Thread:
A Final Logic Question
08-10-2021, 05:34 PM
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A Final Logic Question
This one is about knights and knaves (an island where all inhabitants are either knights or knaves- knights always answer truthfully, knaves always give false answers...you know the deal).
There is a pair of inhabitants on this island, A and B of unknown types (knight/knave). One day they were visited and interviewed by two different logicians from off the island, who were curious to find out what type A and B were. Here is what happened:
The first logician asked A "is it true that B once said you are a knave"? A answered yes or no (it is not given what he answered). Then the logician asked one of the two whether the other was a knave. He answered (yes or no). It is not given whether the logician could then tell what types they were.
The second logician asked A whether B once claimed they were both knaves. A answered (yes or no). Then he asked one of the two whether the other was a knave, and was answered (yes or no). It is not given whether the second logician could then tell what they were.
What is given, is that one of the logicians was able to deduce the types of A and B, and the other logician wasnt. Assume that each logician uses perfect logic (i.e. if a deduction was possible, he would deduce it correctly, if not possible, he would not deduce it).
THE QUESTION: what are A and B? And which logician was able to deduce what they were?*
*: the sneaky miscer might realize there are only 8 possible answers: 4 combinations of Knight/Knave for A,B x 2 combinations of the logicians deducing/not deducing. So there is a 1/8th chance of guessing this problem's answer by random chance. Thus an explanation is needed.
There is a pair of inhabitants on this island, A and B of unknown types (knight/knave). One day they were visited and interviewed by two different logicians from off the island, who were curious to find out what type A and B were. Here is what happened:
The first logician asked A "is it true that B once said you are a knave"? A answered yes or no (it is not given what he answered). Then the logician asked one of the two whether the other was a knave. He answered (yes or no). It is not given whether the logician could then tell what types they were.
The second logician asked A whether B once claimed they were both knaves. A answered (yes or no). Then he asked one of the two whether the other was a knave, and was answered (yes or no). It is not given whether the second logician could then tell what they were.
What is given, is that one of the logicians was able to deduce the types of A and B, and the other logician wasnt. Assume that each logician uses perfect logic (i.e. if a deduction was possible, he would deduce it correctly, if not possible, he would not deduce it).
THE QUESTION: what are A and B? And which logician was able to deduce what they were?*
*: the sneaky miscer might realize there are only 8 possible answers: 4 combinations of Knight/Knave for A,B x 2 combinations of the logicians deducing/not deducing. So there is a 1/8th chance of guessing this problem's answer by random chance. Thus an explanation is needed.
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08-10-2021, 05:39 PM
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Geez.
08-10-2021, 05:52 PM
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#3
08-10-2021, 06:04 PM
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Originally Posted By SuperHercules⏩
STRONG post content to my sig correlationI'd just kick him in the balls and ask if that hurt. If he says yes, he's the knight
Didn't read past the first sentence btw
Didn't read past the first sentence btw
@OP: I think the answer is that with God, all things are possible.
Would kick em in the nuts
08-10-2021, 06:10 PM
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08-10-2021, 06:23 PM
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Originally Posted By SuperHercules⏩
Hmm well if you did, you'd realizeyouthe reader arent even on the island interacting with A or B. You are just being told about what happened to two logicians who were there and their experience. So you cant just kick them in the balls. Although someone may wonder why thelogiciansdidnt just do this (or equivalently, ask "does 2+2=4?"). For whatever reason they didnt.....they just asked the questions given above.I'd just kick him in the balls and ask if that hurt. If he says yes, he's the knight
Didn't read past the first sentence btw
Didn't read past the first sentence btw
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08-10-2021, 06:41 PM
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Originally Posted By numberguy12⏩
If A said yes and was a knave, then it'd be impossible.The first logician asked A "is it true that B once said you are a knave"? A answered yes or no (it is not given what he answered). Then the logician asked one of the two whether the other was a knave. He answered (yes or no). It is not given whether the logician could then tell what types they were.
So, if A said yes, then he was a knight, and B was a knave.
If A said no, then both are knights or B is a knight and A is a knave
The second logician asked A whether B once claimed they were both knaves. A answered (yes or no). Then he asked one of the two whether the other was a knave, and was answered (yes or no). It is not given whether the second logician could then tell what they were.
