You are shipwrecked on an unknown island where there are two kinds of people - Knights & Knaves. Knights always tell the truth and knaves always lie. To survive, you need to know who is who.
For each person in the following scenarios, can you figure out if they are a knight or a knave? Support your answer with a logical justification / proof.
1. Persons: A & B
- A says: “B is a knave.”
- B says: “We are both knights.”
2. Persons: A & B
- A says: “We are both knights."
- B says: “We are both knaves.”
3. Persons: A, B & C
- A says: “B is a knave.”
- B says: “C is a knave.”
- C says: “B and myself are knights.”
4. Persons: A & B
- A says: “At least one of the two of us is a knight.”
- B says: “La la la!”
1. If B is a Knight, then A's statement would be impossible. Therefor B is a Knave. That makes A a Knight.
2. A can't be telling the truth, because then B can't say what he did. So A must be a Knave. However, if B is a Knave, then his statement is then true making it impossible as well, so B can't be a Knave if A is as well, however he can't be a Knight either because then his statement is a lie. If you try to nail down B first then A ends up in the situation where they can't be either, so this is an impossible situation in a Knight and Knave only world.
3. If C is telling the truth, then it would be impossible for B to say what he did because it's a lie. So C must be a Knave. Then B is therefore a Knight, making A a Knave as well.
4. A is a knight then B can be a Knight or a Knave. If A is a Knave, B is also a Knave, but can't tell which is the case.