# Liars, truth-tellers and jokers

In a strange village there are three kinds of persons: knights (always telling the truth), knaves (always lying) and jokers (who may either tell the truth or lie).

A, B, C and D live in this village, and, among them, we know that there is a knight, a knave and a joker, plus a fourth person whose kind we don't know.

Also, among B and D there is one knight and one knave.

Each of them says something.

• A: "The person whose kind you don't know is a knave"
• B: "A and D are a joker and a knave (not necessarily in this order)"
• C: "D is not telling the truth"
• D: "At least one among A and C tells the truth"

Determine the kind of A, B, C, and D.

• Could you please tell us if this is sourced from somewhere or an original puzzle? Plagiarism is not allowed here on Puzzling Stack Exchange. If is not yours, please post something that gives credence to to the original author. – Rewan Demontay May 22 at 18:49
• @RewanDemontay It's an original puzzle, invented by me today. If it coincides with or is similar to an already existing puzzle, I am totally unaware of it. – TheDude May 22 at 18:55
• There is a logical contradiction in your statements, I'll post an answer to show you how I got it, but as it stands I believe there is no solution, unless I'm misunderstanding it – PunPun1000 May 22 at 18:57
• @PunPun1000 I'd like to see how you got to this conclusion, which is in constrast with what I deduced. Let's see if there is a misunderstanding... – TheDude May 22 at 19:00
• Then all is well and good @TheDude! – Rewan Demontay May 22 at 19:01

The solution is:

A is a Joker, B is a Knave, C is a Knave, and D is a Knight

My logic is the follows:

C: "D is not telling the truth"

D: "At least one among A and C tells the truth"

C cannot be telling the truth here. If C is telling the truth, that means D is lying. However, D cannot be lying if C is telling the truth as his statement is true. Therefore C must be lying, and D must be telling the truth

Also, among B and D there is one knight and one knave.

Since D is telling the truth he must be a knight, with B being a knave.

D: "At least one among A and C tells the truth"

Since we know D is telling the truth and C is lying, that means that A must also be telling the truth

A: "The person whose kind you don't know is a knave"

As discussed above, A is telling the truth. This means that we have a total of a Knight, a Joker, and two Knaves. We know the knight is D, so a truth must imply that A is the joker. This makes C the second Knave, which is fine because C is confirmed to be lying.

•   A: "The person whose kind you don't know is a knave"
•   B: "A and D are a joker and a knave (not necessarily in this order)"
•   C: "D is not telling the truth"
•   D: "At least one among A and C tells the truth"


Assume

B is a knight. Then D must be the knave. So A must be the joker. Since D is the knave, this means that neither A nor C tells the truth always. There are two ways to interpret this. A is a joker, which means that they don’t always tell the truth. Further, C would be true, and since C can’t always tell the truth, they must also be a joker (so A’s joker statement is false).

Therefore we have

A: joker, B: knight, C: joker, D: knave.

Alternatively,

Continue from our breakpoint above. If “A doesn’t tell the truth” means that A never tells the truth, then A must be the knave -><- (contradiction)! So B can’t be the knight, and therefore B is the knave. This makes D the knight, and makes C a liar (either a joker or a knave). Here, A must therefore be a truth teller (and therefore a second knight), but that would mean the person whose kind we didn’t know was a knight (and “truthteller” A said it was a knave!) -><- contradiction! Therefore this interpretation, just like me, is dumb and should be ignored.

• You are saying that neither A nor C tells the truth, but then go on to say that C is telling the truth – PunPun1000 May 22 at 19:16
• I’ve interpreted the statement to mean “neither A nor C tells the truth always, which is logically consistent with my answer. – El-Guest May 22 at 19:19