[Guest]

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

Nine inhabitants of the island: Mel, Bart, Sue, Betty, Rex, Zeke, Sally, Zoey and Homer are busy at a conversation. A visitor from a neighboring island stopped by and asked each of the nine inhabitants their respective identities. They say:

Mel: "Only a knave would say that Sally is a knave."

Bart: "Rex is a knave."

Sue: "Mel and Homer are knaves."

Betty: "I know that I am a knight and that Sally is a knave."

Rex : "Betty and I are both knights."

Zeke: "At least one of the following is true: that Sally is a knight or that Sue is a knight."

Sally: "It's false that Betty is a knave."

Zoey: "It's not the case that Sue is a knave."

Homer: "Betty is a knave or Zeke is a knave."

Determine the type of each of the inhabitants from the abovementioned statements.

[Izzy]

Sorry, I don't really include my logic. It pretty much just revolves around the statements of Betty and Sally.

You can get this far without guessing:

Mel: Knight

Bart:

Sue: Knave

Betty: Knave

Rex:

Zeke: Knight

Sally: Knight

Zoey: Knave

Homer: Knight

While Rex is telling the truth that Betty is a knight, because of the word both, he could by lying. So really, it's either:

Mel: Knight

Bart: Knight

Sue: Knave

Betty: Knave

Rex: Knave

Zeke: Knight

Sally: Knight

Zoey: Knave

Homer: Knight

or:

Mel: Knight

Bart: Knave

Sue: Knave

Betty: Knave

Rex: Knight

Zeke: Knight

Sally: Knight

Zoey: Knave

Homer: Knight

[Guest]

1. Sally: "It's false that Betty is a knave."

IF Betty is a knave, Sally has to be a knave to say this.

IF Betty is a knight, Sally has to be a knight to say this

2. Betty: "I know that I am a knight and that Sally is a knave."

From the statement 1 and 2, we can see that Betty is obviously lying as she is contradicting the fact that Betty and Sally are either both knights or both knaves- so both are knaves.

3. Mel: "Only a knave would say that Sally is a knave."

We know that Sally is a knave. But a Knight would say that. Hence, Mel is a Knave.

4. Rex : "Betty and I are both knights."

We know that Betty is a knave. Hence, Rex is a Knave.

5. Bart: "Rex is a knave."

Bart obviously, is telling the truth and is a knight ( see point 4.)

6. Sue: "Mel and Homer are knaves."

What?? Excuse me, but we deduced that Mel was a knave. So Sue is a knave

Note that we cannot say anything about Homer yet.

7. Zoey: "It's not the case that Sue is a knave."

Effectively paraphrases to Sue is a knight. Now that, my friends, we have deduced to be false.

Sorry Zoey, but you are a knave.

8. Homer: "Betty is a knave or Zeke is a knave."

Since the first preposition is true, and it is connected through OR clause, hence the entire statement is true- this means that Homer is telling the truth, and is a Knight.

However, we cannot say anything about Zeke- yet.

9. Zeke: "At least one of the following is true: that Sally is a knight or that Sue is a knight."

We know that both Sally and Sue are knights - so Zeke is a knave.

This was easy, and I just typed out the solution as I was thinking.

Cheers,

[Guest]

this problem can't be answered because

Sally: "It's false that Betty is a knave.

Betty: "I know that I am a knight and that Sally is a knave.

if Betty is a knight then sally would be a knave. But it sally is a knave then Betty would have to be a knave

In return it makes a circle of whither betty is a knight or is sally the knight/ (vice-verse)

making the puzzle impossible to fully answer.

Edited September 26, 2011 by Xxlogic215

[Guest]

this problem can't be answered because

Sally: "It's false that Betty is a knave.

Betty: "I know that I am a knight and that Sally is a knave.

if Betty is a knight then sally would be a knave. But it sally is a knave then Betty would have to be a knave

In return it makes a circle of whither betty is a knight or is sally the knight/ (vice-verse)

making the puzzle impossible to fully answer.

Note that both could be lying, hence both knaves because Betty's statement is false if she is a not a knight and hence says nothing about sally.

[bhramarraj]

I agree with thoughtfulfellow, If a statement has two informations tied with 'AND', then if one or both of the informations are false, then complete statement becomes false. The statement is true only and only when both information are correct.

Sally: "It's false that Betty is a knave.

Betty: "I know that I am a knight and that Sally is a knave.

Let us assume Sally is knight, then her statement should be true, so Betty is not knave, but knight.

So if Betty is knight then both information contained in her statement should be true, i.e. [1] "I know that I am a knight" and [2] "I know that Sally is a knave", both should be true.

Here if Betty is knight then [1] could be correct. But if [2] was correct, then Sally should be knave,which contradicts our assumption that Sally was a Knight. So our assumption that Sally was Knight was wrong.

Therefore Sally must be Knave. Then, her statement is false. So Betty is a knave. Then both or at least one information in Betty's statement is false. So either [1] or [2] is false or both [1] & [2] are false. Here [1] is false, while [2] is true. Nevertheless the complete sentence becomes false, whither she may or may not be knowing that Sally is knave.

Edited September 28, 2011 by bhramarraj