not speak at all, but just point. The last time Spock pinched me that way it was because I was more logical than he, and he was jealous.

 

[Rogerio]

No, for example, if the lier is on the path to heaven, he would say no, so the truthful one would be on the path to hell and also say no. You've got 2 gnomes both saying no, so you have no idea which path they are on. Same if they were on opposite paths, they'd both say yes.

?!
Think again:

"If someone asked you whether your path leads to heaven, would you answer yes?"If the lier was on the path to heaven, he would say "NO" to the person who asked the question.
So, he would say "YES" to me.

Forget the second gnome: ask once, and you will know the right path.

 

[Jimmy Snyder]

If the lier was on the path to heaven, he would say "NO" to the person who asked the question.
So, he would say "YES" to me.

This in answer to the question "What would the other gnome say is the path he guarding?"
Well this is convoluted isn't it. It's not a yes/no question. But let's edit the question to fit the discussion.

Would the other gnome say he is guarding the path to heaven?

Only one of the gnomes is a liar. If the liar was on the path to heaven, he would say no. But then the other gnome is not a liar so he faithfully reports the "no" of the lying gnome.
If on the other hand, the truther was on the path to heaven, he would say yes. But then the other gnome is a liar so he unfaithfully report "no". So no matter which gnome you ask, the one on the road to heaven will say no. And that's a good thing isn't it?

 

[Rogerio]

This in answer to the question "What would the other gnome say is the path he guarding?"
... So no matter which gnome you ask, the one on the road to heaven will say no.

Hi Jimmy,
Thats right, too!
If you use my question, the one on the road to heaven will say "yes".

 

[kaisxuans]

i say you just ask one of the grones which way was heaven. if he lied, run back and take the other path. easy. =)

 

[Rogerio]

i say you just ask one of the grones which way was heaven. if he lied, run back and take the other path. easy. =)

Really easy...:-)

(but how do you know who is the lier?)

 

[kaisxuans]

well, if you find yourself walking on fire then you know you are on the wrong path. but if you see angels, thank the grome!

 

[Jimmy Snyder]

If you use my question, the one on the road to heaven will say "yes".

Sorry Rogerio, I really messed things up. In my mind I was confusing your answer with Remnant's answer. Very embarrassing.

Your answer is good. But then you should have guessed that I would praise it as it matches my own answer in message #3 of this thread.

 

[Evo]

?!
Think again:

"If someone asked you whether your path leads to heaven, would you answer yes?"


If the lier was on the path to heaven, he would say "NO" to the person who asked the question.
So, he would say "YES" to me.

Forget the second gnome: ask once, and you will know the right path.

That doesn't make any sense.

 

[Evo]

This in answer to the question "What would the other gnome say is the path he guarding?"
Well this is convoluted isn't it. It's not a yes/no question. But let's edit the question to fit the discussion.

Would the other gnome say he is guarding the path to heaven?

Only one of the gnomes is a liar. If the liar was on the path to heaven, he would say no. But then the other gnome is not a liar so he faithfully reports the "no" of the lying gnome.
If on the other hand, the truther was on the path to heaven, he would say yes. But then the other gnome is a liar so he unfaithfully report "no". So no matter which gnome you ask, the one on the road to heaven will say no. And that's a good thing isn't it?

WHAT?

OK...

Two gnomes

Only one of the gnomes is a liar

One is on the path to heaven, the other is on the path to hell.

You don't know which gnome is the liar

You don't know which path either gnome is on

So...

Question - Would the other gnome say he is guarding the path to heaven?

If the liar was on the path to heaven, he would say no.

False, he would say yes, because he's lying. Remember, you are asking the lier if the truther on the path to hell would say he is guarding the path to heaven. The truther would say no, so the lier says yes.

But then the other gnome is not a liar so he faithfully reports the "no" of the lying gnome.

What? The truther, when asked if the other gnome would say he's guarding the path to heaven, would say no, because the lier is on the path to heaven, so the lier would say no.

So, you have one gnome saying no and one gnome saying yes, you don't know which is lying and you don't know which path they're on. At this point you know nothing.

This isn't hard to follow guys.

 

[Rogerio]

That doesn't make any sense.

I'm very sorry for you...

