The narrator in "The Pit and the Pendulum" uses his intelligence by carefully observing his surroundings and experimenting with different strategies to escape. For example, he rubs food on the edges of his ropes to attract rats and chew through them, freeing himself. He also calculates the time it takes for the pendulum to descend to avoid being sliced in half. These actions show his resourcefulness and ability to think quickly under pressure.
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