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Topic: FORK IN THE ROAD I (Read 19634 times) |
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Greg
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The answer is "Where do you live?". You can ask either one and they will point ot he same direction. That's the way you would go.
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BNC
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Re: FORK IN THE ROAD I
« Reply #26 on: Jun 13th, 2003, 12:35pm » |
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Q: Where do you live?
A (a lie): Right here, under the tree.
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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Da_Stoph
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Re: FORK IN THE ROAD I
« Reply #27 on: Jul 4th, 2003, 4:01pm » |
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Since some of the people dont understand i want to reiterate that the true answer is that u must ask one of them something of this nature:
What will the other one say if i ask him is this road to the city of safety?
This way if you ask the truthful one he will tell u that the other will point towards city of cannibals since hes a liar.
And if you ask the liar he will also point u to the city of cannibals because he must lie about the fact that the other, the truthful one, will point to the city of safety.
and therefore u know to go in the opposite direction that either of them point u towards.
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rmsgrey
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Re: FORK IN THE ROAD I
« Reply #28 on: Jul 5th, 2003, 8:32am » |
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Actually, the answer I suspect the riddler was looking for is:
*points at one of the roads* "Do you live in that direction?"
This also avoids the problem of misinterpreted referential questions - what happens if the native thinks that your convoluted question is just a ritual form (like "Qu'est-ce que c'est" in french is literally "What is it that it is" but should be interpreted as "What's that")
Da_Stoph's "true" answer also works under the standard assumptions, but the additional asymmetry of home villages between liars and non-liars gives you a simpler line of attack in this case
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zero
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Re: FORK IN THE ROAD I
« Reply #29 on: Jul 12th, 2003, 4:18pm » |
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on Jul 4th, 2003, 4:01pm, Da_Stoph wrote:Since some of the people dont understand i want to reiterate that the true answer is that u must ask one of them something of this nature:
What will the other one say if i ask him is this road to the city of safety?
This way if you ask the truthful one he will tell u that the other will point towards city of cannibals since hes a liar.
And if you ask the liar he will also point u to the city of cannibals because he must lie about the fact that the other, the truthful one, will point to the city of safety.
and therefore u know to go in the opposite direction that either of them point u towards. |
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What will the other one say if i ask him is this road to the city of safety?
if your asking the truthful one he would say no
but if you ask the liar he could say i dont know or even yes
why you think i say yes?
where in the riddles does it say that the twins know that the other lies or the other tells the truth it saisYOU know not the brothers
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william wu
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Re: FORK IN THE ROAD I
« Reply #30 on: Oct 22nd, 2003, 7:56pm » |
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As a colleague pointed out recently, I think it's interesting to note that the liar in this classic problem actually isn't a very good liar, in that he has no intent of deceiving those who query him. He's just a bit flipper  If he actually had some element of deception in him, as usually connotated when one hears the word "liar", then the liar could induce any action on those who query him for advice.
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[ wu ] : http://wuriddles.com / http://forums.wuriddles.com
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Adam Duchesneau
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What...If there was only one person?
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towr
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Re: FORK IN THE ROAD I
« Reply #32 on: Oct 26th, 2003, 11:33pm » |
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If it's either one of the two that are there in this riddle, then you can use the exact same solution, since you only use a random one of the two now as well..
It wouldn't matter if there were twenty thousand of them either.
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James Fingas
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Re: FORK IN THE ROAD I
« Reply #33 on: Nov 17th, 2003, 11:47am » |
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on Oct 22nd, 2003, 7:56pm, william wu wrote:| As a colleague pointed out recently, I think it's interesting to note that the liar in this classic problem actually isn't a very good liar, in that he has no intent of deceiving those who query him. He's just a bit flipper If he actually had some element of deception in him, as usually connotated when one hears the word "liar", then the liar could induce any action on those who query him for advice. |
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But only if the questioner isn't wise to his tricks. If the questioner knows that there is a liar and a truth-teller, but that the lier will meta-lie (tell the most confusing thing), then the liar has in essence become a random-answerer (since there is no way of predicting the output). But then the problem is insoluble.
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Doc, I'm addicted to advice! What should I do?
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rmsgrey
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Re: FORK IN THE ROAD I
« Reply #34 on: Nov 20th, 2003, 7:40am » |
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If you're aiming to maximise your probability of reaching safety, then you can get .75 simply by asking and being trusting...
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James Fingas
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Re: FORK IN THE ROAD I
« Reply #35 on: Nov 20th, 2003, 9:54am » |
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on Nov 20th, 2003, 7:40am, rmsgrey wrote:| If you're aiming to maximise your probability of reaching safety, then you can get .75 simply by asking and being trusting... |
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But the meta-liar will know that's your strategy, and will tell you the wrong way. The problem with the meta-liar is that he knows whatever conclusion you would draw from his answer, and will adjust his answer so that your conclusion is wrong.
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rmsgrey
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Re: FORK IN THE ROAD I
« Reply #36 on: Nov 21st, 2003, 4:49am » |
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Good point!
Rethinking: the meta-liar's best strategy would appear to be that of giving the opposite answer to the one the honest native would give as that leaves you with a .5 probability of safety. Obviously this is optimal because with a probability less than .5 you merely invert your decision...
If there's more than one question allowed, then the meta-liar's strategy becomes more complicated, but I suspect that answering as though he were honest except for inverting any answers that distinguish the two roads turns out to be optimal.