 

[Rogerio]

... it matches my own answer in message #3 of this thread.

I've just read it, and you are right, Jimmy : they are equivalents !

 

[Huckleberry]

No, for example, if the lier is on the path to heaven, he would say no, so the truthful one would be on the path to hell and also say no. You've got 2 gnomes both saying no, so you have no idea which path they are on. Same if they were on opposite paths, they'd both say yes.

There is one gnome standing in front of a door. The door leads to heaven or hell and the gnome always lies or always tells the truth. There is one question (and variations of it) that will determine all of the variables. (edit - not true. It only determines where the door leads. If the gnome is honest or a liar is undetermined, but irrelevent.)

So I ask him, "If I asked you where this door leads, would you tell me it leads to heaven?"

Ok, assume the door leads to heaven.
If someone asked the truthful gnome if the door went to heaven he would answer 'yes,' so his answer is 'yes.'
If someone asked the liar if his door leads to heaven he would answer 'no,' so his answer to me will be 'yes.'

In either case I can be sure that this is indeed the door to heaven. If I ask the same question and the answer is 'no' then I know the door leads to hell. The question isn't asking where the door leads. The question is asking what they would say if asked another question. In this logic argument two truthful statements combined is still a truthful statement, and two lies cancel each other out and become a truthful statement.

 

[kaisxuans]

There is one gnome standing in front of a door. The door leads to heaven or hell and the gnome always lies or always tells the truth. There is one question (and variations of it) that will determine all of the variables.

So I ask him, "If I asked you where this door leads, would you tell me it leads to heaven?"

Ok, assume the door leads to heaven.
If someone asked the truthful gnome if the door went to heaven he would answer 'yes,' so his answer is 'yes.'
If someone asked the liar if his door leads to heaven he would answer 'no,' so his answer to me will be 'yes.'

In either case I can be sure that this is indeed the door to heaven. If I ask the same question and the answer is 'no' then I know the door leads to hell. The question isn't asking where the door leads. The question is asking what they would say if asked another question. In this logic argument two truthful statements combined is still a truthful statement, and two lies cancel each other out and become a truthful statement.

there is a point there. so most likely, you will still go through thedoor right?

 

[Kittel Knight]

I would just say:
"If someone asked you whether your path leads to heaven, would you answer yes?"
And the answer would be true.

It is OK.

No, for example, if the lier is on the path to heaven, he would say no, so the truthful one would be on the path to hell and also say no.

Wrong.
According to your example, if someone had asked the liar gnome, the gnome would have answered "no" . So, that gnome would say "yes" to Rogerio.

BTW, this is a classical puzzle (google: liar truth teller).
Jimmysnyder and Rogerio are absolutely right.

 

[Kittel Knight]

...This isn't hard to follow guys.

I think so but... are you sure of that?

 

[Huckleberry]

there is a point there. so most likely, you will still go through thedoor right?

I didn't complete the comparison because I thought it was obvious.

Ok, assume the door leads to heaven.
If someone asked the truthful gnome if the door went to heaven he would answer 'yes,' so his answer is 'yes.'
If someone asked the liar if his door leads to heaven he would answer 'no,' so his answer to me will be 'yes.'

Ok, now assume the door leads to hell.
If someone asked the truthful gnome if the door went to heaven he would answer 'no,' so his answer is 'no.'
If someone asked the liar if his door leads to heaven he would answer 'yes,' so his answer to me will be 'no.'

The way the question is phrased it is irrelevant if the gnome is honest or if he is lying. Which door I would choose is also irrelevent, but at least I would be able to make an informed choice.

 

[Huckleberry]

I think the misunderstanding here is in the interpretation of the question.

"If I asked you where this door leads, would you tell me it leads to heaven?"

The question is not the same as "Does this door lead to heaven?" The original question is not asking directly where the door leads. It is asking what the gnome would say if asked another question. The lying gnome would lie if someone asked where his door led, and he would also lie to me about what he would say if someone asked him where his door led. So if his door led to heaven and someone asked him "Does this door lead to heaven?" then he would answer 'no.' If I ask him what his answer to that question would be then he would answer 'yes.' So in this scenario the answer to the original question, "If I asked you where this door leads, would you tell me it leads to heaven?" the answer is 'yes.'

