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

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Discussion Overview

The discussion revolves around a logic puzzle involving two gnomes, one who tells the truth and one who lies, guarding two paths—one leading to heaven and the other to hell. Participants explore various questions that could be posed to the gnomes to determine which path leads to heaven, while adhering to the constraint of asking one question to both gnomes.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest asking one gnome, "If I asked you if this is the road to hell, would you say yes?" to determine the correct path.
  • Others propose asking, "What would the other gnome say is the path he is guarding?" arguing that this would reveal the truth through the mechanism of double lies.
  • A participant introduces the question, "If honest gnomes go to heaven and lying ones go to hell, which way do you deserve to go?" suggesting it requires only one gnome.
  • Another participant suggests simply asking, "Are you a liar?" noting that both gnomes would answer "no."
  • Some participants debate the implications of the phrasing of questions, such as whether the gnomes would point to a path or simply answer verbally.
  • One participant critiques a proposed solution for potentially leading to ambiguous answers, suggesting alternative formulations to preserve the logic of the question.
  • There is discussion about the validity of various proposed questions and whether they would effectively lead to the correct path.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best question to ask the gnomes. Multiple competing views and interpretations of the logic puzzle remain, with various proposed solutions being debated and refined.

Contextual Notes

Some participants express uncertainty about the implications of their proposed questions, particularly regarding how the gnomes would interpret and respond to them. There are also concerns about the clarity of the questions and the potential for ambiguous answers.

Remnant
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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).
 
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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?***
 
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
 
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 explanation. 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.
 
Remnant said:
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.
 
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
 
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!
 
"Are you a liar?"
 
billiards said:
"Are you a liar?"
They would both answer no.

Proggle said:
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.

Remnant said:
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.
 
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  • #10
Evo said:
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.

Evo said:
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.
 
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  • #11
Evo said:
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.
 
  • #12
jimmysnyder said:
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.
 
  • #13
Evo said:
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.
 
  • #14
Evo said:
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.
 
  • #15
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
 
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  • #16
Remnant said:
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.
 
  • #17
jimmysnyder said:
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. :devil:

Pointing works for me.
 
  • #18
Rogerio said:
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.
 
  • #19
Evo said:
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.
 
  • #20
Evo said:
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.

:smile:
 
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  • #21
Rogerio said:
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?
 
  • #22
jimmysnyder said:
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".
:smile:
 
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  • #23
i say you just ask one of the grones which way was heaven. if he lied, run back and take the other path. easy. =)
 
  • #24
kaisxuans said:
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?)
 
  • #25
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!
 
  • #26
Rogerio said:
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.
 
  • #27
Rogerio said:
?!
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.

:smile:
That doesn't make any sense.
 
  • #28
jimmysnyder said:
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...
jimmy said:
Question - Would the other gnome say he is guarding the path to heaven?

jimmy said:
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.

jimmy said:
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.
 
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  • #29
Evo said:
That doesn't make any sense.

:cry:

I'm very sorry for you...
 
  • #30
jimmysnyder said:
... it matches my own answer in message #3 of this thread.

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

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