The Riddle of the Twin Paths

Hera Ledro

Hera Ledro

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How do you solve this riddle?

You are leaving your home village for the first time to visit an old friend in the next town. You're walking down the path when you come to a fork in the road. Standing at the fork are two men. You ask them directions on which way to go.

The left man says, "You can only ask one of us for directions. One of us is tells naught but lies."

The right man says, "The other tells naught but truth. You may ask one of us directions, but you must first decide who to trust. To decide this, you can only ask ONE question."

You stand there at the crossroads, confused. What question do you ask?
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I propose the solution is simple: ask them to define the truth.

Since the lieteller can only tell lies, he will identify the truth as a lie, which we know to be false; a value cannot be itself and its negative at the same time outside of advanced quantum physics. Therefore, now that we know who to trust, we know who to ask for directions.

Here is the mathematical proof:

Let truth = x

x =/= -x by its Fundamental Trait (x cannot equal negative x)

Let Truthteller = y
Let Lieteller = z

Y can only tell things which = x, while z can only tell things which = -x
We ask what does x equal? Recall that by its Fundamental Trait, x =/= -x

Since y can only say things which = x, he will therefore identify x as equalling x. Conversely, z can only say things which = -x, thereby identifying x = -x.

We know that x =/= -x, so we now know that y is the truthteller. Before now, we weren't aware exactly who was y, but we are able to discover it through this.

QED
 
Aye, which is where the simplicity of the solution is: You ask something that you already know the answer to. It's easy to know who to trust, then.
 
*ahem*

You're using one of your assumptions as the conclusion of your proof.

You say "let y = TruthTeller", and yet you claim as your conclusion that very point. Why bother with the rest of the proof if you've already established your desired conclusion?

A good try, though. :awesome:
 
Justin said:
You say "let y = TruthTeller", and yet you claim as your conclusion that very point. Why bother with the rest of the proof if you've already established your desired conclusion?

A good try, though. :awesome:
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Aye, but we don't know which one is Y. That's what we're trying to identify. We're just assigning variables to the identities themselves, not to the people. Also, I display that by saying:

Before now, we weren't aware exactly who was y, but we are able to discover it through this.
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So I do account for that.

Jackie said:
But then that uses up your only question, and you're no further forward. :monster:
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It's not the only question, though; just the question you use to determine who is trustworthy.

The right man says, "The other tells naught but truth. You may ask one of us directions, but you must first decide who to trust. To decide this, you can only ask ONE question."
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In other words, 2 questions: one to decide who to trust, one to find out directions.
 
The left man says, "You can only ask one of us for directions. One of us is tells naught but lies."

The right man says, "The other tells naught but truth. You may ask one of us directions, but you must first decide who to trust. To decide this, you can only ask ONE question."

The right man could be telling a lie and the truth would be that you have only one question entirely.
 
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And in that case, it's easy enough to leave, come back later and try again, but you'll still know who to ask :P

I see your point though; that one bit could eff you up real good.
 
What you do is ask either man which town he is from. They will both point you in the same direction, so you know which town is down which path.
 
But that assumes that they're from different towns, and that there is only two more towns nearby. Nowhere does it give their origins nor any evidence of there being only one town around.
 
Well I suppose in that case it depends how you've heard the riddle.

The easiest way is to go home, phone your friend, and ask them for directions.
 
So you're saying you would ask them "What is truth?" and the one who says responds with "truth" is the Truth Teller?

The fact that they're likely not going to respond in terms of one-word answers or even variables kind of throws a wrench in this one, unless you're going to define "x=truth" when you ask them, and require they respond in that same fashion. :monster:
 
If I was visiting a friend from another town across the riverbank or whatever it is, I know where he lives, and I don't need to ask for either one of their directions. Additionally, to know which town to go to is to know which direction to go. It wasn't stated that one path leads down to a dark road of death and the other leads to the town where your friend lives, so I say neither one.
 
I would ask one of them what the other man would say if I asked him which path led to the next town. The truth-teller would say the wrong path. The liar would also say the wrong path, since he would say the opposite of what the truth-teller would say. Then I follow the other path.

x = right path
-x = wrong path

when cross-referencing the men:

(x)(-x) = -x

So I go the other way and choose x.
 
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Justin said:
So you're saying you would ask them "What is truth?" and the one who says responds with "truth" is the Truth Teller?

The fact that they're likely not going to respond in terms of one-word answers or even variables kind of throws a wrench in this one, unless you're going to define "x=truth" when you ask them, and require they respond in that same fashion. :monster:
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Aye, but if they beat around the bush, it's easy enough to tell them to do it in a single phrase. And no matter how much you pretty up one phrase, no matter how long it gets, it's easy to identify its underlying meaning. We intuitively know that truth cannot equal lie, or else its fundamental identity would be violated. Unless they harbour differing views on the identity of truth as compared to us (which, if we're to go by their statements, they do not), then we can find out who the truthteller is.

The key, in essence, is to ask them to define something you both know to be true. It doesn't have to be the truth specifically, but it has to be something of general knowledge. The same thing would work if you asked them which way you came from; the liar would have to point somewhere that you didn't come from, whereas the truthteller would have to point from where you came from. Since you know where you came from (unless you're incredibly lost), you know then who to trust.
 
I would ask them how many paths there were.
Then the one that tells the truth gives the correct number,
while the liar doesn't.
 
I'm sure there are a few holes in my logic, but I came to the conclusion that neither of them are telling the truth.

The left man says, "You can only ask one of us for directions. One of us is tells naught but lies."

The right man says, "The other tells naught but truth. You may ask one of us directions, but you must first decide who to trust. To decide this, you can only ask ONE question."
Click to expand...
The statement "one person tells nothing but lies" can mean one of two things. Either one person tells lies or both tell lies.

Now, if only one person tells lies, that would mean the right man is the liar. Because the left man would be telling the truth (that one of them is a liar) so therefore he can't be the liar if there is only one liar.

However, if there are two liars. The left man would technically not be telling the complete truth if he was to say "one person only tells lies". Likewise, he is not telling a complete lie if he is saying that "one person only tells lies". Therefore it is possible for both of them to be lying and both of them to be telling the truth.

But, both of them cannot be telling the truth because then the left man would be lying in saying that "one person always lies."

From this point there are two options, if one person is lying it is the right man and it is possible that they are both lying.

Here is how the second statement: "The other tells naught but the truth" can be interpreted. If the right man is telling the truth; it can mean that either one person is telling the truth or both are. But as I pointed out above; both cannot be telling the truth because the left man would be lying in saying that "One of us tells nothing but lies".

If only the left man is telling the truth, then that would mean the right man is the liar. But the right man would be telling the truth in saying that "one person always speaks the truth" so there is a contradiction here.

If the right man is the only person telling the truth; that would mean that the left person is lying, but there is another contradiction when he says "one person always lies" (because he would be telling the truth if there was only one liar). Therefore, the only way for the left man to still be lying is if both people are liars. If both people are liars the left man would not be telling the complete truth if he said that "one person always lies" and the right man would be lying when he says "one person is telling the truth".


So I wouldn't trust either of them and I'd probably just call my friend for directions :monster:
 
Seed said:
I would ask them how many paths there were.
Then the one that tells the truth gives the correct number,
while the liar doesn't.
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Seed just pwned this without algebra. Nice. And people are still going on why? :wtf: It's obvious Seed solved the riddle.
:horsebeat:
 
Lol, It took me a few days thinking about it.
Trying to figure out the trick they had going on.
Then when I was taking a hot bath, all naked and stuff, it hit me!
Naked baths, ftw.
 
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