Answer
Person A is the knave, B is the spy, and C is the knight.
Work Step by Step
A says "I am the knight," B says "A is not the knave," and C says "B is not the knave."
A can be the knight. In this case, B is telling the truth and must be a spy. Yet C cannot be the knave, because her statement is true. So A cannot be the knight.
If A is the spy, she is allowed to lie and does so. So B tells the truth and must be the knight. C's statement is correct, so she can't be the knave, as required in the scenario. A cannot be the spy either.
Can A be the knave? Her statement is a lie, as required for her to be the knave. B lies, so she must be the spy as knave is already taken. C's statement is true, so she is the knight, as required.