Interestingly, if you have an honest man, an honest liar and a meta-liar present, with enough questions you're guaranteed to be able to find your way (3 seems to do it - ask each in turn which way home is then follow the majority)
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James Fingas
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Re: FORK IN THE ROAD I
« Reply #37 on: Nov 21st, 2003, 9:44am » |
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on Nov 21st, 2003, 4:49am, rmsgrey wrote:| Interestingly, if you have an honest man, an honest liar and a meta-liar present, with enough questions you're guaranteed to be able to find your way (3 seems to do it - ask each in turn which way home is then follow the majority) |
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Actually, two will do it.
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Sir Col
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Re: FORK IN THE ROAD I
« Reply #38 on: Mar 6th, 2004, 10:22am » |
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I suspect the solution to these types of problems is like the Holy Grail of puzzles.
If I'm a liar and someone asked me a question that would help them, then I'd just play stupid and tell a blatant lie: "I dunno?"
Unless you can be assured that the liar will co-operate by lying superficially and "honestly", then it's pretty much like the real world. You can at best ask a question which returns the desired answer with a high degree of probabilty, but never with certainty.
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hemorraged
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the question you can ask either of them is: "Will the other guy tell me that the City of Safety is on the left fork?"
depending on the answer received: if you get a "yes" then you should go right, if you get a "no" you should go left.
why? two cases:
1) the man you ask is the truth sayer,
if Safety Town is to the left, he will say "no"
else, he will say "yes"
2) the man you ask is the liar,
if Safety Town is to the left, he will say "no" (cause he has to lie)
else, he will say "yes"
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Bon BON
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Re: FORK IN THE ROAD I
« Reply #40 on: Jan 20th, 2005, 4:46pm » |
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all you ask both of them is what city are you from and both of them will be pointing toward the road of truth. its too simple to bee in the hard section.
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Icarus
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Re: FORK IN THE ROAD I
« Reply #41 on: Jan 20th, 2005, 7:01pm » |
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You are only allowed to ask one question of one person, so asking both is not an option. But since they both will give the same answer, you don't need to. Just choose one at random.
You are right about this one being particularly easy. And you will find some others in the Hard section that are even easier. As you yourself have noted, though, what is easy for one person can be hard for another. And what at first seems hard, you will occasionally discover afterwards really was not hard at all. This happened to William on some of the puzzles he placed here, and happens regularly to others.
Most of the problems here are considerably tougher, though. Since you found this one so easy, you might try looking at the other "Fork in the Road" problems (the Search function can find them for you - but be sure to check the "only one post per thread" box). There are several, and they get tougher. Once you have them figured out, try out the "Gods of Gibberland" puzzle. I promise, you'll find that it is hard enough for you!
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Sir Col
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Re: FORK IN THE ROAD I
« Reply #42 on: Jan 30th, 2005, 9:27am » |
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I think it is worthy of being placed in the hard section, as most "answers" to this are naive, as has been pointed out by many of our astute puzzlers. Quite simply there is no single sufficient question, and that, by painful deduction, is the surprising solution.
Even a cleverly designed question like, "Which of these two roads leads to your city?" could result in the liar replying wickedly, but entirely by the rules, "None of them!" 
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towr
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Re: FORK IN THE ROAD I
« Reply #43 on: Jan 30th, 2005, 10:10am » |
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You can limit which answers he can give. And if he doesn't use either of those answers he's simply not answering the question, in which case he's neither lying or telling the truth; so he must use one of the provided answers.
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Sir Col
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Re: FORK IN THE ROAD I
« Reply #44 on: Feb 3rd, 2005, 12:46am » |
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Give me an example that could be used for this problem.
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towr
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Re: FORK IN THE ROAD I
« Reply #45 on: Feb 3rd, 2005, 2:03am » |
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on Feb 3rd, 2005, 12:46am, Sir Col wrote:| Give me an example that could be used for this problem. |
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"One of these two roads, either the left or the right, leads to your city, which of the two is it?"
"Neither" isn't a valid answer to the question, since it conflicts with the assertion in the question that it is either the left or the right.
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| « Last Edit: Feb 3rd, 2005, 2:04am by towr » |
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Sir Col
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Re: FORK IN THE ROAD I
« Reply #46 on: Feb 3rd, 2005, 2:26am » |
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"I banged my head earlier and I have no idea who I am or where I come from." (blatant lie)
or simply
"I dunno?!"
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towr
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Re: FORK IN THE ROAD I
« Reply #47 on: Feb 3rd, 2005, 3:15am » |
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He's not answering the question then though, is he.
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Sir Col
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Re: FORK IN THE ROAD I
« Reply #48 on: Feb 3rd, 2005, 4:16am » |
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Just because you ask a question with two alternatives doesn't mean that it can be answered; for example, "Is it true or false that I like cabbage?"
However, if you were a liar and knew the answer, you would be lying by answering, "Dunno?!"
You have asked a question to which the would liar know the answer, so, according to his/her nature, he/she is lying by saying either of the two answers that I suggested.
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towr
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Re: FORK IN THE ROAD I
« Reply #49 on: Feb 3rd, 2005, 5:08am » |
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on Feb 3rd, 2005, 4:16am, Sir Col wrote:| Just because you ask a question with two alternatives doesn't mean that it can be answered; |
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True, but here you know it can.
Quote:| However, if you were a liar and knew the answer, you would be lying by answering, "Dunno?!" |
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No, you would not be answering. "Dunno" is equivalent to "I can't answer that". It quite literally leaves the question unanswered.
So if the person you ask is obliged to answer your question, he can only do so by giving either of the two options the question allows.
Quote:| You have asked a question to which the would liar know the answer, so, according to his/her nature, he/she is lying by saying either of the two answers that I suggested. |
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I disagree.
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