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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;
$begingroup$
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.
logical-deduction liars
asked May 19 at 11:47
MaiauxMaiaux
4782 silver badges7 bronze badges
$endgroup$
add a comment
|
$begingroup$
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.
logical-deduction liars
asked May 19 at 11:47
MaiauxMaiaux
4782 silver badges7 bronze badges
$endgroup$
$begingroup$
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
add a comment
|
$begingroup$
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.
logical-deduction liars
asked May 19 at 11:47
MaiauxMaiaux
4782 silver badges7 bronze badges
$endgroup$
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
logical-deduction liars
asked May 19 at 11:47
MaiauxMaiaux
4782 silver badges7 bronze badges
asked May 19 at 11:47
MaiauxMaiaux
4782 silver badges7 bronze badges
asked May 19 at 11:47
MaiauxMaiaux
4782 silver badges7 bronze badges
asked May 19 at 11:47
MaiauxMaiaux
4782 silver badges7 bronze badges
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
add a comment
|
$begingroup$
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
add a comment
|
3 Answers
3
active
oldest
votes
$begingroup$
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.
answered May 19 at 12:22
El-GuestEl-Guest
26.4k3 gold badges63 silver badges109 bronze badges
$endgroup$
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
add a comment
|
$begingroup$
Blond
Explanation
See the following images... they also explain the other cases
Conclusion
C is a knave with blond hair, A and B are knights with black/ brown hair
answered May 19 at 12:22
Omega KryptonOmega Krypton
14.4k2 gold badges18 silver badges103 bronze badges
$endgroup$
add a comment
|
$begingroup$
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 .
answered May 19 at 12:35
Ak19Ak19
1,9881 gold badge3 silver badges30 bronze badges
$endgroup$
add a comment
|
Your Answer
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$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.
answered May 19 at 12:22
El-GuestEl-Guest
26.4k3 gold badges63 silver badges109 bronze badges
$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
add a comment
|
$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.
answered May 19 at 12:22
El-GuestEl-Guest
26.4k3 gold badges63 silver badges109 bronze badges
$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
add a comment
|
$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.
answered May 19 at 12:22
El-GuestEl-Guest
26.4k3 gold badges63 silver badges109 bronze badges
$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.
answered May 19 at 12:22
El-GuestEl-Guest
26.4k3 gold badges63 silver badges109 bronze badges
answered May 19 at 12:22
El-GuestEl-Guest
26.4k3 gold badges63 silver badges109 bronze badges
answered May 19 at 12:22
El-GuestEl-Guest
26.4k3 gold badges63 silver badges109 bronze badges
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
add a comment
|
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
add a comment
|
$begingroup$
Blond
Explanation
See the following images... they also explain the other cases
Conclusion
C is a knave with blond hair, A and B are knights with black/ brown hair
answered May 19 at 12:22
Omega KryptonOmega Krypton
14.4k2 gold badges18 silver badges103 bronze badges
$endgroup$
add a comment
|
$begingroup$
Blond
Explanation
See the following images... they also explain the other cases
Conclusion
C is a knave with blond hair, A and B are knights with black/ brown hair
answered May 19 at 12:22
Omega KryptonOmega Krypton
14.4k2 gold badges18 silver badges103 bronze badges
$endgroup$
add a comment
|
$begingroup$
Blond
Explanation
See the following images... they also explain the other cases
Conclusion
C is a knave with blond hair, A and B are knights with black/ brown hair
answered May 19 at 12:22
Omega KryptonOmega Krypton
14.4k2 gold badges18 silver badges103 bronze badges
$endgroup$
Blond
Explanation
See the following images... they also explain the other cases
Conclusion
C is a knave with blond hair, A and B are knights with black/ brown hair
answered May 19 at 12:22
Omega KryptonOmega Krypton
14.4k2 gold badges18 silver badges103 bronze badges
edited May 19 at 12:28
answered May 19 at 12:22
Omega KryptonOmega Krypton
14.4k2 gold badges18 silver badges103 bronze badges
answered May 19 at 12:22
Omega KryptonOmega Krypton
14.4k2 gold badges18 silver badges103 bronze badges
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
add a comment
|
add a comment
|
$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)
$$$$
Next from the blond haired person. If he were a knight, then C would have brown hair. Now C can be a knight or a knave. If C were a knight, A and B both would be knights with any one of them with black hair. So, this would imply that C is a knave. But this is a contradiction.
So if C were a brown-haired knave, A and B would be knaves with any one blond-haired. This would imply that blond haired person is a knave, again a contradiction.
$$$$
So, the blond haired person must be a knave and it must be C .
answered May 19 at 12:35
Ak19Ak19
1,9881 gold badge3 silver badges30 bronze badges
$endgroup$
add a comment
|
$begingroup$
El- Guest and OK have got the answer before me..
C is
Blond haired
Explanation
First let's start from the black haired person. If he were a knight, C would be a knave and can't have black hair. If he were a knave it would directly imply that C can't have black hair. (as he would be telling about himself in both cases)
$$$$
Next from the blond haired person. If he were a knight, then C would have brown hair. Now C can be a knight or a knave. If C were a knight, A and B both would be knights with any one of them with black hair. So, this would imply that C is a knave. But this is a contradiction.
So if C were a brown-haired knave, A and B would be knaves with any one blond-haired. This would imply that blond haired person is a knave, again a contradiction.
$$$$
So, the blond haired person must be a knave and it must be C .
answered May 19 at 12:35
Ak19Ak19
1,9881 gold badge3 silver badges30 bronze badges
$endgroup$
add a comment
|
$begingroup$
El- Guest and OK have got the answer before me..
C is
Blond haired
Explanation
First let's start from the black haired person. If he were a knight, C would be a knave and can't have black hair. If he were a knave it would directly imply that C can't have black hair. (as he would be telling about himself in both cases)
$$$$
Next from the blond haired person. If he were a knight, then C would have brown hair. Now C can be a knight or a knave. If C were a knight, A and B both would be knights with any one of them with black hair. So, this would imply that C is a knave. But this is a contradiction.
So if C were a brown-haired knave, A and B would be knaves with any one blond-haired. This would imply that blond haired person is a knave, again a contradiction.
$$$$
So, the blond haired person must be a knave and it must be C .
answered May 19 at 12:35
Ak19Ak19
1,9881 gold badge3 silver badges30 bronze badges
$endgroup$
El- Guest and OK have got the answer before me..
C is
Blond haired
Explanation
First let's start from the black haired person. If he were a knight, C would be a knave and can't have black hair. If he were a knave it would directly imply that C can't have black hair. (as he would be telling about himself in both cases)
$$$$
Next from the blond haired person. If he were a knight, then C would have brown hair. Now C can be a knight or a knave. If C were a knight, A and B both would be knights with any one of them with black hair. So, this would imply that C is a knave. But this is a contradiction.
So if C were a brown-haired knave, A and B would be knaves with any one blond-haired. This would imply that blond haired person is a knave, again a contradiction.
$$$$
So, the blond haired person must be a knave and it must be C .
answered May 19 at 12:35
Ak19Ak19
1,9881 gold badge3 silver badges30 bronze badges
answered May 19 at 12:35
Ak19Ak19
1,9881 gold badge3 silver badges30 bronze badges
answered May 19 at 12:35
Ak19Ak19
1,9881 gold badge3 silver badges30 bronze badges
answered May 19 at 12:35
Ak19Ak19
1,9881 gold badge3 silver badges30 bronze badges
1,9881 gold badge3 silver badges30 bronze badges
add a comment
|
add a comment
|
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$begingroup$
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