# 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.

• @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. May 22, 2019 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 May 22, 2019 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... May 22, 2019 at 19:00
• @PunPun1000 My bad! There's a typo. I'll fix it May 22, 2019 at 19:01
• @PunPun1000 In B's statement I wrote "knight" but I should have written "knave". Fixed now. Sorry May 22, 2019 at 19:03

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 May 22, 2019 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. May 22, 2019 at 19:19