On an island, knights always tell the truth and knaves always lie. A says: 'B is a knave.' B says: 'A and I are the same type.' What are A and B?
Answer and explanation
Correct answer: D. A is a knight and B is a knave.
- Step 1: Suppose A is a knight. Then B is a knave, and B's statement 'we are the same type' is false, which suits a knave. Step 2. Suppose A is a knave. Then B is a knight, but B's statement would be false, which is impossible. Step 3. So A is a knight and B is a knave. Answer: A is a knight and B is a knave. Why not the others: A and B are both knights.: This fails because then A's statement 'B is a knave' would be false. A and B are both knaves.: This fails because then B's statement would be true, which a knave cannot say. A is a knave and B is a knight.: This fails because then B's statement would be false, which a knight cannot say.
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