[Guest]

A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie.

Seven inhabitants of the island: Zoey, Sally, Zeke, Zed, Abe, Betty and Ted are busy at a conversation. A visitor from a neighboring island stops by and asks each of the nine inhabitants their respective identities. They say:

Zoey: “Ted is a knight or Sally is a knight”

Sally: “Ted is a knave or Betty is a knight.”

Zeke: “I know that Zed is a knave and that Ted is a knight.”

Zed: “Both I am a knight and Abe is a knave.”

Abe: “Only a knave would say that Zoey is a knave.”

Betty: “At least one of the following is true: that Zed is a knight or that Zoey is a knight.”

Ted: “Of Sally and Abe, exactly one is a knight.”

Determine the identity of each inhabitant in conformity with the abovementioned statements.

[Guest]

Zoey: Knight

Sally: Knight

Zeke: knave

Zed: knave

Abe: Knight

Betty: Knight

Ted: knave

[preflop]

Zoey: Knave

Sally: Knave

Zeke: Knave

Zed: Knight

Abe: Knave

Betty: Knight

Ted Knave

[Guest]

The fun is in the journey not the destination.

No-one says anything about Zeke, so lets start with him.

Since you can prove that if he is telling the truth, then Zoey is both a knight and a knave.

I'll shortcut that by assuming he is a Knave.

If Zeke lies, then Zed is a knight and Ted a knave

Zed's truth confirms hiomself as knight and Abe as knave

Ted's lie means that, as Abe is a knave, then so too is Sally

Sally's lie means that as Ted is already a knave, Betty must be a Knight

Stepping back a bit, Abe's lie means that a knight would say Zoey is a Knave so she is.

So - Zed and Betty are Knights, the rest Knaves

all statements now hold true.

Edited December 4, 2009 by Ringer

[Guest]

I have a question

If

Zoey: “Ted is a knight or Sally is a knight” KNAVE

Sally: “Ted is a knave or Betty is a knight.” KNAVE

and

Ted: “Of Sally and Abe, exactly one is a knight.” knave

Knave means they're lying correct? So all statements are false.

If Zoey is a knave then all of his statements need to be false. If one of them is true then he is a knight right ?

Zoey said ted is a knight, since zoey is a knave that is a lie and ted is a knave. Fine

Now Sally is supposedly a knvae, zoey's options says she might be a knight... which isnt the case so zoey , as a knave, is lying. Fine.

But with that logic, Sally who is a knave, should hold all false statements like zoey who likewise is a knave. Then why is sallys first statement saying ted is a knave which is a true statement? I know it has the option of "or" in there. But are you allowed to pick and choose?

[preflop]

Knave means they're lying correct? So all statements are false.

I think you need to look at each statement as a whole. If I were to say 1 + 1 = 2 and 2 + 2 = 5. I would be lying since I was indicating that both statements are true. Even though one is, I only need one to be false for it to be a lie.

both sally and zoey statements are false because the used the term or. so back to my example if I were to say 1+1=2 or 2+2=4 i would be lying because I am indicating that only one of those statements are true, when in fact both are

I hope this helps.

[Guest]

Zoey: Knave

Sally: Knave

Zeke: Knave

Zed: Knight

Abe: Knave

Betty: Knight

Ted Knave

With your solution Saly is Knave so she should lie but her sentence is true. Usualy in logic A OR B is true when A is true or B is TRUE or both are TRUE.

[Guest]

I think you need to look at each statement as a whole. If I were to say 1 + 1 = 2 and 2 + 2 = 5. I would be lying since I was indicating that both statements are true. Even though one is, I only need one to be false for it to be a lie.

both sally and zoey statements are false because the used the term or. so back to my example if I were to say 1+1=2 or 2+2=4 i would be lying because I am indicating that only one of those statements are true, when in fact both are

I hope this helps.

This doesn't help at all. In Logic/math puzzles section I expect logical reasoning and OR in meaning of logical disjunction. See en.wikipedia.org/wiki/Logical_or . I could agree that this is point of view matter. But nobody would convince me that my solution is wrong.

[preflop]

This doesn't help at all. In Logic/math puzzles section I expect logical reasoning and OR in meaning of logical disjunction. See en.wikipedia.org/wiki/Logical_or . I could agree that this is point of view matter. But nobody would convince me that my solution is wrong.

I would wholeheartedly agree with you if we were doing bit wise operations (binary math). But this is a puzzle written in English language, so I believe the English language conventions should take precedence. And they do not follow the binary rule system for AND and OR. In everyday conversation we use the word "or" to mean one or the other but not both, so If I were to say the wall is red or white - I would mean that is either red or white, but not some combination of red and white. which is different that a binary OR in which a red, white and (red and white) walls would all qualify.

[Guest]

Right. Think of 'or' as XOR. Another indicator of this is that Betty's statement explicitly defines a logical disjuntion. So, it is reasonable to assume an exclusive disjuntion in a case where the inclusivity is not explicit.