Talk:Knights and Knaves

message: As usually described, problems don't say what they mean.  What is actually meant in a Knights and Knaves problem is that a knave negates the answer a knight would give, a la boolean logic.  This is what makes asking about future questions work in those "one question" problems, because the knave is forced to double negate, meaning both the knight and the knave will give the same answer.  It is most definitely possible to tell a lie that is not a negation of a true statement.  I am the lying guard in the two paths/doors problem. if someone asks me "if i were to ask you if this path is correct, would you say yes?" and I give an answer of "I don't know", I have just told a lie.  In fact it's an incredibly obvious lie, but it doesn't give the poor sap any information other than that i'm the liar.  u mad, logician? u mad bro?74.211.60.216 (talk) 05:37, 13 June 2018 (UTC)
thread_title: Lying and truthtelling

message: Did anyone notice this rather strange edit? Haven't deleted it cause I'm wondering if this might be in some pop cultural joke reference that could be noted on this page.  — Preceding unsigned comment added by 76.184.6.193 (talk) 20:35, 4 March 2013 (UTC)
replies: text: It's just garbage. Herr Gruber (talk) 10:38, 9 March 2013 (UTC)
thread_title: Tacos and Beer

message: Here is the text in the article after establishing that John is  knave.
Since knaves lie, and one statement is true, the other statement must be false
Wouldn't it be clearer, given the construction of the Question, to say:
Since knaves lie, then both statements cannot be true.  Therefore, the other statement must be false
Also, is it an unspoken assumption that the knights and the knaves know among themselves which is which?  That is to say that John and Bill know the truth about each other?  If so, perhaps that should be premised. Dawgknot 21:00, 24 August 2007 (UTC)
thread_title: Solution to Question 1 

message: I think there's an episode of Samurai Jack that features a version of this puzzle, but I can't recall which episode. B7T 20:11, 2 December 2007 (UTC)
replies: text: Also used in The Book of Lost Things by John Connolly. cryptoboy (talk) 19:54, 17 January 2015 (UTC)
replies: text: I realise these comments are from some years ago, but there's a long list of examples in which a puzzle like this is set on tvtropes.org. Aoeuidhtns (talk) 16:25, 18 April 2023 (UTC)
thread_title:  More popular culture references 

message: Has anyone ever heard of this here?
It's a very good read in regards to the problem of the Knights and Knaves.
203.188.235.14 (talk) 14:41, 18 January 2008 (UTC)
thread_title:  Boolean Equality 

message: An early example of this type of puzzle involves three inhabitants referred to as A, B and C. The visitor asks A what type he is, but does not hear A's answer. B then says "A said that he is a knave" and C says "Don't believe B: he is lying!" To solve the puzzle, note that no inhabitant can say that he is a knave. Therefore B's statement must be untrue, so he is a knave, making C's statement true, so he is a knight and A is a knight.
I don't know where this example comes from, but I don't think it's true. We can't make any conclusions about A in this puzzle, the statements of the other  two work whether A is a knight or a knave.
99.241.128.44 (talk) 06:44, 11 February 2008 (UTC)
replies: text: The example comes from "What is the name of this book?" by Raymond Smullyan, an excellent book if you like these kind of puzzles. In this book, the answer correctly states that A's type cannot be determined. The answer has now been fixed, I see, but it is still not entirely correct. The fact that A did not say that he is a knave (because nobody can), does not mean that he said that he is a knight. We simply don't know what A said, other than that it is not what B stated. Which makes A's type truly undecided. 212.61.144.123 (talk) 15:32, 11 September 2008 (UTC)
thread_title:  Intro 

message: Question one is really strange.
Look at this statement: "If John was a knight, he would not be able to say that he was a knave since he would be lying. Therefore the statement 'John is a knave' must be true."
Sentence one is right, but sentence one does not imply sentence two at all. If John was a knave, he would not be able to say that was a knave either, because he would be telling the truth. This contradicts with the fact that knaves always lie.
Also, although I'm not an expert on Boolean algebra, could an expert verify if the Boolean algebra performed is correct?
--Freiddie 12:22, 26 May 2008 (UTC)
replies: text: It is very subtle: There are not two statements "John is a knave" and "Bill is a knave". In that case you would indeed get a contradiction. There is a single statement: "John is a knave AND Bill is a knave". John as a knight could not say that, because the statement would be untrue (since John would not be a knave), hence John must be a knave. Then the statement "John is a knave and Bill is a knave" must be untrue. Since John is a knave, then Bill cannot also be a knave (then the statement would be true), so Bill is a knight, and the statement is untrue (because Bill is not a knave, although John is). 212.61.144.123 (talk) 09:26, 3 June 2008 (UTC)
replies: text:  Oh I see now. The "AND" operator is also being said, but it's not assumed. Okay, I get it now. Thank you. --Freiddie 00:59, 5 June 2008 (UTC)
replies: text: I'm going to reword the question to remove the ambiguity; as it stands it is very unclear. bokkibear (talk) 12:15, 15 December 2009 (UTC)
thread_title:  Question 1: fallacy? 

