I stared at this for a second because both statements together create a contradiction if you assume B is a knight.
Treat each person's type as a boolean variable (knight = true, knave = false) and translate the statements into logical constraints. Systematically test both possible types for A and check consistency with B's truthfulness and the content of B's statements.
Pro tip: After finding a consistent assignment, briefly verify that the other assignment leads to a contradiction, demonstrating thoroughness and logical rigor.
Let A and B represent whether each is a knight (true) or knave (false). Recall that a knight's statements are true and a knave's statements are false.
B says: (1) 'A and I are the same type' → A = B. (2) 'A always lies' → A is a knave (A = false).
If B is a knight, both statements must be true: A = B and A = false. Since B = true, A = true from the first, but A = false from the second → contradiction. If B is a knave, both statements must be false: A ≠ B and A ≠ false (i.e., A = true). Since B = false, A ≠ false means A = true, which also satisfies A ≠ B. Consistent.
The only consistent assignment is A = knight (true) and B = knave (false). Verify: B's first statement 'A and I are the same type' is false (they are different), and second statement 'A always lies' is false (A is a knight). Both false, as required for a knave.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.