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Three knights or knaves, three different hair colors


Knights , Knaves and Spies - Part 1Knights , Knaves and Spies - Part 2Knights and Knaves : Liar , Liar - How many are you?Knights, Knaves and NormalsKnights, Knaves and Normals - the tough oneWhat color is the drummer's hair?Island of Knights, Knaves and SpiesLiars, truth-tellers and jokers






.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty
margin-bottom:0;

.everyonelovesstackoverflowposition:absolute;height:1px;width:1px;opacity:0;top:0;left:0;pointer-events:none;








7














$begingroup$


In a group of three people (A, B and C), everyone has a different hair color (blond, black or brown, not necessarily in this order) and everyone may be either a knight (always telling the truth) or a knave (always lying).
This is what they say.



  • Blond-haired person: "C has brown hair".

  • Black-haired person: "C is a knave".

  • Brown-haired person: "A and B are knights".

Determine the hair color of C.










share|improve this question










$endgroup$














  • $begingroup$
    A tiny little doubt - According to your question, is it that they all are knights or all are knaves. or one knight and the others knaves and so on.
    $endgroup$
    – Ak19
    May 19 at 11:55







  • 1




    $begingroup$
    @Ak19 Each of them can be either a knight or a knave - they don't have to be all of the same kind.
    $endgroup$
    – Maiaux
    May 19 at 11:56










  • $begingroup$
    @Ak19 - In fact, they cannot all be the same kind by the second question. If they're all knaves or all knights, the black-haired person could not say that "C is a knave".
    $endgroup$
    – David Hammen
    May 19 at 16:10

















7














$begingroup$


In a group of three people (A, B and C), everyone has a different hair color (blond, black or brown, not necessarily in this order) and everyone may be either a knight (always telling the truth) or a knave (always lying).
This is what they say.



  • Blond-haired person: "C has brown hair".

  • Black-haired person: "C is a knave".

  • Brown-haired person: "A and B are knights".

Determine the hair color of C.










share|improve this question










$endgroup$














  • $begingroup$
    A tiny little doubt - According to your question, is it that they all are knights or all are knaves. or one knight and the others knaves and so on.
    $endgroup$
    – Ak19
    May 19 at 11:55







  • 1




    $begingroup$
    @Ak19 Each of them can be either a knight or a knave - they don't have to be all of the same kind.
    $endgroup$
    – Maiaux
    May 19 at 11:56










  • $begingroup$
    @Ak19 - In fact, they cannot all be the same kind by the second question. If they're all knaves or all knights, the black-haired person could not say that "C is a knave".
    $endgroup$
    – David Hammen
    May 19 at 16:10













7












7








7





$begingroup$


In a group of three people (A, B and C), everyone has a different hair color (blond, black or brown, not necessarily in this order) and everyone may be either a knight (always telling the truth) or a knave (always lying).
This is what they say.



  • Blond-haired person: "C has brown hair".

  • Black-haired person: "C is a knave".

  • Brown-haired person: "A and B are knights".

Determine the hair color of C.










share|improve this question










$endgroup$




In a group of three people (A, B and C), everyone has a different hair color (blond, black or brown, not necessarily in this order) and everyone may be either a knight (always telling the truth) or a knave (always lying).
This is what they say.



  • Blond-haired person: "C has brown hair".

  • Black-haired person: "C is a knave".

  • Brown-haired person: "A and B are knights".

Determine the hair color of C.







logical-deduction liars






share|improve this question














share|improve this question











share|improve this question




share|improve this question










asked May 19 at 11:47









MaiauxMaiaux

4782 silver badges7 bronze badges




4782 silver badges7 bronze badges














  • $begingroup$
    A tiny little doubt - According to your question, is it that they all are knights or all are knaves. or one knight and the others knaves and so on.
    $endgroup$
    – Ak19
    May 19 at 11:55







  • 1




    $begingroup$
    @Ak19 Each of them can be either a knight or a knave - they don't have to be all of the same kind.
    $endgroup$
    – Maiaux
    May 19 at 11:56










  • $begingroup$
    @Ak19 - In fact, they cannot all be the same kind by the second question. If they're all knaves or all knights, the black-haired person could not say that "C is a knave".
    $endgroup$
    – David Hammen
    May 19 at 16:10
















