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.
Answer
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.
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