3. Three argumentative friends are sitting in front of the TV. It is known about each of them that she either is always right about everything or always wrong about everything. The first one said: "None of us have seen this movie." The second one said: "I have seen this movie, but you both haven't." The third one said: "I have seen this movie." Determine how many of these friends are always right, given that one of them said everything correctly, and one of them was wrong.
Solution. If the first girlfriend is right, then the statements of the second and third are false. If the second girlfriend is right, then the statements of the first and third are false. If the third girlfriend is right, then the statements of the second and third are false. Two girlfriends cannot be right at the same time. Since at least one of the girlfriends made a true statement, there is exactly one true statement.

Answer. Among the girlfriends, exactly one is always right.