Your decision to change the second question depending on the first is shown above, either it starts with T or it starts with F, those are the 2 bases for the choices for the second question.
and 6 permutations of the inhabitants.
KNI KNA RAN KNI RAN KNA KNA KNI RAN KNA RAN KNI RAN KNI KNA RAN KNA KNI
so it's impossible to align the possible answers to the possible inhabitants.
But, Mark said try 3 questions, so it should be easy.
If one allows 'can't respond' as a response, there's the "Is your answer to this question going to be no?" route. The knight can't answer that one, but the other two can. Then "Is your answer to this question going to be yes?" to pick out the knave. Whoever's left is the randomizer. That's 5 questions tops.
With yes or no as only possible answers, the existance of the randomizer person makes it impossible to solve (two questions, each only to one person) unless a rather large number of questions are allowed in order to deduce whom that randomizer is. Now if a question can be asked to all three at once, then....maybe the randomizer can be eliminated ("are you a knight?" and "are you a knave?" would give that possibility - but no more than that.
Hmmm..the answer would be unknowable because the listeners would not know *what* the question might be (eg: are you a knight-->Y, are you a knave-->N would follow what you say, BUT are you a randomizer-->may or may not be the same; so does not follow AFAIK).
Is that right? What are the liar's rules for when he doesn't know the answer? If the liar says "I don't know," or "I can't be sure enough to answer," then isn't he telling the truth?
This is a tricky topic, but it feels like a liar could safely answer either "Yes" or "No" in a clear, authoritative voice and feel confident that he is lying to you.
Sure, but you can fix that easily enough with "If I asked you and B whether 2+2=4, would you both give the same answer?"
However, I'm still not sure how a knave could best "lie" when asked that about himself and the randomizer. It wouldn't be a lie to say "I don't know," or "I can't answer that."
That's three answers, which violates the rule by assuming that more than one person will answer a question addressed to a single person: "You are permitted 2 questions, each question addressed to a single (not both the same) person, and must determine their identities."
Reading this, I suddenly remember that the last time we did a problem with a "randomizer-type" character, we found this slightly easier way to phrase a question that would get a similar outcome. Something like:
Ask A: Does B tell the truth more often than C? (for the sake of ease of reading, imagine that you say "Point to the guy who tells the truth more, B or C.")
When A's a knave, he points to the Randomizer. When A's a knight, he points to the Randomizer. When A's a Randomizer, he might point to anyone.
Still, you can now identify whoever A *didn't* point at as being "Consistent," and go from there.
Q1 to P1 - If you are the knave, then is P2 the randomizer, else if you are the knight, then is P3 the randomizer, else do you like eggs?
If P1 is the knave, and P2 is the randomizer, then answers no -> P3 not randomizer. and P2 is not the randomizer, then answers yes -> P2 not randomizer.
If P1 is the knight and P3 is the randomizer, then answers yes -> P2 not randomizer. and P3 is not the randomizer, then answers no -> P3 not randomizer.
If P1 is the randomizer, then neither P2 nor P3 is the randomizer anyway.
So a yes answer implies that P2 is not the randomizer, and a no answer implies that P3 is not the randomizer, which is some information. This despite the fact that the question may have been asked of the randomizer.
Thus asking a question can yield information even if you don't know whether the answer comes from a randomizer. It yields no information if you know that you're asking it of a randomizer.
Having the randomizer in the group certainly destroys some of the potential information obtainable, but three questions would normally be enough to distinguish betweeen 8 alternatives, and we need to deal with only six. Maybe the randomizer doesn't destroy enough information to prevent a solution.
It doesn't violate that rule. You ask the question once, to one person, who gives one of the three possible answers listed above. Then you ask it to one other person. Like this:
You ask A: "What is the largest currently known prime number?" A says "12". You ask B: "What is the largest currently known prime number?" B says "no".
So A is the knave, B is the randomiser, and C is the knight.
No, that's not true. There have been several solutions using three questions. For example: Here are three questions:
"If I asked you whether the second person was the randomizer, would you answer 'yes'?"
"If I asked you whether you are a knight, would you answer 'yes'"?
"If I asked you whether the first person was the randomizer, would you answer 'yes'?
Ask the first person the first question. If he answers "yes", then ask the third person the last two questions. If he answers "no", ask the second person the last two questions.
Nope: if P2 is the randomizer, then he'd answer either yes or no randomly. That is what the randomizer does, you can't trust his answer, half the time it is going to be wrong.
Nope: if P3 is the randomizer, then he'd answer either yes or no randomly. That is what the randomizer does, you can't trust his answer, half the time it is going to be wrong.
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