If A said yes, then B is a knave and A is a knight or vice-versa.If A said no, then A is a knight and B is a knight or A is a knight and B is a knave.
So, the only certainty is the first one and A said yes, so A is a knight and B is a knave
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08-10-2021, 07:29 PM
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Originally Posted By mp83⏩
Reps for a srs, thought-out answer. I do not agree with it though.If A said yes and was a knave, then it'd be impossible.
So, if A said yes, then he was a knight, and B was a knave.
If A said no, then both are knights or B is a knight and A is a knave
If A said yes, then B is a knave and A is a knight or vice-versa.
If A said no, then A is a knight and B is a knight or A is a knight and B is a knave.
So, the only certainty is the first one and A said yes, so A is a knight and B is a knave
So, if A said yes, then he was a knight, and B was a knave.
If A said no, then both are knights or B is a knight and A is a knave
If A said yes, then B is a knave and A is a knight or vice-versa.
If A said no, then A is a knight and B is a knight or A is a knight and B is a knave.
So, the only certainty is the first one and A said yes, so A is a knight and B is a knave
Without getting into whether I agree with the particular statements, I do not see anywhere in the analysis the impact of the second question: "is the other a knave", which is relevant to the problem.
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08-10-2021, 07:32 PM
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#9
08-11-2021, 09:15 AM
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Originally Posted By mp83⏩
To dig deeper into this....what would A answer to the first logician's initial question if they were both knaves?If A said yes and was a knave, then it'd be impossible.
So, if A said yes, then he was a knight, and B was a knave.
If A said no, then both are knights or B is a knight and A is a knave
So, if A said yes, then he was a knight, and B was a knave.
If A said no, then both are knights or B is a knight and A is a knave
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08-17-2021, 08:16 AM
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Bump. This puzzle is unsolved and still open.
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10-07-2021, 11:44 PM
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This is tough and not sure if I am doing it right but I don't think I can take it further than this with my brain, it was fun though.
The only sure conclusion I can draw from the questions is that inhabitant if inhabitant B did claim 'we're both knaves' then inhabitant A would be a knight, and inhabitant B would be a knave. If inhabitant B was a knight, he would not be able to lie about them both being knaves. Inhabitant B can lie and say they are both knaves, but can only do this, if A is not a knave, otherwise it would be true. Knaves do not tell the truth.
This leads me to believe the only viable line of questions/answers to give you an answer with certainty are as follows.
If inhabitant A answers 'no' to the first question, it would confirm they are a knight with no other possible conclusions. (If he was a knave, he would not say 'no' as it would then imply it was actually claimed by inhabitant B, but as I mentioned earlier, they both cannot be knaves.) A 'yes' answer leaves too many possibilities.
We then need to use the second question to confirm. The only certain answer I can come to is a 'no' from either inhabitant A or B which has them both as knights, the rest leave too many variables.
My answer is that the second logician determined they were both knights, based on a 'no' from inhabitant A on the first question, and a 'no' from either of them on the second question.
I am certain I am missing something, but even if I get it at this point the time invested is probably beyond what was intended for the exercise. Thanks OP.
The only sure conclusion I can draw from the questions is that inhabitant if inhabitant B did claim 'we're both knaves' then inhabitant A would be a knight, and inhabitant B would be a knave. If inhabitant B was a knight, he would not be able to lie about them both being knaves. Inhabitant B can lie and say they are both knaves, but can only do this, if A is not a knave, otherwise it would be true. Knaves do not tell the truth.
This leads me to believe the only viable line of questions/answers to give you an answer with certainty are as follows.
If inhabitant A answers 'no' to the first question, it would confirm they are a knight with no other possible conclusions. (If he was a knave, he would not say 'no' as it would then imply it was actually claimed by inhabitant B, but as I mentioned earlier, they both cannot be knaves.) A 'yes' answer leaves too many possibilities.
We then need to use the second question to confirm. The only certain answer I can come to is a 'no' from either inhabitant A or B which has them both as knights, the rest leave too many variables.
My answer is that the second logician determined they were both knights, based on a 'no' from inhabitant A on the first question, and a 'no' from either of them on the second question.
I am certain I am missing something, but even if I get it at this point the time invested is probably beyond what was intended for the exercise. Thanks OP.