In order to answer the question, the gnome must answer two questions. First he must determine what he would say if someone asked him where his door led. Then he must respond to the question asking him what he would say. The lying gnome would lie if asked where his door leads and would lie to me about his response. The lying gnome would be lying about a lie, and with the only options being 'yes' or 'no' his answer will be the truth.

Ofcourse, the honest gnome tells the truth no matter how many times he is asked a question. He would tell the truth if asked where his door leads and he would tell the truth if I asked him how he would answer that question. His answer will always be the truth because he doesn't contradict himself with lies.

So it is irrelevant if the gnomes are always honest or always lying.

 

[Huckleberry]

This in answer to the question "What would the other gnome say is the path he guarding?"
Well this is convoluted isn't it. It's not a yes/no question. But let's edit the question to fit the discussion.

Would the other gnome say he is guarding the path to heaven?

Only one of the gnomes is a liar. If the liar was on the path to heaven, he would say no. But then the other gnome is not a liar so he faithfully reports the "no" of the lying gnome.
If on the other hand, the truther was on the path to heaven, he would say yes. But then the other gnome is a liar so he unfaithfully report "no". So no matter which gnome you ask, the one on the road to heaven will say no. And that's a good thing isn't it?

WHAT?

OK...

Two gnomes

Only one of the gnomes is a liar

One is on the path to heaven, the other is on the path to hell.

You don't know which gnome is the liar

You don't know which path either gnome is on

So...

Question - Would the other gnome say he is guarding the path to heaven?

If the liar was on the path to heaven, he would say no.

False, he would say yes, because he's lying. Remember, you are asking the lier if the truther on the path to hell would say he is guarding the path to heaven. The truther would say no, so the lier says yes.

But then the other gnome is not a liar so he faithfully reports the "no" of the lying gnome.

What? The truther, when asked if the other gnome would say he's guarding the path to heaven, would say no, because the lier is on the path to heaven, so the lier would say no.

So, you have one gnome saying no and one gnome saying yes, you don't know which is lying and you don't know which path they're on. At this point you know nothing.

This isn't hard to follow guys.

You are right about how the gnomes would answer the question. Jimmy should be expecting his Vulcan death pinch any time now.

You are wrong that the information provided is meaningless. The way this question is phrased you can be sure the answer is a lie.

Question - Would the other gnome say he is guarding the path to heaven?
If the gnome you are asking is guarding the door to heaven,
truther = yes
liar = yes

If the gnome you are asking is guarding the door to hell,
truther = no
liar = no

yes = heaven
no = hell

edit - I think Jimmy was answering the question "Would the other gnome say you are guarding the path to heaven?" In that scenario the 'no' door would be heaven and the 'yes' door would be hell. The answer is still a lie because you are asking one gnome what the other would say.

 

[Evo]

Thank you Huck!

I was wrong about assuming the answer. Too many versions and not enough sleep, it would appear we were interpreting versions differently.

In the correct version, only one gnome would be asked and this would be the answer.

Answer: Ask if the other person would say that this is the right path?

Lets say the door is the right path
The truth person would say that the lier would say no.
The lier woud say that the truth person would say no.

Lets say the door is the wrong path.
The truth person would say the door yes.
The lier would say the truth person would say yes.

Do the opposite of what they say.

When Rogerio said the gnome would tell him yes after saying no. I took him literally to mean that the gnome verbally gave two answers "yes and no", which made no sense. What he meant was if the gnome said "no" Rogerio would know that "yes" was the correct answer. I *really* do need sleep.

 

[Astronuc]

This logic problem was in a Dr. Who (Tom Baker) episode.

 

[Huckleberry]

It was also in my favorite movie, 'Labyrinth.'

 

[Rogerio]

...
When Rogerio said the gnome would tell him yes after saying no. I took him literally to mean that the gnome verbally gave two answers "yes and no", which made no sense. What he meant was if the gnome said "no" Rogerio would know that "yes" was the correct answer.

It is wrong again.
What I meant is clearly the opposite - read carefully my first post:

Post #16
I would just say:
"If someone asked you whether your path leads to heaven, would you answer yes?"
And the answer would be true.

