[roolstar]

OK, I thought of this one myself, So I hope I will not find it somewhere on this Board!!

In the land of Knights, Commoners & Knaves:

The Knights can only say the truth

The Knaves can only lie

The Commoners can go either way

WHAT IS THE QUESTION THAT KNAVES CANNOT ANSWER?

& A follow-up question

WHAT IS THE QUESTION THAT KNIGHTS CANNOT ANSWER?

Have fun!

[roolstar]

Follow-up 3:

WHAT QUESTION CAN THE KNIGHT ANSWER IN 2 DIFFERENT WAYS?

Foolow-up 4:

WHAT QUESTION CAN THE KNAVE ANSWER IN 2 DIFFERENT WAYS?

WOW I'm on fire....

[roolstar]

Oh and YES OR NO answers only allowed!

[roolstar]

And if you want to be really smart, do not use paradoxes like:

Did the chiken come before the egg?

[bonanova]

Will your answer to this question be "Yes"?

Will your answer to this question be "No"?

... working on it ...

What two answers are permitted for questions in this riddle?

[unreality]

For bonanova's unsolved #3 the answer is obviously:

Ask a question, wait for two answers, then tape the Knave's mouth shut

[roolstar]

What two answers are permitted for questions in this riddle?

YES or NO...

In this case a YES answer and a NO answer can both be given by a Knight to the same question!

Will your answer to this question be "Yes"?

It looks like your questions in both cases [1] & [2] would work and would prevent a knave and a knight from answering.

In fact, your question in case [1] will force a commoner to be TRUTHFUL about his answer, since only a Knight can answer this question!

And your question in case [2] will do just the opposite!

Still they (your questions) may go against the NO PARADOXES condition set by the OP.

PARADOX means (to me at least) that there is no definite answer for a question (yet). And the question you asked a knave does not have a definite answer right now. The true answer will be determined by the answer itself...

So this got me thinking about 2 possible conditions:

C1- A person can only lie or be truthful only if he/she already knew the answer to the question! (It will show on the lie-detector machine)

or

C2- We determine if a person is lying by simply comparing his answer with reality and see if it portraits it! (It will not show on the lie-detector)

A lot of questions will fit C2 and even a lot of paradoxes:

Is the chicken before the egg?

Is the universe expanding?

Is 9827672763655662773 a prime number? (just an example)

Will it rain in an hour?

Is roolstar a genius? (Althought a definite answer exists, it's probably not known for the knave in question)

So in C2 and for your question (will your answer to this question be yes), the knave cannot answer and is considered all-knowing!

But according to C1, the knave can in fact answer in TWO WAYS! < Hey I may have found another answer for followup [4]!!!!

In fact: The knave knows exactly what his answer will be (let's say he WILL answer NO), by answering YES to the question, he just lied and it will show on the lie-detector! And by saying YES, he did NOT answer TRUTHFULLY the question: "WILL your answer to this question be YES?" , because in his mind his answer WILL be NO!!

And if we argue by saying that he said he will say YES and He did, we will be applying the C2 condition and not C1

So the answer I'm looking for fits the C1 condition for lying: a person can only lie or be truthful if he/she already knew the answer to the question!

Very small hint: The answer I was looking for in case [1] will help provide the answers for the rest of the cases!!! And has actually a definite answer!

My advice: Try to find a different answer for case [1]...

[roolstar]

For bonanova's unsolved #3 the answer is obviously:

Ask a question, wait for two answers, then tape the Knave's mouth shut

Nice try...

A bit violent though...

Do you ask a question, wait for him to answer then wait for him to say something else later on???

Or maybe you were only joking and I'm taking it a lot more seriously than intended?

[bonanova]

So it seems you're posing this problem:

[1] There is a Yes/No question Q1 whose known answer does not depend on the reply given when it's asked.

[2] There is a Yes/No question Q2 whose known answer does not depend on the reply given when it's asked.

[3] If you ask a Knave Q1, he cannot answer it.

[4] If you ask a Knight Q2, he cannot answer it.

[5] What are Q1 and Q2?