10-08-2021, 12:12 AM
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Originally Posted By Savux⏩
I agree with your very first conclusion that if B claimed they were both knaves, then A is a knight and B is a knave.This is tough and not sure if I am doing it right but I don't think I can take it further than this with my brain, it was fun though.
The only sure conclusion I can draw from the questions is that inhabitant if inhabitant B did claim 'we're both knaves' then inhabitant A would be a knight, and inhabitant B would be a knave. If inhabitant B was a knight, he would not be able to lie about them both being knaves. Inhabitant B can lie and say they are both knaves, but can only do this, if A is not a knave, otherwise it would be true. Knaves do not tell the truth.
This leads me to believe the only viable line of questions/answers to give you an answer with certainty are as follows.
If inhabitant A answers 'no' to the first question, it would confirm they are a knight with no other possible conclusions. (If he was a knave, he would not say 'no' as it would then imply it was actually claimed by inhabitant B, but as I mentioned earlier, they both cannot be knaves.) A 'yes' answer leaves too many possibilities.
We then need to use the second question to confirm. The only certain answer I can come to is a 'no' from either inhabitant A or B which has them both as knights, the rest leave too many variables.
My answer is that the second logician determined they were both knights, based on a 'no' from inhabitant A on the first question, and a 'no' from either of them on the second question.
I am certain I am missing something, but even if I get it at this point the time invested is probably beyond what was intended for the exercise. Thanks OP.
The only sure conclusion I can draw from the questions is that inhabitant if inhabitant B did claim 'we're both knaves' then inhabitant A would be a knight, and inhabitant B would be a knave. If inhabitant B was a knight, he would not be able to lie about them both being knaves. Inhabitant B can lie and say they are both knaves, but can only do this, if A is not a knave, otherwise it would be true. Knaves do not tell the truth.
This leads me to believe the only viable line of questions/answers to give you an answer with certainty are as follows.
If inhabitant A answers 'no' to the first question, it would confirm they are a knight with no other possible conclusions. (If he was a knave, he would not say 'no' as it would then imply it was actually claimed by inhabitant B, but as I mentioned earlier, they both cannot be knaves.) A 'yes' answer leaves too many possibilities.
We then need to use the second question to confirm. The only certain answer I can come to is a 'no' from either inhabitant A or B which has them both as knights, the rest leave too many variables.
My answer is that the second logician determined they were both knights, based on a 'no' from inhabitant A on the first question, and a 'no' from either of them on the second question.
I am certain I am missing something, but even if I get it at this point the time invested is probably beyond what was intended for the exercise. Thanks OP.
Now if Im reading your thought process correctly, you are only focusing on the second logician, and you are trying to argue that the Yes's and No's must be a certain way in order for him to be certain what A and B are. But what if Logician #2 is the one who couldnt figure it out, and Logician #1 was the one who could? Then the Yes's and No's would be given to Logician #2 such that he wouldnt know. The problem's given info says merely that one of the logicians was able to figure it out, and the other did not- we dont know which. It seems you have to figure out what's going on with the first logician's questions as well.
So I will not say anything about the final answer- could be wrong, could be right. I can say that it has not been proven. Repped for a thought out answer.
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10-08-2021, 12:35 AM
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Originally Posted By numberguy12⏩
I had thought about the first question, but I was unable to arrive at any conclusions from it and ultimately determined the answer would lie in the second logicians questions.I agree with your very first conclusion that if B claimed they were both knaves, then A is a knight and B is a knave.
Now if Im reading your thought process correctly, you are only focusing on the second logician, and you are trying to argue that the Yes's and No's must be a certain way in order for him to be certain what A and B are. But what if Logician #2 is the one who couldnt figure it out, and Logician #1 was the one who could? Then the Yes's and No's would be given to Logician #2 such that he wouldnt know. The problem's given info says merely that one of the logicians was able to figure it out, and the other did not- we dont know which. It seems you have to figure out what's going on with the first logician's questions as well.
So I will not say anything about the final answer- could be wrong, could be right. I can say that it has not been proven. Repped for a thought out answer.
Now if Im reading your thought process correctly, you are only focusing on the second logician, and you are trying to argue that the Yes's and No's must be a certain way in order for him to be certain what A and B are. But what if Logician #2 is the one who couldnt figure it out, and Logician #1 was the one who could? Then the Yes's and No's would be given to Logician #2 such that he wouldnt know. The problem's given info says merely that one of the logicians was able to figure it out, and the other did not- we dont know which. It seems you have to figure out what's going on with the first logician's questions as well.
