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#19
Oct507, 06:18 PM

P: 2,179




#20
Oct507, 07:26 PM

P: 403

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. 


#21
Oct507, 08:16 PM

P: 2,179

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
Oct507, 08:24 PM

P: 403

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


#23
Oct507, 08:29 PM

P: 105

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
Oct507, 08:32 PM

P: 403

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


#25
Oct507, 08:45 PM

P: 105

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
Oct507, 09:12 PM

P: 2,179

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. 


#28
Oct507, 10:21 PM

Mentor
P: 26,523

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... 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. 


#29
Oct507, 10:43 PM

P: 403

I'm very sorry for you... 


#30
Oct507, 10:50 PM

P: 403




#31
Oct607, 12:57 AM

P: 606

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. 


#32
Oct607, 01:05 AM

P: 105




#33
Oct607, 01:20 AM

P: 106

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. 


#34
Oct607, 01:29 AM

P: 106




#35
Oct607, 01:57 AM

P: 606

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 irrelevent 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. 


#36
Oct607, 03:02 AM

P: 606

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. 


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