As so often happens in fairy tales, there once was a king who had an intractable problem, one that even his wisest advisers could not solve. After many years of frustration, the exasperated king eventually declared that any who could solve his dilemma would earn his favor and join his royal court.
And as so often happens in these tales, these decrees eventually reached the ears of an clever commoner named Jack. Jack and his two brothers, Kevin (strong as an ox and nearly as bright) and Lewis (simple-minded but generous) set out, and against all odds found a solution to the kings dilemma.
Unfortunately, as happens too often in these tales, the king had second thoughts about his promises after his crisis was resolved. As mere commoners, Jack and his brothers would ill-suit the Kings royal court, thus he schemed to cheat the brothers out of their reward. He claimed that what he actually said was that the people who solved his dilemma would come to live at the castle, but not necessarily as nobility...
In this vein, he has gathered nine people from around the castle, nobility, but also commoners and servants; and the brothers can choose three of the presented people and take their places at the castle.
The king allows one question to be asked to each person present, but aware of Jacks sharp wit, prevents him from asking any of the questions.
Kevin and Lewis query the nine people, but being much less bright than their brother they fail to ask the most useful questions; and receive the less-than-helpful statements below:
- Andrew: “I am a higher rank than Edward”
- Bernard: “Ivan is a noble”
- Charlie: “Andrew is a lower rank than me”
- David: “Charlie is not the same rank as me”
- Edward: “I am not the same rank as Bernard”
- Frederick: “George is not a servant”
- George: “That's right, I'm not a servant”
- Harold: “Frederick told me he is a servant”
- Ivan: “Harold is a commoner”
Despite this, clever Jack believes he can still best the king, and elevate himself and his brothers to nobility. He quickly deduces the following facts about the people gathered before him:
Despite his disinclination to actually grant his promised reward, the king wants to at least appear fair.
Thus there must be at least three nobles amongst the people presented.
Nobles would fear to lose their own position to a commoner, but would find amusement in the idea of their peers losing theirs.
As such they would lie about themselves, but tell the truth about anyone else in the castle, including other nobles.
Commoners would have nothing to gain or lose, but would be jealous of their countrymen being elevated.
Thus they will lie about nobles to prevent Jack picking them, but otherwise tell the truth about themselves and others.
Servants would grasp this opportunity to escape their life of servitude, and do anything to be picked.
Thus they will lie about themselves and anyone of higher rank than themselves to make their position sound better; though they tell the truth about other servants, who present no competition.
Note that these rules are subjective, and not necessarily consistent; It’s hard for liars to keep their stories straight!
- A noble asked if he is the same rank as a servant would say yes, as he lies about himself.
- The same noble asked if the servant is the same rank as him would say no, as he tells the truth about servants.
From this, which three people of the nine presented should Jack choose so that he and his brothers become nobility?
(Clarifications moved up from the comments)
Ok, sorry does seem to be more uncertainty here than expected; none of it intended to add complications.
1 - To confirm what people have inferred, the ranks at the castle go Noble > Commoner > Servant. There are no intended "ranks within ranks", eg every noble is the same rank as every other noble.
I don't think it matters, but FWIW Jack and his brothers are considered commoners.
2 - All statements are made with the truth values above, even between individuals presented. Thus "X told me he is a Y" is true only if X could tell Jack he is a Y.
The truth value of the second order statement is only intended to be about whether X truly did say Y, modified by whether or not the speaker of the second order statement lies about people of X's rank.
The intention was not to create a lie from whole cloth (X said Y is a lie because X never said Y nor anything like it).
I have spent 15 minutes trying to put my intentions around this clause into clear language, and am still pretty sure I failed. In retrospect this means I should have avoided that sentence type. Live and learn I guess...
3 - My intended syntax and phrasing for determining who the subject of a statement is (in lieu of looking up grammar and syntax etc) is that a sentence is always about the first person mentioned in it, eg: 'I am better than X' is a sentence about oneself, and will be true or false based on whether one lies about themselves; 'X is better than I am' is a sentence about X (even though it refers to ones self), and is true or false depending whether one lies about people of X's rank.
This seems natural to me, but may not be standard (or even technically correct) - and is probably hell for non-native English speakers. Sorry.