Discuss episodes in which Odysseus triumphs through his own ingenuity and where he receives help from an immortal.

Gods and goddesses are present and potent throughout The Odyssey and often intervene to help Odysseus.
The goddess Athena, for example, who has Odysseus's interests at heart, orchestrates events so that Odysseus can escape from sea nymph Calypso. Calypso, who is in love with him, has held Odysseus for seven years, delaying his homecoming. Athena thinks this is enough, for Odysseus wants to return to Penelope.
Athena therefore approaches Zeus and persuades him to intervene. Zeus sends his messenger god Hermes to Calypso to tell her to release Odysseus. Calypso is reluctant but doesn't dare to refuse Zeus. She helps Odysseus build a boat and stocks it with ample supplies. She also provides good winds. Without Athena's intervention, it seems doubtful Odysseus would have ever escaped the seductive charms of Calypso.
Despite Calypso's help, Odysseus is blown off course by his enemy, the god Poseidon. Athena again comes to his rescue, and aided as well by Leukothea, a sea goddess, Odysseus swims for several days to the isle of Scheria.
When Odysseus gets into a fix with Circe, Hermes helps him out. Circe has turned all but six of Odysseus's men into swine. Yet because Hermes gives Odysseus the herb moly, he can overcome Circe’s sorceries and have his men transformed back from swine. Without Hermes's help, Odysseus would have been in deep trouble.
Odysseus, however, also uses his own ingenuity.
When Polyphemus, the cyclops, eats Odysseus's men, he tricks Polyphemus into drinking a very strong wine that causes him to pass out. Because Odysseus has sent him into a drunken stupor, Odysseus and his men are able to poke out Polyphemus’s eye with a wooden stake. Polyphemus awakes and tries to block the entrance to the cave with his body, but by using his wits, Odysseus manages to escape.
Odysseus is an intelligent, brave, and resourceful man, but having gods and goddesses on his side is a great help to him as he makes his epic voyage home.