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.

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

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

I could have figured that out myself

Spoiler:
true
false
true

😕

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? 😕

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.

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 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

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

I don't like puzzles....

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

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.

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

Wait... I still have hope

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

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

Gender is no object.

Originally posted by Storm
Gender is no object.

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

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 !

no tips

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.

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.