A Knight or a Knave stood at a fork in the road

Question

A competent logician was traveling home down an unfamiliar road. As he approached a fork heading in two different directions, he noticed a lone figure standing directly between the two routes. The person was dressed in a full suit of armor, holding a sword.

As the logician got closer, he recognized the stranger as one of the accursed twins that he had encountered previously at another crossroads. With them being identical he could not tell which twin stood before him, the one who always spoke the truth or the one who could only ever lie.

Being familiar with the brothers, he approached and waved.

“Hello sir! I believe we’ve met before, do you remember me?”

The man looked at the logician, but did not say anything.

“Would I be correct in assuming that you are the knightly brother who always tells the truth?”

The brother continued to stare at the logician, offering no indication of an answer. The logician wasn’t sure if he had heard the question.

“Are you the knight, sir?”

“Yes, I’m the truth-telling brother,” came the courteous reply.

“You’re not the knave are you?”

“I am not,” the stranger responded immediately. It occurred to the logician that if he were, that was hardly the correct question to ask.

Considering that there was no one else around, he decided it would be best to attempt to deduce which twin this was, so that he could find the correct way to get home.

“Sir, do you know the correct way to go to get to town?”

The armored man did not respond to the question.

“I say, if I asked you for the correct route to take to get to town, would you point the way?”

“Yes, of course I would,” he replied graciously.

“Excellent! Which way is it?”

Again the man simply stared blankly at him.

“Do you have troubling hearing me?”

No reply was forthcoming.

“Will you please give me the answers I seek?”

“Yes,” the stranger repeated.

The logician started to get annoyed. This person could clearly answer his questions, but with him deciding to answer some questions and not others he could not be sure whether he could correctly identify which twin he was.

“Which way should I take to get to town?”

Again the brother did not say a word.

“Do I take the road to my left to get to town?” The man said nothing.

“Do you have some sort of issue with responding to my questions?”

“No, of course not!” Came his ready reply.

“Very well, do I take the road to my right to get to town?” No response.

The logician threw his hands up in frustration “Argh! Will you please just tell me what I want to know?”

“I will,” the man before him intoned.

“You say that, but then you do not respond to my questions! You say you’re a knight, but you do not have any honor… if only your brother were here as well then this would be much easier!”

As he watched, the man before him burst into tears, which took the logician aback. In deciding whether this person was a liar or a truth-teller, he had momentarily forgotten that he was a human.

“I'm ever so sorry my friend, is your brother ok?” the logician ventured.

The sobbing man looked up at him, his eyes pleading. No words were said, but the logician suddenly thought he understood the predicament this person was in, and what was causing him to only answer certain questions.

“Is the lying twin ok?” He asked.

The brother before him shook his head. “No, he’s not.”

With his suspicions confirmed, the logician sat with the brother for a while to comfort him. He then asked one last question of the twin, which he knew would be answered, and then the logician headed home down the left fork.

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For full points, one must answer:

• What was the predicament the twin was in, causing him to be unable to answer all of the questions asked?

• What question did the logician finally ask to find the correct route home?

• Which twin could it have been that he had been talking to?

Answer 1

He's avoiding certain questions

if the knight and knave would give different answers to them, thus trivializing the process of working out which is which. In his brother's absence, the illusion is much harder to maintain.

To get home, then:

The standard question should work: 'What would your twin have said if I asked whether the route to the right was safe?'

The twin is:

The knight. I'm not 100% sure on this, admittedly, but clearly neither twin is 'ok' - one is missing, and the other is deeply upset by their absence. "No, he's not" is the closest thing to an unambiguously true answer that we've seen either of the two. The rest of the puzzle is unaffected by their identity (edited in response to comment from OP)

Answer 2

This chap appears to be

A superposition of both Knight and Knave. He only answers if both Knight and Knave would give the same answer.

So I believe the question is

If I asked you, does the road on the left lead to town, would you respond affirmatively.

The only question I'm questioning is

"Is the lying twin ok?" getting a response of No. My guess is that whichever brother is not present is in a lot of trouble, so the Knight part thinks the Knave is screwed, but the Knave part thinks the Knave is ok?

Answer 3

Let's give this a go

He seems to only answer questions that are clearly about him. Therefor asking him if his brother is ok will be ignored, but asking him if the liar is ok will get an answer which also means that he is the liar.
The fact that he is the liar is also strongly suggested by the fact that he always insist that there are no problems, and that he will tell him what he wants yet he clearly has a problem and doesn't tell him what he wants. The trick would be to ask him a question about him that will lead you to town.
Such as : Will you say yes if I ask you if the left path is the right one? (then reverse then answer since he is the liar.)

Answer 4

None of the answers so far seem to have it fully right, and OP seems to have missed some things as well. So here's my answer.

What was the predicament the twin was in, causing him to be unable to answer all of the questions asked?

His brother was missing, dead, or otherwise out of commission. Though I don't see a reason for this to make it impossible for him to answer, that seems to be the premise.

What question did the logician finally ask to find the correct route home?

If your brother was here and able to answer, which would he say was the correct route?

Which twin could it have been that he had been talking to?

Because he claimed he would answer the way when asked and then would not, it could only have been the liar.

Some problems:

"Would I be correct in assuming that you are the knightly brother who always tells the truth?" and "Are you the knight, sir?" are essentially the same question. So there's not a consistent logic applied to what questions would or would not be answered. (Not only those which both would answer the same as suggested) Many of the questions posed would have easily identified the liar or truth-teller if they were both there, so not answering them because one was missing doesn't really have the desired effect.