two_person_accusation

Example Problem

Example: A says: 'B is a liar.' B says: 'A is a truth-teller.' Determine their types. Solution: Step 1: Let T=Truth-teller, L=Liar. Step 2: Consider TT: A says 'B is liar' (B is T, so statement is false). A is T but made a false statement → invalid. Step 3: Consider TL: A says 'B is liar' (B is L, so statement is true). A is T, statement true → valid. B says 'A is T' (A is T, so statement is true). B is L but made a true statement → invalid. Step 4: Consider LT: A says 'B is liar' (B is T, so statement is false). A is L, statement false → valid. B says 'A is T' (A is L, so statement is false). B is T but made a false statement → invalid. Step 5: Consider LL: A says 'B is liar' (B is L, so statement is true). A is L but made a true statement → invalid. Step 6: No valid combination? Let's re-evaluate. Wait, the classic solution for this is TL or LT? Let's check LT carefully: A(L) says false statement (B is liar is false) → liar telling falsehood is ok. B(T) says 'A is T' is false, but B is T cannot lie. So LT invalid. For TL: A(T) says truth (B is liar) ok, B(L) says 'A is T' is true, but liar cannot tell truth. So invalid. This specific pair has no solution! This shows the importance of checking all combos. Answer: No consistent assignment (paradoxical).