What we know about Knaves and Knights tells us that

If a Knave knows Q1's answer is Yes [No], he will say No [Yes].

If a Knight knows Q2's answer is Yes [No], he will say Yes [No].

I confess I don't see any room for a riddle here, and wait with interest to hear the answer.

[roolstar]

So it seems you're posing this problem:

[1] There is a Yes/No question Q1 whose known answer does not depend on the reply given when it's asked.

[2] There is a Yes/No question Q2 whose known answer does not depend on the reply given when it's asked.

[3] If you ask a Knave Q1, he cannot answer it.

[4] If you ask a Knight Q2, he cannot answer it.

[5] What are Q1 and Q2?

What we know about Knaves and Knights tells us that

If a Knave knows Q1's answer is Yes [No], he will say No [Yes].

If a Knight knows Q2's answer is Yes [No], he will say Yes [No].

I confess I don't see any room for a riddle here, and wait with interest to hear the answer.

You are right about all of the above.

remember that I started this thread during my thinking process in your puzzle "Four Knight and Knave problems". So if you want to give this another shot before spoiling the answer, try to trace back my thoughts there...

Only for case 1:

Just ask the KNAVE: What COULD a commoner say when asked if XXXXX?

XXXXX = anything you can think of (ex: 1+1 =2)

In fact a commoner CAN answer either YES or NO to any question and therefore the Knave cannot answer by a YES or a NO without saying the truth...

Remember that this is a puzzle I made up, just because I found it very interesting that there are some questions that cannot be answered and not because they will make people fall into a paradoxical situation...

I await your critique on the answer or your take at the rest of the cases anxiously...

Edited January 30, 2008 by roolstar

[roolstar]

One more thing...

The answer I posted under the spoiler just now works since the people in this land can only say YES or NO otherwise there's no point to this riddle since a KNAVE can answer "I don't care" to any question asked of him...

[bonanova]

I think the Knave is able to answer the question.

Here are two comments.

Just ask the KNAVE: What COULD a commoner say when asked if XXXXX?

XXXXX = anything you can think of (ex: 1+1 =2)

but even tho it's not a Yes/No question, the knave still has a knavish answer:

Hello Mr Knave, I have a question for you:

What COULD a commoner say if I were to ask him if 1+1=2?

The correct answer is: The commoner could answer with either a Yes or a No.

Mr. Knave would answer: The commoner could not answer with either a Yes or a No.

You want it to be a Yes/No question, but I think neither Yes nor No could be called the correct answer.

The tersest version of the correct answer I can think of is: Yes or No.

And that still gives Mr. Knave an answer: Neither Yes nor No.

Hello Mr. Knave, I have a Yes/No question for you:

If I were to ask a commoner if 1+1=2, could he answer with either a Yes or a No?

Now the correct answer is: Yes.

Mr. Knave would answer: No.

[roolstar]

I think the Knave is able to answer the question.

Here are two comments.

but even tho it's not a Yes/No question, the knave still has a knavish answer:

Hello Mr Knave, I have a question for you:

What COULD a commoner say if I were to ask him if 1+1=2?

The correct answer is: The commoner could answer with either a Yes or a No.

Mr. Knave would answer: The commoner could not answer with either a Yes or a No.

You want it to be a Yes/No question, but I think neither Yes nor No could be called the correct answer.

The tersest version of the correct answer I can think of is: Yes or No.

And that still gives Mr. Knave an answer: Neither Yes nor No.

Hello Mr. Knave, I have a Yes/No question for you:

If I were to ask a commoner if 1+1=2, could he answer with either a Yes or a No?

Now the correct answer is: Yes.

Mr. Knave would answer: No.

[roolstar]

You have a point there Bonanova, and the way I posted the question I have to agree...

Still

Dear Mr. Knave, what is one of the two answers (YES or NO) that a commoner can give if I asked him if 1 + 1 = 2?

Of course this can also be viewed as an essay question if we argue that the Knave can say: "A commoner cannot answer" or "I don't know"...

But I don't think we can do that.

In fact we can then consider all questions to have more than a YES or NO possibility with a Knave!

