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Storm
Black belt BJJ

Gender: Female
Location:

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Puzzles & Paradoxes

The Island of Knights and Knaves

On the fictional island of Knights and Knaves, every inhabitant is either a knight or a knave. Knights are honest and virtuous, and always tell the truth. Knaves are base and shameful, and always lie.
A stranger comes to the island and encounters three inhabitants, referred to as A, B and C. The visitor asks A whether he' s a knight or a knave. Inhabitant A mumbles an answer the stranger cannot understand. B then says: "A said that he is a knave" while C says: "Don' t believe B, he is lying!"

It is not possible to determine A' s type from this conversation, but it is possible to tell what type B and C are.

Aug 9th, 2005 03:13 PM

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Shakyamunison
Nam Myoho Renge Kyo

Gender: Male
Location: Southern Oregon, Looking at you.

A is a knight
B is a Knave
C is a Knight

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Aug 9th, 2005 03:58 PM

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Shakyamunison
Nam Myoho Renge Kyo

Gender: Male
Location: Southern Oregon, Looking at you.

OK I asked my friend Jerry (he is good at this stuff) he said the there are two possibilities.

1.
A = Knight
B = Knight
C = Knave

2.
A = Knave
B = Knave
C = Knight

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Aug 9th, 2005 04:37 PM

Fire
Senior Member

Gender: Male
Location: On vacation

I could have figured that out myself

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Aug 9th, 2005 04:43 PM

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Clovie

Gender: Female
Location: lost in your dreams

[SPOILER - highlight to read]: true
false
true

confused

because:
if B told truth..the first one would be a knave..so he wouldn't admit it.. and this means the B one lied...so the last one said the turth

do i make sense? confused

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tricked me once - shame on you, tricked me twice - shame on me

Last edited by Clovie on Aug 9th, 2005 at 04:52 PM

Aug 9th, 2005 04:50 PM

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Atlantis001
The one without a name

Gender: Male
Location:

Re: Puzzles & Paradoxes

quote: (post)
Originally posted by Storm
It is not possible to determine A' s type from this conversation, but it is possible to tell what type B and C are. [/B]

Strange, I reached a different conclusion I detemined A, but couldn�t determine B, and C. Maybe you confused yourself there.

A is a knave, but for B and C there are two possibilities.

Possibility 1
A. Knave
B. Knight
C. Knave

Possibility 2
A. Knave
B. Knave
C. Knight

Possibility 3
- Both cannot be knights togheter, because one of them says that the other is lying, if both say just truth they must agree.

Possibility 4
- Both cannot be Knaves togheter, because C would be saying the truth when he says that B is lying.

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Aug 9th, 2005 05:01 PM

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Fishy
Senior Member

Gender: Male
Location: The Netherlands

A his answer can not be heard, does that mean he is lying or he's just speaking softly... Personally I think the first, so that would mean

A. Knave
B. Knave
C. Knight

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Aug 9th, 2005 05:46 PM

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Creshosk
Senior Member

Gender: Male
Location:

If C is telling the truth then B lied and A claimed to be a knight. But this doesn't show wether or not he IS a knight as a knave would lie and say he was a knight, and a knight would truthfully say he was a knight.

A = ?
B = Knave
C = Knight

If C is lying then B would br telling the truth about. . . a knave really claiming to be a knave? But wouldn't the knave lie about it? And if A was a knave he would have claimed to be a knight. But B would have said that the a claimed to be a knight. But he didn't. A either way would have claimed to be a knight. So B has to be lying. So B has to be a knave so C was telling the truth.

1. ?
knave
knight

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Aug 9th, 2005 06:29 PM

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Creshosk
Senior Member

Gender: Male
Location:

quote: (post)
Originally posted by Fishy
A his answer can not be heard, does that mean he is lying or he's just speaking softly... Personally I think the first, so that would mean

A. Knave
B. Knave
C. Knight

If A was a knight he would have claimed to be a knight and B would have lied about the claim.
If A was a knave he would have claimed to be a knight and B would have lied about the claim.

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Last edited by Creshosk on Aug 9th, 2005 at 06:36 PM

Aug 9th, 2005 06:30 PM

debbiejo
Dreamer

Gender: Unspecified
Location:

I don't like puzzles....

Aug 9th, 2005 06:36 PM

Atlantis001
The one without a name

Gender: Male
Location:

quote: (post)
Originally posted by Creshosk
If C is telling the truth then B lied and A claimed to be a knight. But this doesn't show wether or not he IS a knight as a knave would lie and say he was a knight, and a knight would truthfully say he was a knight.

