a logic puzzle

Yes, that's been discussed elsewhere in this thread. Unfortunately OP's description of the problem appears to have differed from the problem that he was probably referring to, being the one that Wanderer provided the answer to.

As you point out, it also contained the inherent problem that it would be possible to ask questions that the knight or knave didn't know the answers to, while still requiring them to give an answer.

The intended problem probably involved knights and knaves who would answer a yes/no question if they could determine what answer they should give, and not answer it otherwise.

Sylvia.

I think this problem has been discussed to death. But if I ever decide to ask anyone else this problem, I plan to make the rule that all questions must be answerable by yes or no, and if any of the people are asked a question that that do not know the answer to or which for some reason is unanswerable then they will behave like the randomizer and answer yes or no at random 50/50. It has already been shown several times now that the original problem is solvable with three questions but not with two questions with those rules.

Derek Holt.

or

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That's three questions assuming that they all know who they all are. Was there a solution in any fixed number of questions if they do not know the tribes of the other two? I don't think there was.

Derek Holt.

IMHO, the problem where the knight and knave don't answer questions they don't know the answer to has a more interesting 2 question solution.

Sylvia.

I don't think there can be. When they know, you can ask questions that distinguish a truth teller from a randomiser stuck on a run of truth. When they don't know you can't - because they can't either.

Hmm - that's not quite as convincing now I've written it down - after all, each of them has one bit of information you don't (what they are).

Nick wrote: ) Derek Holt writes: ) )> That's three questions assuming that they all know who they all are. )> Was there a solution in any fixed number of questions if they do not )> know the tribes of the other two? I don't think there was. ) ) I don't think there can be. When they know, you can ask questions that ) distinguish a truth teller from a randomiser stuck on a run of truth. ) When they don't know you can't - because they can't either. ) ) Hmm - that's not quite as convincing now I've written it down - after ) all, each of them has one bit of information you don't (what they are).

Well, no. Effectively the randomizer has no information to give. That is, he cannot convey any information to you through his answers.

To put it differently: A randomizer will still behave exactly the same if he believes he is a knight.

SaSW, Willem

On further reflection, I agree.

I can't tell if you're joking. But in case you're not, I used a bit of shorthand to convey that the guy's answer (which is either Yes or No) will point you in the correct direction.

Example (repasting my text which you shortened):

Question 1. Ask A "Does B tell the truth more often (per question) than C?"

Liar A will point to the randomizer as being more honest. Knight A will point to the randomizer as being more honest.

The problem I have with this variation is that it defies the "common sense" idea behind the puzzle. It doesn't seem correct that a knight, given a question he can't answer will basically choose to lie to you rather than remain quiet.

Did I read that we found a solution that worked in two questions if the knight and knave keep their mouths shut when they can't ascertain what a truthful yes/no answer would be?

Don't know about "we", but Wanderer posted a solution to that problem (indeed at the root of this subthread). At least, I believe it's a solution. I haven't gone through it in detail.

Sylvia.

dgates wrote: ) The problem I have with this variation is that it defies the "common ) sense" idea behind the puzzle. It doesn't seem correct that a knight, ) given a question he can't answer will basically choose to lie to you ) rather than remain quiet. ) ) Did I read that we found a solution that worked in two questions if ) the knight and knave keep their mouths shut when they can't ascertain ) what a truthful yes/no answer would be?

I didn't come across one but here's a go:

Ask Person 1 the following question: "What would Person 2 answer if I asked him if he is a Knight ?"

If the answer is silence, ask Person 1 the following question, else ask Person 2 the following question: "What would Person 3 answer if I asked him if he is a Knight ?"

Elegantly solved with versions of one question, if I do say so myself.

Details of how this works left to the reader.

SaSW, Willem

The puzzle contains the rule that the two questions cannot be asked of the same person.

Sylvia.