  • $begingroup$
    A tiny little doubt - According to your question, is it that they all are knights or all are knaves. or one knight and the others knaves and so on.
    $endgroup$
    – Ak19
    May 19 at 11:55







  • 1




    $begingroup$
    @Ak19 Each of them can be either a knight or a knave - they don't have to be all of the same kind.
    $endgroup$
    – Maiaux
    May 19 at 11:56










  • $begingroup$
    @Ak19 - In fact, they cannot all be the same kind by the second question. If they're all knaves or all knights, the black-haired person could not say that "C is a knave".
    $endgroup$
    – David Hammen
    May 19 at 16:10















$begingroup$
A tiny little doubt - According to your question, is it that they all are knights or all are knaves. or one knight and the others knaves and so on.
$endgroup$
– Ak19
May 19 at 11:55





$begingroup$
A tiny little doubt - According to your question, is it that they all are knights or all are knaves. or one knight and the others knaves and so on.
$endgroup$
– Ak19
May 19 at 11:55





1




1




$begingroup$
@Ak19 Each of them can be either a knight or a knave - they don't have to be all of the same kind.
$endgroup$
– Maiaux
May 19 at 11:56




$begingroup$
@Ak19 Each of them can be either a knight or a knave - they don't have to be all of the same kind.
$endgroup$
– Maiaux
May 19 at 11:56












$begingroup$
@Ak19 - In fact, they cannot all be the same kind by the second question. If they're all knaves or all knights, the black-haired person could not say that "C is a knave".
$endgroup$
– David Hammen
May 19 at 16:10




$begingroup$
@Ak19 - In fact, they cannot all be the same kind by the second question. If they're all knaves or all knights, the black-haired person could not say that "C is a knave".
$endgroup$
– David Hammen
May 19 at 16:10










3 Answers
3






active

oldest

votes


















5
















$begingroup$

One possibility is that




The brown-haired person and black-haired person are A and B in some order. Then since they are both knights, the black-haired person speaks the truth when he says that C is a knave.




This means that




C is the blond-haired man, who is clearly lying when he says that C has brown hair (because he's describing himself!) Therefore C has blond hair.







share|improve this answer










$endgroup$










  • 1




    $begingroup$
    oops sniped... bye
    $endgroup$
    – Omega Krypton
    May 19 at 12:22










  • $begingroup$
    coming back with explanations for other cases :) +1!
    $endgroup$
    – Omega Krypton
    May 19 at 12:28











  • $begingroup$
    I'll accept your answer because you were the first to answer correctly, but how did you rule out all the other cases?
    $endgroup$
    – Maiaux
    May 19 at 13:01


















5
















$begingroup$


Blond




Explanation




See the following images... they also explain the other cases
enter image desc here
enter image description here




Conclusion




C is a knave with blond hair, A and B are knights with black/ brown hair







share|improve this answer












$endgroup$






















    3
















    $begingroup$

    El- Guest and OK have got the answer before me..



    C is




    Blond haired




    Explanation




    First let's start from the black haired person. If he were a knight, C would be a knave and can't have black hair. If he were a knave it would directly imply that C can't have black hair. (as he would be telling about himself in both cases)
    $$$$
    Next from the blond haired person. If he were a knight, then C would have brown hair. Now C can be a knight or a knave. If C were a knight, A and B both would be knights with any one of them with black hair. So, this would imply that C is a knave. But this is a contradiction.
    So if C were a brown-haired knave, A and B would be knaves with any one blond-haired. This would imply that blond haired person is a knave, again a contradiction.
    $$$$
    So, the blond haired person must be a knave and it must be C .







    share|improve this answer










    $endgroup$
















      Your Answer








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      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      5
















      $begingroup$

      One possibility is that




      The brown-haired person and black-haired person are A and B in some order. Then since they are both knights, the black-haired person speaks the truth when he says that C is a knave.




