Which goddess seems to guide Odysseus and Penelope by suggesting the contest with the bow?
Athena is Odysseus' patron goddess. Athena is the Greek goddess of wisdom and war. Odysseus is known for his intelligence and cunning nature, aptly displayed with his idea of the Trojan Horse during the Trojan War. Athena consistently assists Odysseus throughout his travels and reminds the other gods about his plight. In Book 1, Athena reminds her father, Zeus, about the fact that Odysseus still hasn't returned home to Ithaca after his exploits during the 10 year Trojan War. She speaks to Zeus about Odysseus' faithfulness and sacrifices and Zeus agrees to help Odysseus return to Ithaca, regardless of how Poseidon feels. Immediately following this conversation, Athena assumes the guise of Mentes to inform Telemachus, Odysseus' son, about his father's impending return. Upon her arrival, Athena, disguised as Mentes, witnesses the poor behavior of Penelope's suitors and in Book 19 of the Odyssey, Penelope converses unknowingly with Odysseus. In their conversation, Odysseus tries to find out how loyal Penelope has been to him and she quickly proves her undying love and loyalty. Penelope recounts her dreams, sent by Athena, and Odysseus deciphers their "true" meaning: That Odysseus will return and rout the guilty and unfaithful before him, claiming his kingdom and queen.
Upon hearing that, Penelope reveals that she will be holding a contest on the very next day where anyone who successfully strings and shoots Odysseus' bow through a line of axes will be Odysseus' successor.