Sylvia Else wrote: ) Willem wrote: )> dgates wrote: )> ) The problem I have with this variation is that it defies the "common )> ) sense" idea behind the puzzle. It doesn't seem correct that a knight, )> ) given a question he can't answer will basically choose to lie to you )> ) rather than remain quiet. )> ) )> ) Did I read that we found a solution that worked in two questions if )> ) the knight and knave keep their mouths shut when they can't ascertain )> ) what a truthful yes/no answer would be? )> )> I didn't come across one but here's a go: )> )> Ask Person 1 the following question: )> "What would Person 2 answer if I asked him if he is a Knight ?" )> )> If the answer is silence, ask Person 1 the following question, )> else ask Person 2 the following question: )> "What would Person 3 answer if I asked him if he is a Knight ?" )> )> )> Elegantly solved with versions of one question, if I do say so myself. )> )> Details of how this works left to the reader. )> )> )> SaSW, Willem ) ) The puzzle contains the rule that the two questions cannot be asked of ) the same person.

Oh I had forgotten that. Slight amendment:

Ask Person 1 the following question: "What would Person 2 answer if I asked him if he is a Knight ?"

In case of silence, ask Person 3 the following question: "What would Person 1 answer if I asked him if he is a Knight ?"

Else ask Person 2 the following question: "What would Person 3 answer if I asked him if he is a Knight ?"

Better ?

SaSW, Willem

Gives silence if p2 is a randomizer, else yes if p1 is a knight, and no if p1 is a knave, and either yes or no if p1 is a randomizer. So the answer actually only tells you whether or not p2 is the randomizer.

Since silence implies p2 is the randomizer, this question yields yes if p3 is the knight, and no if p3 is the knave.

So we know that p2 is not the randomizer. Silence from p2 indicates that p3 is the randomizer. Unfortunately, we're out of questions, and we still don't know which way round p1 and p2 are.

Sylvia.

Sylvia Else wrote: ) Willem wrote: )> Oh I had forgotten that. Slight amendment: )> )> Ask Person 1 the following question: )> "What would Person 2 answer if I asked him if he is a Knight ?" ) ) Gives silence if p2 is a randomizer, else yes if p1 is a knight, and no ) if p1 is a knave, and either yes or no if p1 is a randomizer. So the ) answer actually only tells you whether or not p2 is the randomizer. ) )> In case of silence, ask Person 3 the following question: )> "What would Person 1 answer if I asked him if he is a Knight ?" ) ) Since silence implies p2 is the randomizer, this question yields yes if ) p3 is the knight, and no if p3 is the knave. ) )> )> Else ask Person 2 the following question: )> "What would Person 3 answer if I asked him if he is a Knight ?" ) ) So we know that p2 is not the randomizer. Silence from p2 indicates that ) p3 is the randomizer. Unfortunately, we're out of questions, and we ) still don't know which way round p1 and p2 are.

Look at question 1 again.

SaSW, Willem

Let's try that again.

If I ask a Knight whether a Knave would say he's a Knight - the Knave would say yes, so the Knight would say yes. If I ask a Knave whether a Knight would say that he's a Knight, the Knight would say yes, so the Knave would say no.

Considering the permuatations, R randomizer, T knighT, E knavE, and the resulting answers, ? = Y/N, - = no answer.

R T E ? Y (Q2 is to P2 about P3). R E T ? N ditto. T R E - N (Q2 is to P3 about P1). E R T - Y ditto. T E R N - (Q2 is to P2 about P3). E T R Y - ditto.

Yes, seems OK.

Sylvia.

Sylvia Else wrote: ) Willem wrote: )> Sylvia Else wrote: )> ) So we know that p2 is not the randomizer. Silence from p2 indicates that )> ) p3 is the randomizer. Unfortunately, we're out of questions, and we )> ) still don't know which way round p1 and p2 are. )> )> Look at question 1 again. ) ) Let's try that again.

I actually meant that quite literally. 'We don't know which way round p1 and p2 are':

Looking at question 1 (which was answered 'yes' or 'no'), with the additional information that p1 is not a randomizer, you can deduce if p1 is Knave or Knight.

SaSW, Willem

Yes, I know. But having reached the wrong conclusion once, I wanted to be sure I hadn't missed something else.

Sylvia.

with 6 possible arrangements and only two bits of information there is no way to identify all the people.