Knights, Knaves, and 2 Types of Jokers

Logic Level 3

After Albert, Bernard and Cheryl learnt about Denise's birthday, Denise decided to have them play another challenging logic game! Here are the rules of the game: Each of them will be a knight, knave, or joker. - Knights always speak the truth, - Knaves always speak lies, The Jokers are classified into 2 types of Jokers: - Truthful Jokers, which tell the truth, and - Lying Jokers, which tell lies. Each of them are given 2 cards, each card revealing the roles of the other 2 friends. Note that on each card, the roles can be a Knight , a Knave , or a Joker , where it will not reveal what type of joker it actually is. Albert, Bernard, Cheryl laughingly said: "This will be so easy like last time!" Denise smirked: "Let's see then!" Albert, Bernard and Cheryl looked at each of their 2 cards, while Denise read out the instructions of the game: Each and every one of you must correctly identify your role through a series of conversations. You may NOT show your cards to anyone else, except your own eyes. Through the series of conversations, you will say which friend you want to make a sentence about, and I will make sure the sentence will follow the character of your own role. Hence, once you are certain what your role is, say you figured your own role. "Interesting game, let's do this!" they said cheeringly.

This was what happened during the series of conversations:

Albert: I don't know my role, but Bernard is not a knave. Bernard: I also do not know my role, but Cheryl is not a knight. Cheryl: Me neither! However, I am sure Albert is not a knave! Albert: Still haven't. However, Cheryl is not a knight. Bernard: Not yet, but Albert is not a knave. Cheryl: I figured my role! Yay! Albert: I still have no idea! But Bernard is not a knight. Bernard: I figured my role! Cheryl: Albert is not a joker. Albert: I figured my role! Nice one guys!

After looking at this very challenging problem, you will need to give an answer. By using logical deduction, and given that all 3 friends are very logical and did not make any mistakes, find the roles of Albert, Bernard and Cheryl.

Inout your answer as a series of 3 digits, with Albert first, then Bernard, and lastly Cheryl.

Knight = 1, Knave = 2, Truthful Joker = 3, Lying Joker = 4

Note: Whatever Albert, Bernard and Cheryl said is not a paradox to the character of their own roles, so use every logical deduction you have on this problem!

The answer is 133.

2 solutions

Winston Choo
Sep 7, 2018

Since Bernard knows Albert's role, if Albert was a Knave, that means Bernard would know that everything Albert says is a lie, which would mean that he himself is a knave! So since he said that he doesn't know his role yet, that means Albert is not a knave. Similarly, till the second time Albert says a statement, we can conclude Albert, Bernard and Cheryl are not Knaves! That means each of them are either a Knight, or a type of Joker. But if any of them was a Lying Joker, that would result in the same contradiction as if any of them were a Knave, for the previous statements! Hence, we shorten them down to either a Knight or a Truthful Joker. Now, we can safely assume that whatever Albert and Bernard says is the truth, so hence Cheryl is not a knight, therefore a Truthful Joker. Albert also said that Bernard is not a Knight, so Bernard is therefore another Truthful Joker. Lastly, Cheryl said Albert is not a joker, which infers that Albert cannot be a Truthful Joker, hence he is a Knight! So in conclusion, Albert is a Knight, Bernard is a Truthful Joker, and Cheryl is a Truthful Joker --------> Answer: 133

Saya Suka
Mar 18, 2021

In the first round, Albert, Bernard and Cheryl all told the next person of their NOT-ROLE, and since none of them can logically deduce their own roles from the NOT-ROLES told to them, that must be because they knew that the ones doing the telling are not knaves, so all three are either Knights or Jokers.

DIALOGUES OF THE CONVERSATION
A : ???, B ≠ knave
B : ???, C ≠ Knight
C : ???, A ≠ knave
A : ???, C ≠ Knight
B : ???, A ≠ knave
C : Yay, got it!
A : ???, B ≠ Knight
B : Yay, got it!
C : A ≠ Joker
A : Yay, got it!

In the second round, Cheryl managed to figure out her own roles despite the fact that Albert just repeated the same statement as what Bernard already said before, is because she knew that Albert is more trustworthy than Bernard, as in Albert is a Knight compared to the other's Joker as printed on the cards in her hands. Cheryl's been led to tell the truth by Denise the moderator, and she knew that none of them are knaves and the confirmation from a Knight Albert (of her not-Knight status) is everything that she needed to deduce her own role as a Truthful Joker.

Again, Bernard also just need another confirmation from Al the Knight to discover himself, too. The same way Cheryl did it, Bernard's been led to tell the truth by Denise the moderator, and he knew that none of them are knaves and the confirmation from a Knight Albert (of his not-knave AND not-Knight statuses) is everything that she needed to deduce his own role as a Truthful Joker.

On the other hand, in all three rounds, Albert was only told twice of the same fact of his not-knave status, which he could have inferred by himself from Bernard's reaction to his own first statement in the first round. Led to be telling the truth but with no useful info and no reliable informers (with 2 Joker's cards in his hands), the passing rounds told him that the other two must have been Truthful Jokers who he must have unknowingly helped himself by being their trustworthy source of information, and thus, a Knight.

Answer = 133

Knights, Knaves, and 2 Types of Jokers

The answer is 133.

2 solutions

0 pending reports