A. How do Odysseus and his men sneak out of the cyclops' cave? They tied themselves underneath the sheep as they so left the cave so that the blind cyclops would not feel them leave the cave. ... He taunts the cyclops after they leave the island and makes the cyclops mad. (The plan to sneak out.) Odysseus's plan called for one man to remain outside the horse; he would act as though the Greeks had abandoned him, leaving the horse as a gift for the Trojans. An inscription was engraved on the horse reading: "For their return home, the Greeks dedicate this offering to Athena". (His plan to win the Trojan war)