So I will not say anything about the final answer- could be wrong, could be right. I can say that it has not been proven. Repped for a thought out answer.
I had started to speculate on whether either of the logicians would be able to compare the results of the other logicians answers, or if the second logician was able to base his questions on the first logicians questioning.
However, I figured I was just overthinking at that point, as it would all just be speculation (seemingly). Interested to learn the answer though eventually.
10-08-2021, 02:00 AM
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Originally Posted By Savux⏩
That's a good point, and nope no communication between the two logicians. Merely by the answers to the questions they personally asked, one was able to deduce A and B, and the other wasnt. And by wasnt, it is meant it wasntpossibleto deduce A and B from their answers, because if it were possible, then he would have deduced it, being a perfect logician. But of course the given info doesnt tell us which logician deduced and which one didnt, and thats one reason why the solution given above does not work.I had thought about the first question, but I was unable to arrive at any conclusions from it and ultimately determined the answer would lie in the second logicians questions.
I had started to speculate on whether either of the logicians would be able to compare the results of the other logicians answers, or if the second logician was able to base his questions on the first logicians questioning.
However, I figured I was just overthinking at that point, as it would all just be speculation (seemingly). Interested to learn the answer though eventually.
I had started to speculate on whether either of the logicians would be able to compare the results of the other logicians answers, or if the second logician was able to base his questions on the first logicians questioning.
However, I figured I was just overthinking at that point, as it would all just be speculation (seemingly). Interested to learn the answer though eventually.
The answer will eventually be given.
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10-08-2021, 02:07 AM
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10-08-2021, 02:15 AM
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Originally Posted By Spazzzzy⏩
What is your answer- which logician could deduce, and what are A and B?My Answer
The second question in each scenario: "Is the other a knave" is irrelevant to the solution as the answer is consistent in all outcomes i.e. the answer is always yes.
Statistician 1 does not get an outcome regardless of whether we assume one has claimed the other is a knave or not.
Has B claimed that you arebotha knave
Person A (knave) Yes
Person A (knight) No
The knave doesn't tell the truth so he would never claim that they are BOTH knaves.
Statistician 2 arrives at the correct solution.
The second question in each scenario: "Is the other a knave" is irrelevant to the solution as the answer is consistent in all outcomes i.e. the answer is always yes.
Statistician 1 does not get an outcome regardless of whether we assume one has claimed the other is a knave or not.
Has B claimed that you arebotha knave
Person A (knave) Yes
Person A (knight) No
The knave doesn't tell the truth so he would never claim that they are BOTH knaves.
Statistician 2 arrives at the correct solution.
In the first conclusion, why is it that they must always say yes to "is the other a knave"?
It is not proven here, but repped for a serious answer.
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10-08-2021, 03:03 AM
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Originally Posted By Spazzzzy⏩
Yep can be any of the four combinations of Knave Knight between A,B. So possibly both the same type.I didn't read OP properly sorry. I read it as one is a knight and one is a knave not the possibility that they could both be the same type.
Follow up questions:
Can we assume that the statement of "you are a knave" has been said.
Can we assume that the knave would say to the knight "we are both knaves" which is a lie (but the knave would never say they are a knave) which is telling the truth.
when you state the statistician asks ONE of the two, are we assuming question two can be posed to the same person who answered question 1 or is it always the other person
Follow up questions:
Can we assume that the statement of "you are a knave" has been said.
Can we assume that the knave would say to the knight "we are both knaves" which is a lie (but the knave would never say they are a knave) which is telling the truth.
when you state the statistician asks ONE of the two, are we assuming question two can be posed to the same person who answered question 1 or is it always the other person
I wont give out a ton of hints (the problem can definitely be solved as stated), but yes the second question could have been posed to either one: same person, the other person.....we dont know who it was posed to.
The point above with Savux, you were only considering logician 2, but what happens if both answers given to logician 1 are "no" (is this possible?)....what are the implications. To illustrate some of the nuance.
Wont be able to respond for awhile, but if anyone has a solution feel free to write it up
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10-08-2021, 04:30 AM
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Originally Posted By numberguy12⏩
Am I missing some rules here?This one is about knights and knaves (an island where all inhabitants are either knights or knaves- knights always answer truthfully, knaves always give false answers...you know the deal).
