Knight and Knave Riddle tough puzzle?

Question

On the island of Knights and Knaves, everybody is either a knight or a knave. Knights always tell the truth and knaves always lie. Two islanders approach you. One says, "I am a knave or he is a knight." What follows with respect to the identities of the two islanders?

can't figure it out.

no you can not ask questions, however the way its presented in multiple choice, "None of the above" is also a possible answer along with the other 4 obvious possibilities.

Answer 1

1) They are both Knights.
2) They are both Knaves.
3) Speaker is knight, friend is knave.
4) Speaker is knave, friend is knight.

Only one of the two parts ("I am a knave" and "he is a knight") must follow the law of what the person speaking is. 3 is wrong because the speaker (knight) would be lying on both counts. 4 is wrong because the speaker (knave) would be telling the truth in both parts. I'm not sure what my reasoning was, but when I started typing, I thought the correct answer was 1, both are knights. Sorry about that, but at least I narrowed it down to two choices.

Of course, this is all assuming that "islanders" means they're from the island of knights and knaves.

Why did pri go into so much detail, yet throughout that whole thing, I don't see any sort of answer. Also, half of where things should be, seems to be blank.

Answer 2

Here is the basic rule of the Island of Knights and Knaves: Knights always tell the truth, and Knaves always lie. As you might expect, this makes communication a little complicated. Knights and Knaves look the same, so it’s not immediately clear if a person is one or the other. Of course, you can ask the person which he or she is – but they’ll say “I’m a Knight” either way! (Knights will say this because it’s true, Knaves because it’s false.) So how can you tell who is who, and which sentences to believe? Formal Logic is the key.

For example, suppose on the beach you meet two natives of the island, named “P” and “Q”; and P says “Either I am a knave or Q is a knight”.

The first step in sorting out such a situation is to translate the claim into formal language. Let’s use the following translation table:


P: P is a knight
Q: Q is a knight


Now, what if we want to say that P is a knave? Do we need another sentence letter for that sentence (maybe “R”)? NO – because on the island of Knights and Knaves everybody is either one or the other. So saying that P isn’t a Knight, is on the island equivalent to saying that P is a Knave. Using our translation table, “P isn’t a Knight” would be “~P”. And we know that this is equivalent to saying “P is a Knave”. The same trick works if you want to say that Q is a Knave: that’s the same as saying that Q isn’t a Knight.


P: P is a Knight
Q: Q is a Knight

~P: P is a Knave
~Q: Q is a Knave.


Now we can translate what P said into formal notation. P said:


Either I am a knave or Q is a knight


This translates as:





But what do we do with this sentence? We apply the two laws of the Island to it.

The First Law of the island is this: if P is a knight, then what P says really is so. And what P says is: “Either P is a Knave, or Q is a Knight.” So, according to the First Law: if P is a Knight, then (Either P is a Knave, or Q is a Knight). Using the same translation table, we translate the First Law into formal notation:





The Second Law of the island is the reverse of the first law: if what P says really so, then P is a Knight. In formal notation:





Now, both of these laws are guaranteed to be true: on the island, Knights always tell the truth (First Law), and if someone tells the truth, that person is a Knight (Second Law). So, in the current situation, we know that both of these sentences must be true:





With our semantic methods, we can use sentences (1) and (2) to figure out what P and Q are. Using truth tables, we can figure out the situations where both of these sentences are true.





It turns out that the only valuation where sentences (1) and (2) are both true, is the first valuation.





And in the first valuation, the sentences “P” and “Q” are both true. Remember: by our translation table, “P” means “P is a Knight,” and “Q” means “Q is a Knight”. So in a situation making sentences (1) and (2) true, both P and Q are Knights. But we know that in the situation we’re in here, sentences (1) and (2) must be true. So: in this situation, P and Q are both Knights.


That’s how to solve a Knight-Knave problem.


1. Translate what the speaker said into formal language.

2. Build two conditional ‘law-sentences’ which are guaranteed to be true:

• If that person is a Knight, then [sentence the person said].
• If [sentence the person said], then that person is a Knight.


3. Then use the semantic rules to figure out where those two sentences are both true. You are there.

Answer 3

Knights And Knaves Puzzles

Answer 4

Ask the one islander if the other is a knave, yes/no. If he says no, the other guy is not the knave, then he must be a knave. This is because the knave will lie to you, so if he says the other guy is the knave then he is really the knight. The knight will tell the truth, so the knight would not be able to say the other guy is not a knave.

Answer 5

Well, the one saying "I am a knave" can't exist, can he. If he was a knave, he'd lie and say he's a knight. If he was knight, he'd say he was a knight.

As for the one saying "He is a knight," you can't trust that one. It might be a knight telling the truth that the other fellow is a knight too. It could be a knave lying and saying another knave was a knight.

Am I allowed to ask them questions?

Then given what we know, my analysis above holds.

Answer 6

"None of the above" is the answer because the two islanders who approached me were from another island...like me they were visitors to the island of the Knights and Knaves.

Answer 7

O_o thats quite mind boggling... my head.. whats the answer!!

Answer 8

im sorry but pri...its a riddle! not an operation! you got so technical

Answer 9

that really is a tough one...thx...good question..a star..looking fwd..:-)