Answer
Either:
A is the knight, B is the spy, and C is the knave
or
A is the knave, B is the knight, and C is the spy.
Work Step by Step
Person A says, "I am not the spy," B says "I am not the spy," and C says "A is the spy."
If A is the knight, she is not the spy. Person B may or may not be lying, and person C is definitely lying because A is not the spy. B can be the knave or spy. B's statement is true if B is the knave, so B is the spy and C is thus the knave.
If A is the spy, A is lying. B is telling the truth and so is C. Neither of them can be the knave, so there are no solutions where A is the spy.
If A is the knave, she is indeed lying. Person B can be the knight or the spy. If knight, B is telling the truth, and if spy, B is choosing to lie. C's statement is a lie, so she must be the spy as the knave position is already taken. B can be the knight.
