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   Fork in the Road III
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   Author  Topic: Fork in the Road III  (Read 5169 times)
James Fingas
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Fork in the Road III  
« on: Nov 14th, 2002, 8:25am »
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Fork in the Road III
 
Willywutang had been travelling for nearly two days when he came to the fork in the road. Willy knew it was inevitable, but he was prepared. Willy knew from the various puzzles he had solved that one path led to the City of Safety, and the other path led to the City of Cannibals. There should also be two people waiting at the intersection, who, willingly or not, would tell him how to get to the City of Safety ...
 
Slouched against a tree trunk near the intersection was a scruffy stranger. Willy stopped in his tracks and stared at the man, very worried. He was certain to be from one of the two cities, but which one? Where was the second person? The man returned Willy's gaze, saying nothing.
 
There was a tense silence, broken only when the mysterious stranger finally spoke up.  
 
"If you're wonderin' where the other guy is, he's home sick today. You see, he's from the City of Cannibals, and someone came through here with a bad cold. You're lucky that I'm here, from the City of Safety!"
 
Willy was too much on his guard to be reassured by the scruffy man's story. Perhaps it was true, and perhaps it wasn't. Willy also knew the rules about getting directions--he could ask just one yes/no question. Is there any way Willy could find out which path led to the City of Safety?
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Eric S
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Re: Fork in the Road III  
« Reply #1 on: Nov 15th, 2002, 8:42am »
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Copied from my solution to Fork in the Road I and II (it works on this one too).
 
You simply ask him:  
 
"What will the other guy tell me if I ask him if this path goes to the city of safety (point to a path)"  
 
If you are pointing to the City of Safety:  
 
1) You talk to the Truth Teller, he will say No because he knows the other guy will lie and say No.  
 
2) You talk to the Liar, he will say No because he knows the other guy will say Yes, but he is a liar so he will lie about that and say No.  
 
If you are pointing to the City of Cannibals  
 
1) You talk to the truth teller, he will say Yes because he knows the other guy will lie and say Yes this is the City of Safety  
 
2) You talk to the liar, he will say Yes because he knows the other guy will say No this is not the path to the city of safety, so he has to lie and say Yes.  
 
If he says No, you are pointing to the city of safety.
 
This solution works because it's essentially the same problem as Fork in the road with both of them present. This guy still knows of the other guy's existance, therefore he knows if he is a liar or a truth teller (city of safety or city of caniibals). So you can use the fact that he knows this (whether that guy is present or not), and get him to spit out the truth.
 
Hope i'm right Wink
 
Good twist to the riddle though.
 
I'm sure you were looking for a better answer though. I'll think about it some more (a question to ask him that doesn't involve the other guy).
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Pietro K.C.
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Re: Fork in the Road III  
« Reply #2 on: Nov 15th, 2002, 9:04am »
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Well, I was stumped for a while! Go figure. Unless I'm much mistaken, the solution is as follows.

  I haven't read any of the "Fork in the road" boards, because the first solution I ever came up with pretty much solves all of them, and I believe it solves this one as well. The thing to do is indicate one of the roads and ask, "would the other guy tell me this is the road to safety?" If he answers "yes", take the other road; if he answers "no", take the road you indicated.
 
  My solution is based on the fact that another guy exists, as the problem statement clearly says. Since the two guys are by assumption indistinguishable, it doesn't matter which one you ask the question to, and hence it doesn't matter if the other guy is there or not, as long as you can reference him.
 
  Also, you don't have to assume that each guy is from a different town; if there is no evidence of that, you can just ask, "would someone from the other city tell me this is the road to safety?" In fact, to get an answer, all you need is:
 
- the behavior of the person whom you ask the question to be consistent;
- the questionee to understand references to behavior opposite their own.

 
Dude! We were minutes apart!  Smiley Smiley Smiley
« Last Edit: Nov 15th, 2002, 9:06am by Pietro K.C. » IP Logged

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Re: Fork in the Road III  
« Reply #3 on: Nov 15th, 2002, 9:36am »
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I haven't been reading these threads either, but the answer I know to this type of old chestnut works still more generally:
 
Point to a road, fix your gaze on a native, and say, "If someone asked you whether this was the road to safety, what would you say?"
 