There is a pair of inhabitants on this island, A and B of unknown types (knight/knave). One day they were visited and interviewed by two different logicians from off the island, who were curious to find out what type A and B were. Here is what happened:
The first logician asked A"is it true that B once said you are a knave"?A answered yes or no (it is not given what he answered). Then the logician asked one of the two whether the other was a knave. He answered (yes or no). It is not given whether the logician could then tell what types they were.
The second logicianasked A whether B once claimed they were both knaves.
A answered (yes or no). Then he asked one of the two whether the other was a knave, and was answered (yes or no). It is not given whether the second logician could then tell what they were.
What is given, is that one of the logicians was able to deduce the types of A and B, and the other logician wasnt. Assume that each logician uses perfect logic (i.e. if a deduction was possible, he would deduce it correctly, if not possible, he would not deduce it).
THE QUESTION: what are A and B? And which logician was able to deduce what they were?*
*: the sneaky miscer might realize there are only 8 possible answers: 4 combinations of Knight/Knave for A,B x 2 combinations of the logicians deducing/not deducing. So there is a 1/8th chance of guessing this problem's answer by random chance. Thus an explanation is needed.
There is a pair of inhabitants on this island, A and B of unknown types (knight/knave). One day they were visited and interviewed by two different logicians from off the island, who were curious to find out what type A and B were. Here is what happened:
The first logician asked A"is it true that B once said you are a knave"?A answered yes or no (it is not given what he answered). Then the logician asked one of the two whether the other was a knave. He answered (yes or no). It is not given whether the logician could then tell what types they were.
The second logicianasked A whether B once claimed they were both knaves.
A answered (yes or no). Then he asked one of the two whether the other was a knave, and was answered (yes or no). It is not given whether the second logician could then tell what they were.
What is given, is that one of the logicians was able to deduce the types of A and B, and the other logician wasnt. Assume that each logician uses perfect logic (i.e. if a deduction was possible, he would deduce it correctly, if not possible, he would not deduce it).
THE QUESTION: what are A and B? And which logician was able to deduce what they were?*
*: the sneaky miscer might realize there are only 8 possible answers: 4 combinations of Knight/Knave for A,B x 2 combinations of the logicians deducing/not deducing. So there is a 1/8th chance of guessing this problem's answer by random chance. Thus an explanation is needed.
10-08-2021, 08:55 AM
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Originally Posted By capowt⏩
I dont know what is meant by rules, by I can assure you the problem is solvable as statedAm I missing some rules here?
Originally Posted By Spazzzzy⏩
This will not work. One thing to keep in mind is the reader, as well as the logician that is able to deduce, can determine what A and B are- that's required in the answer.My Correct Answer Having Read the Question Properly
So I think I have the right thought process here:
KnaveKnave
KnaveKnight
KnightKnave
KnightKnight
Has the statement occurred
Yes
No
Is the other a knave
Asking person 1 again
Asking person 2
----------------------------------------------------
KnaveKnave Yes | No No
KnaveKnight No Yes | Yes Yes
KnightKnave Yes No | Yes Yes
KnightKnight No | No No
-----------------------------------------------------
Statistician 2
Assuming the knave would not say they are both knaves because despite the statement of them both being knaves is a lie, the knave would not tell the truth to begin with thus would never admit they are a knave.
KnaveKnave
KnaveKnight
KnightKnave
KnightKnight
Has the other claimed you are both knaves:
KnaveKnave Yes (the statement never occurred)
KnaveKnight Yes (the statement never occurred)
KnightKnave No (knave did not admit to being a knave)
KnightKnight No (the statement never occured)
Is the other person a knave
KnaveKnave No
KnaveKnight Yes
KnightKnave Yes
KnightKnight No
Double up of answers cannot determine
------------------------------------------------------------------------------------------------
Statistician 1 arrives at correct answer
KnaveKnave Yes | No No
KnaveKnight No Yes | Yes Yes
KnightKnave Yes No | Yes Yes
KnightKnight No | No No
Stating yes to question 1 while no to question 2 means two knaves
Stating yes/no to question 1 whilst stating yes to question two means knave knight
Stating no to question 1 whilst stating no to question two means two knights
There we go cheers.