      This means that




      C is the blond-haired man, who is clearly lying when he says that C has brown hair (because he's describing himself!) Therefore C has blond hair.







      share|improve this answer










      $endgroup$










      • 1




        $begingroup$
        oops sniped... bye
        $endgroup$
        – Omega Krypton
        May 19 at 12:22










      • $begingroup$
        coming back with explanations for other cases :) +1!
        $endgroup$
        – Omega Krypton
        May 19 at 12:28











      • $begingroup$
        I'll accept your answer because you were the first to answer correctly, but how did you rule out all the other cases?
        $endgroup$
        – Maiaux
        May 19 at 13:01















      5
















      $begingroup$

      One possibility is that




      The brown-haired person and black-haired person are A and B in some order. Then since they are both knights, the black-haired person speaks the truth when he says that C is a knave.




      This means that




      C is the blond-haired man, who is clearly lying when he says that C has brown hair (because he's describing himself!) Therefore C has blond hair.







      share|improve this answer










      $endgroup$










      • 1




        $begingroup$
        oops sniped... bye
        $endgroup$
        – Omega Krypton
        May 19 at 12:22










      • $begingroup$
        coming back with explanations for other cases :) +1!
        $endgroup$
        – Omega Krypton
        May 19 at 12:28











      • $begingroup$
        I'll accept your answer because you were the first to answer correctly, but how did you rule out all the other cases?
        $endgroup$
        – Maiaux
        May 19 at 13:01













      5














      5










      5







      $begingroup$

      One possibility is that




      The brown-haired person and black-haired person are A and B in some order. Then since they are both knights, the black-haired person speaks the truth when he says that C is a knave.




      This means that




      C is the blond-haired man, who is clearly lying when he says that C has brown hair (because he's describing himself!) Therefore C has blond hair.







      share|improve this answer










      $endgroup$



      One possibility is that




      The brown-haired person and black-haired person are A and B in some order. Then since they are both knights, the black-haired person speaks the truth when he says that C is a knave.




      This means that




      C is the blond-haired man, who is clearly lying when he says that C has brown hair (because he's describing himself!) Therefore C has blond hair.








      share|improve this answer













      share|improve this answer




      share|improve this answer










      answered May 19 at 12:22









      El-GuestEl-Guest

      26.4k3 gold badges63 silver badges109 bronze badges




      26.4k3 gold badges63 silver badges109 bronze badges










      • 1




        $begingroup$
        oops sniped... bye
        $endgroup$
        – Omega Krypton
        May 19 at 12:22










      • $begingroup$
        coming back with explanations for other cases :) +1!
        $endgroup$
        – Omega Krypton
        May 19 at 12:28











      • $begingroup$
        I'll accept your answer because you were the first to answer correctly, but how did you rule out all the other cases?
        $endgroup$
        – Maiaux
        May 19 at 13:01












      • 1




        $begingroup$
        oops sniped... bye
        $endgroup$
        – Omega Krypton
        May 19 at 12:22










      • $begingroup$
        coming back with explanations for other cases :) +1!
        $endgroup$
        – Omega Krypton
        May 19 at 12:28











      • $begingroup$
        I'll accept your answer because you were the first to answer correctly, but how did you rule out all the other cases?
        $endgroup$
        – Maiaux
        May 19 at 13:01







      1




      1




      $begingroup$
      oops sniped... bye
      $endgroup$
      – Omega Krypton
      May 19 at 12:22




      $begingroup$
      oops sniped... bye
      $endgroup$
      – Omega Krypton
      May 19 at 12:22












      $begingroup$
      coming back with explanations for other cases :) +1!
      $endgroup$
      – Omega Krypton
      May 19 at 12:28





      $begingroup$
      coming back with explanations for other cases :) +1!
      $endgroup$
      – Omega Krypton
      May 19 at 12:28













      $begingroup$
      I'll accept your answer because you were the first to answer correctly, but how did you rule out all the other cases?
      $endgroup$
      – Maiaux
      May 19 at 13:01




      $begingroup$
      I'll accept your answer because you were the first to answer correctly, but how did you rule out all the other cases?
      $endgroup$
      – Maiaux
      May 19 at 13:01













      5
















      $begingroup$


      Blond




      Explanation




      See the following images... they also explain the other cases
      enter image desc here
      enter image description here




      Conclusion




      C is a knave with blond hair, A and B are knights with black/ brown hair







      share|improve this answer












      $endgroup$



















        5
















        $begingroup$


        Blond




        Explanation




        See the following images... they also explain the other cases
        enter image desc here
        enter image description here