A = ?
B = Knave
C = Knight

Yeah you are right. If:
B said "A is a knave"
C said "B is lying"

If C tells the truth, and B lies one can conclude from what C said that B is a knave, and from B that "A is a knave" is a lie, so A must be a knight.
So in this case:

A.Knight
B.Knave
C.Knight

quote:
If C is lying then B would br telling the truth about. . . a knave really claiming to be a knave? But wouldn't the knave lie about it? And if A was a knave he would have claimed to be a knight. But B would have said that the a claimed to be a knight. But he didn't. A either way would have claimed to be a knight. So B has to be lying. So B has to be a knave so C was telling the truth.

1. ?
knave
knight

B said "A is a knave"
C said "B is lying"

If C is lying then B said the truth(he is a knight not a knave). If B said the truth he is a knight, and the sentence "A is a knave" is true. So:

A. Knave
B. Knight
C. Knave

But logic is evil... so... be careful.

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Last edited by Atlantis001 on Aug 9th, 2005 at 08:08 PM

Aug 9th, 2005 07:57 PM

Storm
Black belt BJJ

Gender: Female
Location:

Moderator

Should I shed light on the Island of Knights and Knaves or do you want to rack your brain some more?

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Make poverty history.

Aug 9th, 2005 08:09 PM

Atlantis001
The one without a name

Gender: Male
Location:

Wait... I still have hope

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Aug 9th, 2005 08:16 PM

debbiejo
Dreamer

Gender: Unspecified
Location:

Does it have something to do with the word "he?"

The visitor asks A whether he' s a knight or a knave.

Aug 9th, 2005 08:30 PM

Storm
Black belt BJJ

Gender: Female
Location:

Moderator

Gender is no object.

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Aug 9th, 2005 08:35 PM

debbiejo
Dreamer

Gender: Unspecified
Location:

quote: (post)
Originally posted by Storm
Gender is no object.

But as the real object of the question?....OH, forget it...I hate logic puzzels...

Aug 9th, 2005 08:47 PM

Atlantis001
The one without a name

Gender: Male
Location:

I think I got it...

First for reasons that I already said B, and C can�t be both knights, or knaves at the same time.

Now lets remenber what B, and C said:

B said "A said he is a knave".
C said "Don�t believe B, he�s lying" what is the same as just "B is lying".

Now we analyze the remaining possibilies, and figure out which one is right:

Possibility 1 (wrong)
A. Neither
B. Knight
C. Knave

If C is a knave he lied about "B is lying" what means that B is telling the truth.If B tells the truth so A really said he is a knave; if A is a knave he should have said that he is a knight. So he can�t be a knave. If he was a knight then he would never say that he is a knave. So he can�t be a knight too. The island only has knights, and knaves so this possibility cannot be true.

Possibility 2 (right)
A. Can�t be determined
B. Knave
C. Knight

If C is a knight he tells the truth about B lying, and he is indeed a knave, so... no contradictions here. If B is a knave he lied about "A said he is a knave", so we have no information about A and can�t determine what he is.

Ufff... crazy puzzle this one !

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Last edited by Atlantis001 on Aug 9th, 2005 at 09:21 PM

Aug 9th, 2005 09:18 PM

Fire
Senior Member

Gender: Male
Location: On vacation

no tips

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Aug 9th, 2005 09:25 PM

Creshosk
Senior Member

Gender: Male
Location:

It all has to do with "A said that"

It's like the door puzzle. "what did the other person say."

A's Claim in this case and what B thinks of it.

A said that he was a knight.
B sais that A said that he was a knave.
C says B is lying about what A claimed.

A had to have claimed he was a knight, after all if A was a knight, it'd be the truth. If he was a knave it'd be a lie.

Now B had to have lied about A's claim. Since a knight wouldn't claim to be a knave, and a knave would not admit he was a knave.

And of course C Was telling the truth about B lying.

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Aug 10th, 2005 12:39 AM

WanderingDroid
THE LOOSE CANNON

Gender: Male
Location: Welfare Kingdom of California

Observation: A knave will never call himself a Knave for he then is telling the truth.

Answer: No inhabitant can say that he is a knave. Therefore B's statement must be untrue, so he is a knave, and C's statement must be true, so he is a knight.

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Last edited by WanderingDroid on Aug 10th, 2005 at 12:54 AM

Aug 10th, 2005 12:50 AM

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