It doesn't matter which gnome I'm talking to.
If the gnome says "yes" to me, then I will know that "yes" is the correct answer.
And if the gnome says "no" to me, then I will know that "no" is the correct answer.

When I ask a gnome about what he would say to someone who (hypothetically) would have asked him, then, if he is a liar, he will lie twice, and will give me verbally the correct answer. And if he is the truth gnome, of course he will tell me the correct answer, too.

 

[belliott4488]

This is, indeed, an oldie but a goodie. I like to explain it (when asked) by using a truth table. I hope this will help anyone who's still unsure about the solution.

You pick Gnome A and ask him, "If I asked Gnome B if his path led to heaven, would he answer 'Yes'?"

Here are the possible answers, given the possible situations:

...Gnome.A...Gnome.B
....is.the...is.the
.....liar...liar
...------------------------
..Path.A.|...|...|
leads.to.|.."Yes"...|.."Yes"...|
..heaven.|...|...|
...|----------|-----------|
..Path.B.|...|...|
leads.to.|..."No"...|..."No"...|
..heaven.|...|...|
...------------------------

The "yes" answers both correspond to the case that Path A leads to heaven, as the "no" answers correspond to Path B leading to heaven, so you know exactly what to do.

Note that there are two binary unknowns, i.e. the path to heaven (Path A or Path B) and the identity of the liar (Gnome A or Gnome B), but with only one Y/N question, you can resolve only one binary unknown, so you have to sacrifice any chance to learn who's the liar, in favor of learning which path leads to heaven. You could devise a different question that would tell you who was the liar, but you wouldn't learn which path led to heaven.

 

[Remnant]

I like the logic of Proggle's solution, and after all, it is a logic puzzle. But it does have a minor flaw. The danger is that the answer will be "I deserve to take the road to heaven.". This would not be helpful. It is easily fixed though, the logic can be preserved with a question like:


If honest gnomes go to heaven and lying ones go to hell, do you deserve to go to the left or to the right?

If you ask that.. then they could reply "the right" or "the left" you would have no clue which path leads where.. or which one is false or true

 

[Proggle]

I like the logic of Proggle's solution, and after all, it is a logic puzzle. But it does have a minor flaw. The danger is that the answer will be "I deserve to take the road to heaven.". This would not be helpful. It is easily fixed though, the logic can be preserved with a question like:


If honest gnomes go to heaven and lying ones go to hell, do you deserve to go to the left or to the right?

If you ask that.. then they could reply "the right" or "the left" you would have no clue which path leads where.. or which one is false or true

No...

The honest gnome ("deserves" to go to heaven) will tell you on which side the path to heaven is. Suppose he says "I deserve to go left".

The lying gnome ("deserves" hell) would deserve the one on the right, but since he lies, he will tell you "I deserve to go left" as well.

In fact, you just need one gnome.

 

[DeLorean03]

I don't know about you guys, but I'd just look at both of them and ask:

"Gnomes, is there a fork in the road?"

One would say "yes" and one would say "no". Problem solved =).

Then I'd know which would be telling the truth and could ask "Is this the road to heaven?" to the one who answered "yes". From there depending on his answer, I'd know which road to take.

 

[Jimmy Snyder]

I don't know about you guys, but I'd just look at both of them and ask:

"Gnomes, is there a fork in the road?"

One would say "yes" and one would say "no". Problem solved =).

Then I'd know which would be telling the truth and could ask "Is this the road to heaven?" to the one who answered "yes". From there depending on his answer, I'd know which road to take.

That would be two questions.

 

[country boy]

You might ask "Why is one path heading up and the other heading down?"

 

[j0nis0n]

is there an answer? i doubt there is one.
it's like determining which of the statements is true and false:
The statement below is true.
The statement above is false.

 

[belliott4488]

is there an answer? i doubt there is one.
it's like determining which of the statements is true and false:
The statement below is true.
The statement above is false.

No, it's not like that example, which has no resolution. The puzzle in this thread does indeed have a completely logical solution, which has been stated repeatedly.

 

[gutti]

After much thought I came to this conclusion

You ask each gnome what the other gnome would say if you asked them which way was heaven, the lying gnome would point to hell so that you would walk there and the gnome that tells the truth would poin to hell because that is where the liar gnome would tell you to go so you go down the other path.