So I think I have the right thought process here:
KnaveKnave
KnaveKnight
KnightKnave
KnightKnight
Has the statement occurred
Yes
No
Is the other a knave
Asking person 1 again
Asking person 2
----------------------------------------------------
KnaveKnave Yes | No No
KnaveKnight No Yes | Yes Yes
KnightKnave Yes No | Yes Yes
KnightKnight No | No No
-----------------------------------------------------
Statistician 2
Assuming the knave would not say they are both knaves because despite the statement of them both being knaves is a lie, the knave would not tell the truth to begin with thus would never admit they are a knave.
KnaveKnave
KnaveKnight
KnightKnave
KnightKnight
Has the other claimed you are both knaves:
KnaveKnave Yes (the statement never occurred)
KnaveKnight Yes (the statement never occurred)
KnightKnave No (knave did not admit to being a knave)
KnightKnight No (the statement never occured)
Is the other person a knave
KnaveKnave No
KnaveKnight Yes
KnightKnave Yes
KnightKnight No
Double up of answers cannot determine
------------------------------------------------------------------------------------------------
Statistician 1 arrives at correct answer
KnaveKnave Yes | No No
KnaveKnight No Yes | Yes Yes
KnightKnave Yes No | Yes Yes
KnightKnight No | No No
Stating yes to question 1 while no to question 2 means two knaves
Stating yes/no to question 1 whilst stating yes to question two means knave knight
Stating no to question 1 whilst stating no to question two means two knights
There we go cheers.
As for the knave saying "we are both knaves" if the other is a knight, yes he can absolutely say this: because it's false. And knaves give false statements. Picture the knave uttering it as two successive statements,
Knave: "I am a knave"
Knave: "He is a knave"
The knavecantsay it this way, it's impossible. A knave cannot utter a true statement, and his first statement here would be true.
But a knave, with the other being a knight, could certainly say it in this way:
Knave: "We are both knaves"
Now the knave is uttering just a single statement, which happens to be false, which is fine since it's a knave.
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10-08-2021, 09:28 AM
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#21
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Originally Posted By numberguy12⏩
The second logician can tell what they are.This one is about knights and knaves (an island where all inhabitants are either knights or knaves- knights always answer truthfully, knaves always give false answers...you know the deal).
There is a pair of inhabitants on this island, A and B of unknown types (knight/knave). One day they were visited and interviewed by two different logicians from off the island, who were curious to find out what type A and B were. Here is what happened:
The first logician asked A "is it true that B once said you are a knave"? A answered yes or no (it is not given what he answered). Then the logician asked one of the two whether the other was a knave. He answered (yes or no). It is not given whether the logician could then tell what types they were.
The second logician asked A whether B once claimed they were both knaves. A answered (yes or no). Then he asked one of the two whether the other was a knave, and was answered (yes or no). It is not given whether the second logician could then tell what they were.
What is given, is that one of the logicians was able to deduce the types of A and B, and the other logician wasnt. Assume that each logician uses perfect logic (i.e. if a deduction was possible, he would deduce it correctly, if not possible, he would not deduce it).
THE QUESTION: what are A and B? And which logician was able to deduce what they were?*
*: the sneaky miscer might realize there are only 8 possible answers: 4 combinations of Knight/Knave for A,B x 2 combinations of the logicians deducing/not deducing. So there is a 1/8th chance of guessing this problem's answer by random chance. Thus an explanation is needed.
There is a pair of inhabitants on this island, A and B of unknown types (knight/knave). One day they were visited and interviewed by two different logicians from off the island, who were curious to find out what type A and B were. Here is what happened:
The first logician asked A "is it true that B once said you are a knave"? A answered yes or no (it is not given what he answered). Then the logician asked one of the two whether the other was a knave. He answered (yes or no). It is not given whether the logician could then tell what types they were.
The second logician asked A whether B once claimed they were both knaves. A answered (yes or no). Then he asked one of the two whether the other was a knave, and was answered (yes or no). It is not given whether the second logician could then tell what they were.
What is given, is that one of the logicians was able to deduce the types of A and B, and the other logician wasnt. Assume that each logician uses perfect logic (i.e. if a deduction was possible, he would deduce it correctly, if not possible, he would not deduce it).