A literal-minded cannibal will dutifully lie about what it was he would say, thus ending up giving the same answer the truth-teller would. I've heard this solution objected to because a cannibal who is out to deceive you and eat you will say whatever he needs to to fool you; he won't be that literal-minded. But that's an objection to all the other solutions too; I don't see that this one is any worse.
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James Fingas
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Re: Fork in the Road III  
« Reply #4 on: Nov 15th, 2002, 1:41pm »
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Sorry guys, I screwed the puzzle statement up. What I was meaning to do was to eliminate the solutions from Fork in the Road I and Fork in the Road II (where you ask about the person's hometown, or about their partner's answer).
 
Looks like Tim has the answer I was looking for anyways, though. Good work! I was trying to illustrate here the third and simplest possible answer for Fork in the Road problems, where you just ask the guy what he would say if you were to ask him.
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Eric S
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Re: Fork in the Road III  
« Reply #5 on: Nov 15th, 2002, 9:27pm »
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I didn't think too hard about Tim's answer, but from what I see, it won't work:
 
Suppose the man is the cannibal.
 
If you point to the road of safety, he will say "No" since it is the road of safety and he needs to lie.
 
If You point to the road of cannibals, he will say "Yes", because it isn't the road of safety but he needs to lie.
 
Suppose the man is the truth teller.
 
If you point to the road of safety, he will say "Yes" since it is and he tells the truth.
 
If you point to the road of cannibals, he will say "No" because it is not the road of safety and he tells the truth.
 
Thus, the answers diverge i.e., a "Yes" or "No" could mean either road depending on which of the two says it (you don't know).
 
Ok, so the guy says Yes to your question. If he is the cannibal, you pointed to the road of cannibals. If he is the truth teller, you pointed to the road of safety. Now what?
 
And I haven't been here very long (posted maybe 5-6 posts), but I think you guys should give a little bit more credit to correct answers. Pietro K.C.'s answer is as much of a copy of my answer as there is without just simply cutting and pasting what I said.
 
Sorry ahead of time, but I'm not one of those people who knows a million different riddle answers. I pretty much think of these things when I see them. I don't just say.. oh I remember this one. So when I post an answer to a riddle, I worked hard on it.  
 
-Eric
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Eric S
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Re: Fork in the Road III  
« Reply #6 on: Nov 15th, 2002, 9:42pm »
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The more I think of it, I get what you mean.
 
If it were the road to safety, he would answer the question as No, but since he's a liar he has to change the answer to Yes.
 
I'm not that fond of the solution because it's using the fact that he lies twice, but either way good job on the logic behind it Smiley
 
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TimMann
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Re: Fork in the Road III  
« Reply #7 on: Nov 15th, 2002, 9:52pm »
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Eric, no one is denying you credit. Pietro probably posted his answer before seeing yours. The posts are only 22 minutes apart.
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Re: Fork in the Road III  
« Reply #8 on: Nov 16th, 2002, 7:16am »
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My bad guys. What a bad way to start off Sad
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Pietro K.C.
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Re: Fork in the Road III  
« Reply #9 on: Nov 16th, 2002, 9:18am »
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Sorry, Eric, you posted while I was writing up my soution, so I couldn't see it coming. You see, I write really slowly, be it e-mails or posts or whatever, in any language. Smiley
 
  It really seems like our answers are the same, though I admit I like TimMann's a lot better for its simplicity.
« Last Edit: Nov 16th, 2002, 9:24am by Pietro K.C. » IP Logged

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Re: Fork in the Road III  
« Reply #10 on: Nov 20th, 2002, 12:30pm »
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This puzzle is a lot simpler than you're all making it.  
The reason there's only one guy to ask is because he ate the other!  Thus, he's from the City of Cannibals and a liar.
 
Smiley
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Re: Fork in the Road III  
« Reply #11 on: Nov 20th, 2002, 10:31pm »
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Grin I love that answer.This is the first post ever and I am amazed at how much time one can take to think of such a simple question.
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Re: Fork in the Road III  
« Reply #12 on: Aug 8th, 2003, 7:07am »
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The obvious way to a solution is to bring up something that is will negate the liar's lie. The home city (since it changes with the answerer) seems to be the perfect way to do this.
 
Point down one roads leading onward and ask, "Are you from that-a-way"?  
 
If it is the cannibal talking, he will lie about his home and will give you an answer that is exactly the same as the City of Safety guy would.
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