Odysseus refrains from killing the sleeping Cyclops, Polyphemus, because he realizes that doing so would trap him and his men inside the cave, as they would be unable to move the massive boulder blocking the entrance. Instead, he devises a clever plan to blind Polyphemus and escape under the guise of being named "Nobody," ensuring that when the Cyclops calls for help, he cannot reveal who attacked him. This strategic thinking highlights Odysseus' intelligence and resourcefulness in dire situations.
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