THE QUESTION: what are A and B? And which logician was able to deduce what they were?*
*: the sneaky miscer might realize there are only 8 possible answers: 4 combinations of Knight/Knave for A,B x 2 combinations of the logicians deducing/not deducing. So there is a 1/8th chance of guessing this problem's answer by random chance. Thus an explanation is needed.
A knave can never claim he is a knave because that would be the truth. A knight can never claim he is a knave because that would be a lie. Therefore, edit:B can never have claimed that A and B are both knaves. --> this is wrong, my bad
Thus, if A says yes B did claim they are both knaves, then A is lying and is a knave. If A says no to the same question, then A is telling the truth and he is a knight.
Once it is determined whether A is a knight or knave, the second logician can ask A if B is a knight or knave. If A is a knave, then B is the opposite of what A says and if A is a knight then B is whatever A says.
edit: not sure how I can tell which is which though, still thinking on that
edit2: ignore my answer, B could say they are both knaves but as long as one of them is not it would be a lie, so technically a knave could answer yes to that
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10-08-2021, 09:44 AM
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#22
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Ok I got it.
Logician 1 asks A if B said he was a knave.
Then logician 1 can verify A's answer by asking B if A is a knave. Since B cannot change his answer, we will know if A was telling the truth based on how B answers.
If A was telling the truth, then A is a knight else a knave.
Once we know what A is, we will know what B is based on whether B truthfully or untruthfully tells us what A is.
I still don't know which is which though.
Logician 1 asks A if B said he was a knave.
Then logician 1 can verify A's answer by asking B if A is a knave. Since B cannot change his answer, we will know if A was telling the truth based on how B answers.
If A was telling the truth, then A is a knight else a knave.
Once we know what A is, we will know what B is based on whether B truthfully or untruthfully tells us what A is.
I still don't know which is which though.
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10-08-2021, 10:07 AM
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#23
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logician # 2 Asked a knight(a) if b ever said they were both knaves, a says no, then asks a again if the other (b) is a knave and says no. From this and the other variables logician 2 can deduct that both a and b are knights.
Impossible for logician #1 to deduct who is who.
Impossible for logician #1 to deduct who is who.
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10-08-2021, 10:20 AM
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#24
10-08-2021, 10:42 AM
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#25
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Originally Posted By Spazzzzy⏩
Negative. Logician 1 can't come to an accurate conclusion with the questions being asked, logician 2 can.This is the most obvious answer and works in both questions, so it can't be correct and is also in working out above which OP said doesn't work lol.
If you ask a knight in Q1 if the other has called you a knave he will say No. If you ask A or B if the other is a knave he will answer no.
Two no's in both mean you're talking to Knights for sure, but the answer is only available in one solution so can't be correct.
If you ask a knight in Q1 if the other has called you a knave he will say No. If you ask A or B if the other is a knave he will answer no.
Two no's in both mean you're talking to Knights for sure, but the answer is only available in one solution so can't be correct.
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10-08-2021, 10:53 AM
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#26
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Originally Posted By l2ambo⏩
What if both answers were "no" to Logician 1. What would he conclude....anything?Negative. Logician 1 can't come to an accurate conclusion with the questions being asked, logician 2 can.
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10-08-2021, 10:55 AM
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#27
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Originally Posted By numberguy12⏩
You can go through every single variable with logician #1 and he will not draw an accurate conclusion as to what types they both are. Correct?What if both answers were "no" to Logician 1. What would he conclude....anything?
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10-08-2021, 10:57 AM
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#28
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Originally Posted By l2ambo⏩
see post 26 and tell me where I'm wrongYou can go through every single variable with logician #1 and he will not draw an accurate conclusion as to what types they both are. Correct?
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10-08-2021, 10:57 AM
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#29
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Originally Posted By l2ambo⏩
Is there any other combination of Knave/Knight for A,B besides Knight-Knight that results in a "no" answer to both of Logician 1's questions? If so, what?You can go through every single variable with logician #1 and he will not draw an accurate conclusion. Correct?
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10-08-2021, 10:59 AM
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#30
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Originally Posted By numberguy12⏩
Bruh, did i get the answer right in my first post in the most simple way possible, yes or no?Is there any other combination of Knave/Knight for A,B besides Knight-Knight that results in a "no" answer to both of Logician 1's questions?
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