ME: What would a non-commoner from amongst B or C reply if I asked him if C is a commoner?

KNAVE: I don't know (AND HE DOES KNOW)

ME: Will your answer to this question be YES?

KNAVE: I will not answer your question (AND HE DID ANSWER)

And therefore, we have to review most of the answers to similar puzzles and add this mysterious parameter that will render it impossible to solve them.

Unless we add before every question: "Please answer by either yes or no, what will..."

[bonanova]

Dear Mr. Knave, what is one of the two answers (YES or NO) that a commoner can give if I asked him if 1 + 1 = 2?

I think that's still an essay question.

And his answer can still be: one of the two answers a commoner can give is neither yes nor no.

or equivalently, neither of the two answers he can give is yes or no.

or, one of the two answers he can give is not either yes or no.

In other words, you can invite him to choose from the two words yes and no, but he can decline to do so.

The statements above are responsive to the question, and are lies, and so they qualify as knave responses.

I think a yes/no question has the form: Is it true that _____ ?

In other words the yes/no answer affirms or denies the truth of a proposition.

A question like: what kind of an answer could a ___ give to such and such a question? asks for a statement or a phrase.

[Guest]

You have a point there Bonanova, and the way I posted the question I have to agree...

Still

Dear Mr. Knave, what is one of the two answers (YES or NO) that a commoner can give if I asked him if 1 + 1 = 2?

Of course this can also be viewed as an essay question if we argue that the Knave can say: "A commoner cannot answer" or "I don't know"...

But I don't think we can do that.

In fact we can then consider all questions to have more than a YES or NO possibility with a Knave!

ME: What would a non-commoner from amongst B or C reply if I asked him if C is a commoner?

KNAVE: I don't know (AND HE DOES KNOW)

ME: Will your answer to this question be YES?

KNAVE: I will not answer your question (AND HE DID ANSWER)

And therefore, we have to review most of the answers to similar puzzles and add this mysterious parameter that will render it impossible to solve them.

Unless we add before every question: "Please answer by either yes or no, what will..."

In my opinion, the knave is not answering the question. He is responding to it, but not answering it. I think it has generally been agreed upon with this type of riddle that the question will be answered to the best of the persons ability. Otherwise, the knight and knave could both answer, "I am a knight" to each and every question asked of them. There is a line in which a riddle or joke gets broken down too much. I've seen this line get passed many times, and while it is interesting conversation, I hope that people will not use the logic in this conversation to "answer" other riddles.

[Guest]

In addition...

You have to look at the meaning of a yes or no question. It is a question that can be answered with either an affirmation or a negation. So while "Are you a knight?" is a yes or no question, "What does Y-E-S spell?" is not. By the rules of the original question, you could not ask him "What COULD a commoner say if I were to ask him if 1+1=2?".

Going with this and possibly creating a tangent, are there any such yes-or-no questions that do not begin with (or reply upon) a form of the verb "to be".

"Is that the path of death?"

"Are you the knight?"

"Will you tell the truth?"

I realize that there are different ways of phrasing questions to try to get around this, but I think it clearly proves that "To be or not to be?" really is the question.

[roolstar]

In my opinion, the knave is not answering the question. He is responding to it, but not answering it. I think it has generally been agreed upon with this type of riddle that the question will be answered to the best of the persons ability. Otherwise, the knight and knave could both answer, "I am a knight" to each and every question asked of them. There is a line in which a riddle or joke gets broken down too much. I've seen this line get passed many times, and while it is interesting conversation, I hope that people will not use the logic in this conversation to "answer" other riddles.

Right!!

The last paragraph of my past spoiler: "And therefore, we have to review most of the answers to similar puzzles and add this mysterious parameter that will render it impossible to solve them."

I meant here that this last paragraph explains why we CANNOT use this logic, so I totally agree with your post.

And Bonanova, even if YES or NO are the possible answers to a question, this doesn't always make it a YES or NO question... And therefore my Solution doesn't work.

And with these conditions, I don't think we can find a non-paradoxical question that a Knave cannot answer...

Edited February 1, 2008 by roolstar