message: The solution given for Question 2 is incorrect and the question itself is ugly and confusing. John didn't say "we are not of different kinds". John's asserting that the two person's states are dependent on each other, which is a higher level statement than simply "we are the same". Such a statement can be false simply because the dependency doesn't exist regardless of what states they actualy are.
This is my attempt at a 'solution':
Purely based on Bill's statement, John can't be a knight because that would mean Bill is saying "I am a knave" which is paradoxical. Since John is a knave, Bill can be either a knight or a knave.
All we can know from John's statement being false is that one can be a knave (such as John) without the other also being a knave. The only way for John's statement to be provably false by itself would be if Bill were a knight, but as pleasing as this solution is it doesn't negate the possibility that Bill is a knave and that John's statement is false for other reasons such as admitting the possibilty of himself being a knave. He is of course a knave, but you can't be consistent while suggesting you might be lying.
Be careful with those implications; they make assertions about possibilities that in these puzzles don't exist.86.5.179.220 (talk) 03:07, 25 August 2011 (UTC)
thread_title: Solution for Question 2

message: John says: We are both knaves.
Who is what?
John's statement can't be true because nobody can admit to being a knave (see Liar paradox). Since John is a knave this means he must have been lying about them both being knaves, and so Bill is a knight...... However!  after John admits being a knave we realise  he can also tell the truth and since we are not told of anything that negates  the possibility of them both being knaves or knights (that is because John could have told truth about Bill being a knave just like a told the truth about himself being a knave) it is  possible for the other character (Bill) to be a knave as well.
The second writing was my thought but the simple fact that negates it is this:
If john can only lie then it is not possible for him to admit be a person who only lies. Therefore the lie must be in the other part of his statement (which makes the entire statement a lie and then it doesn't matter that john told the truth about himself being a liar in the first part of the statement.) which says that bill is a liar.
After writing this I thought: "then perhaps he is a knight (which can only tell the truth"
But then I remembered that it is not possible for a knight to say he is a knave for that would be a lie. 
All this mistake came after I read the riddle and it's answer and started thinking this:
(this is only true if john  uses two separate statements for this, the statements being: "I am a knave" and "the second character is a knave". That is because John already lies about himself being.
one could say it is a "smart ass" riddle since it's solution is only possible if you refer to  the statements/the two parts of the same statement as one.
Yuval.  — Preceding unsigned comment added by 46.116.154.228 (talk) 01:13, 18 January 2012 (UTC)
thread_title: Question 1

message: The version in Labyrinth does have an issue as a riddle since one of the two guards actually explains the conditions to Sarah; that means he has to be the knight if the terms of the puzzle are accepted as true, so it's rather self-defeating. Accepting he's the knave would mean he was lying about the two being a knight and a knave. (It can also be assumed that the two lower heads are not knights or knaves since one says they don't know the answer and the other agrees with him). Herr Gruber (talk) 10:45, 9 March 2013 (UTC)
thread_title:  Labyrinth 

message: It has to be said that I don't know the original text referred to, but there is a logical problem with the way this is put:
"with nobles never lying and hunters never telling the truth"
and then swapping further down the text to:
"a hunter always lies".
The negation of a specific condition, as opposed to the affirmation of a different specific condition, doesn't work here.  The two things do not mean the same.
That is, to never tell the truth does not rule out the possibility of uttering paradoxes, as paradoxes aren't the truth (and vice versa: to never tell lies would not rule out the possibility of making paradoxical statements).
This category of puzzle relies on the notion that people don't utter paradoxes, but the use of "never" leaves that possibility open, and causes problems with the terms of the puzzle.
Could this be considered, and perhaps corrected in some way?
:I guess there are tacit assumptions at play here:
:#That every response has a well-defined truth-value (which is what you're getting at).
:#That any response is given at all (as not giving a reply would also be permitted by the rules "never tell the truth" and "never tell a lie").
:It probably bears mention though probably as a footnote at best. Nbrader (talk) 13:42, 19 July 2022 (UTC)
thread_title:  Problem with the Noble/Hunter variant 

message: So, in the Labyrinth version of the riddle, the rules are told to us by one of the guards. Part of the rules is, that the truthful one is ALWAYS truthful and vice versa. This means the first problem is, what if we were lied to about the rules?
There's another version where each guard tells us half of the rules. This is impossible to solve, assuming a liar is always lying and vice versa.
However, it's possible to solve it if one or both guards don't have to be consistent.
Am I missing something?
Lise, 20231107. 83.94.61.104 (talk) 15:04, 7 November 2023 (UTC)
thread_title:  Labyrinth version, unsolvable?