Many of characters other than Oedipus contribute to solving the central mystery in Oedipus Rex by Sophocles.
Teiresias: a blind prophet of Apollo gives several prophecies which point towards the resolution of the plot. This adds suspense as the audience, who would have known the story in advance, can understand the meaning of his words and how they foretell the end of the play when he says:
But I say that you, with both your eyes, are blind:
You cannot see the wretchedness of your life,
Nor in whose house you live, no, nor with whom.
Messenger: The messenger tells Oedipus that Polybos, who has recently died, was not Oedipus' real father.
Shepherd of Laius: This shepherd reveals to Oedipus his true parentage.