Bart the Knave

Let's analyze the statements: 1. Bart claims, "I and Ted are both knights or both knaves." 2. Ted claims, "Bart would tell you that I am a knave." If Bart is a Knight, then his statement would be true, which means both he and Ted would be Knights. But then Ted's statement would be false, since he said Bart would say he is a Knave, which contradicts the fact that Knights always tell the truth. If Bart is a Knave, then his statement would be false, which means Bart and Ted cannot both be Knights or both be Knaves. Since Bart is a Knave, the only other option is for Ted to be a Knight. In this case, what Ted said is true because a Knave (Bart) would claim that a Knight (Ted) is a Knave. In conclusion, Bart is the Knave and Ted is the Knight.