Knights and Knaves question












4












$begingroup$


You are on a land inhabited by Knights and Knaves. Knights will always tell the truth and knaves always lie.



You meet three inhabitants(A, B, and C), and ask how many of them are knaves. A answers so quietly, so you ask B what A had said. B says that A had said that exactly two of them were knaves. C says B is lying.



Is it possible to know what A is?
Further, what are B and C.










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  • $begingroup$
    Please don't change your question after someone has answered it. Now the answer references D, E, and F, and makes no sense. I'm editing the answer to match the revised question, but in the future it's best not to make changes that make the answers obsolete ... especially when the changes are superficial like this.
    $endgroup$
    – Rubio
    17 mins ago
















4












$begingroup$


You are on a land inhabited by Knights and Knaves. Knights will always tell the truth and knaves always lie.



You meet three inhabitants(A, B, and C), and ask how many of them are knaves. A answers so quietly, so you ask B what A had said. B says that A had said that exactly two of them were knaves. C says B is lying.



Is it possible to know what A is?
Further, what are B and C.










share|improve this question









New contributor




user58804 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$












  • $begingroup$
    Please don't change your question after someone has answered it. Now the answer references D, E, and F, and makes no sense. I'm editing the answer to match the revised question, but in the future it's best not to make changes that make the answers obsolete ... especially when the changes are superficial like this.
    $endgroup$
    – Rubio
    17 mins ago














4












4








4





$begingroup$


You are on a land inhabited by Knights and Knaves. Knights will always tell the truth and knaves always lie.



You meet three inhabitants(A, B, and C), and ask how many of them are knaves. A answers so quietly, so you ask B what A had said. B says that A had said that exactly two of them were knaves. C says B is lying.



Is it possible to know what A is?
Further, what are B and C.










share|improve this question









New contributor




user58804 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




You are on a land inhabited by Knights and Knaves. Knights will always tell the truth and knaves always lie.



You meet three inhabitants(A, B, and C), and ask how many of them are knaves. A answers so quietly, so you ask B what A had said. B says that A had said that exactly two of them were knaves. C says B is lying.



Is it possible to know what A is?
Further, what are B and C.







logical-deduction liars






share|improve this question









New contributor




user58804 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question









New contributor




user58804 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question








edited 55 mins ago







user58804













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asked 2 hours ago









user58804user58804

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New contributor




user58804 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor





user58804 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






user58804 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












  • $begingroup$
    Please don't change your question after someone has answered it. Now the answer references D, E, and F, and makes no sense. I'm editing the answer to match the revised question, but in the future it's best not to make changes that make the answers obsolete ... especially when the changes are superficial like this.
    $endgroup$
    – Rubio
    17 mins ago


















  • $begingroup$
    Please don't change your question after someone has answered it. Now the answer references D, E, and F, and makes no sense. I'm editing the answer to match the revised question, but in the future it's best not to make changes that make the answers obsolete ... especially when the changes are superficial like this.
    $endgroup$
    – Rubio
    17 mins ago
















$begingroup$
Please don't change your question after someone has answered it. Now the answer references D, E, and F, and makes no sense. I'm editing the answer to match the revised question, but in the future it's best not to make changes that make the answers obsolete ... especially when the changes are superficial like this.
$endgroup$
– Rubio
17 mins ago




$begingroup$
Please don't change your question after someone has answered it. Now the answer references D, E, and F, and makes no sense. I'm editing the answer to match the revised question, but in the future it's best not to make changes that make the answers obsolete ... especially when the changes are superficial like this.
$endgroup$
– Rubio
17 mins ago










1 Answer
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3












$begingroup$


It's not possible to know what A is.


C says B is lying. So either C is a knave and B is a knight or C is a knight and B is a knave. Therefore there is one knave among (B,C).


Assume A is a knave. Then there are 2 knaves and A would lie about it. Therefore B is lying about what A said, so A, B are knaves and C is a knight.


Assume A is a knight. Then there is only one knave and B is lying about what A said, so A, C are knights and B is a knave.


In both scenarios B is a knave and C is a knight. A could be either a knight or a knave.







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    1 Answer
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    1 Answer
    1






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    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    3












    $begingroup$


    It's not possible to know what A is.


    C says B is lying. So either C is a knave and B is a knight or C is a knight and B is a knave. Therefore there is one knave among (B,C).


    Assume A is a knave. Then there are 2 knaves and A would lie about it. Therefore B is lying about what A said, so A, B are knaves and C is a knight.


    Assume A is a knight. Then there is only one knave and B is lying about what A said, so A, C are knights and B is a knave.


    In both scenarios B is a knave and C is a knight. A could be either a knight or a knave.







    share|improve this answer











    $endgroup$


















      3












      $begingroup$


      It's not possible to know what A is.


      C says B is lying. So either C is a knave and B is a knight or C is a knight and B is a knave. Therefore there is one knave among (B,C).


      Assume A is a knave. Then there are 2 knaves and A would lie about it. Therefore B is lying about what A said, so A, B are knaves and C is a knight.


      Assume A is a knight. Then there is only one knave and B is lying about what A said, so A, C are knights and B is a knave.


      In both scenarios B is a knave and C is a knight. A could be either a knight or a knave.







      share|improve this answer











      $endgroup$
















        3












        3








        3





        $begingroup$


        It's not possible to know what A is.


        C says B is lying. So either C is a knave and B is a knight or C is a knight and B is a knave. Therefore there is one knave among (B,C).


        Assume A is a knave. Then there are 2 knaves and A would lie about it. Therefore B is lying about what A said, so A, B are knaves and C is a knight.


        Assume A is a knight. Then there is only one knave and B is lying about what A said, so A, C are knights and B is a knave.


        In both scenarios B is a knave and C is a knight. A could be either a knight or a knave.







        share|improve this answer











        $endgroup$




        It's not possible to know what A is.


        C says B is lying. So either C is a knave and B is a knight or C is a knight and B is a knave. Therefore there is one knave among (B,C).


        Assume A is a knave. Then there are 2 knaves and A would lie about it. Therefore B is lying about what A said, so A, B are knaves and C is a knight.


        Assume A is a knight. Then there is only one knave and B is lying about what A said, so A, C are knights and B is a knave.


        In both scenarios B is a knave and C is a knight. A could be either a knight or a knave.








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        share|improve this answer



        share|improve this answer








        edited 16 mins ago









        Rubio

        30.8k567189




        30.8k567189










        answered 2 hours ago









        JayJay

        2,8742922




        2,8742922






















            user58804 is a new contributor. Be nice, and check out our Code of Conduct.










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