        Conclusion




        C is a knave with blond hair, A and B are knights with black/ brown hair







        share|improve this answer












        $endgroup$

















          5














          5










          5







          $begingroup$


          Blond




          Explanation




          See the following images... they also explain the other cases
          enter image desc here
          enter image description here




          Conclusion




          C is a knave with blond hair, A and B are knights with black/ brown hair







          share|improve this answer












          $endgroup$




          Blond




          Explanation




          See the following images... they also explain the other cases
          enter image desc here
          enter image description here




          Conclusion




          C is a knave with blond hair, A and B are knights with black/ brown hair








          share|improve this answer















          share|improve this answer




          share|improve this answer








          edited May 19 at 12:28

























          answered May 19 at 12:22









          Omega KryptonOmega Krypton

          14.4k2 gold badges18 silver badges103 bronze badges




          14.4k2 gold badges18 silver badges103 bronze badges
























              3
















              $begingroup$

              El- Guest and OK have got the answer before me..



              C is




              Blond haired




              Explanation




              First let's start from the black haired person. If he were a knight, C would be a knave and can't have black hair. If he were a knave it would directly imply that C can't have black hair. (as he would be telling about himself in both cases)
              $$$$
              Next from the blond haired person. If he were a knight, then C would have brown hair. Now C can be a knight or a knave. If C were a knight, A and B both would be knights with any one of them with black hair. So, this would imply that C is a knave. But this is a contradiction.
              So if C were a brown-haired knave, A and B would be knaves with any one blond-haired. This would imply that blond haired person is a knave, again a contradiction.
              $$$$
              So, the blond haired person must be a knave and it must be C .







              share|improve this answer










              $endgroup$



















                3
















                $begingroup$

                El- Guest and OK have got the answer before me..



                C is




                Blond haired




                Explanation




                First let's start from the black haired person. If he were a knight, C would be a knave and can't have black hair. If he were a knave it would directly imply that C can't have black hair. (as he would be telling about himself in both cases)
                $$$$
                Next from the blond haired person. If he were a knight, then C would have brown hair. Now C can be a knight or a knave. If C were a knight, A and B both would be knights with any one of them with black hair. So, this would imply that C is a knave. But this is a contradiction.
                So if C were a brown-haired knave, A and B would be knaves with any one blond-haired. This would imply that blond haired person is a knave, again a contradiction.
                $$$$
                So, the blond haired person must be a knave and it must be C .







                share|improve this answer










                $endgroup$

















                  3














                  3










                  3







                  $begingroup$

                  El- Guest and OK have got the answer before me..



                  C is




                  Blond haired




                  Explanation




                  First let's start from the black haired person. If he were a knight, C would be a knave and can't have black hair. If he were a knave it would directly imply that C can't have black hair. (as he would be telling about himself in both cases)
                  $$$$
                  Next from the blond haired person. If he were a knight, then C would have brown hair. Now C can be a knight or a knave. If C were a knight, A and B both would be knights with any one of them with black hair. So, this would imply that C is a knave. But this is a contradiction.
                  So if C were a brown-haired knave, A and B would be knaves with any one blond-haired. This would imply that blond haired person is a knave, again a contradiction.
                  $$$$
                  So, the blond haired person must be a knave and it must be C .







                  share|improve this answer










                  $endgroup$



                  El- Guest and OK have got the answer before me..



                  C is




                  Blond haired




                  Explanation




                  First let's start from the black haired person. If he were a knight, C would be a knave and can't have black hair. If he were a knave it would directly imply that C can't have black hair. (as he would be telling about himself in both cases)
                  $$$$
                  Next from the blond haired person. If he were a knight, then C would have brown hair. Now C can be a knight or a knave. If C were a knight, A and B both would be knights with any one of them with black hair. So, this would imply that C is a knave. But this is a contradiction.
                  So if C were a brown-haired knave, A and B would be knaves with any one blond-haired. This would imply that blond haired person is a knave, again a contradiction.
                  $$$$
                  So, the blond haired person must be a knave and it must be C .








                  share|improve this answer













                  share|improve this answer




                  share|improve this answer










                  answered May 19 at 12:35









                  Ak19Ak19

                  1,9881 gold badge3 silver badges30 bronze badges




                  1,9881 gold badge3 silver badges30 bronze badges































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