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what did the king do with the princess and perseus?
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In Greek mythology, King Polydectes (who desired Perseus' mother Danaë) tricked Perseus into retrieving the head of Medusa, hoping he would die in the attempt. Meanwhile, he planned to force Danaë into marriage. When Perseus returned victorious, he used Medusa's head to turn Polydectes to stone. Additionally, in some versions, the king (Polydectes) had previously cast Perseus and Danaë adrift at sea in a wooden chest, though Danaë is Perseus' mother, not the princess tied to a rock—that is Andromeda, whom Perseus rescued. If referencing the king who exposed Andromeda, King Cepheus was forced by Poseidon to chain his daughter Andromeda to a rock to be eaten by a sea monster, which Perseus defeated to save her, after which Cepheus allowed Perseus to marry Andromeda. The most common pairing with Perseus and a royal figure is Polydectes' scheme against him and his mother, or Cepheus' sacrifice of Andromeda.
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In the standard Greek myth, King Polydectes, who lusted after Perseus' mother Danaë, sent Perseus on a seemingly impossible quest to slay the Gorgon Medusa, intending for him to be killed so he could take Danaë. When Perseus returned successfully, he used Medusa's head to turn Polydectes and his court to stone. If referring to Princess Andromeda, her father King Cepheus was forced by the god Poseidon to chain her to a rock as a sacrifice to a sea monster; Perseus killed the monster to save her, and Cepheus then permitted Perseus to marry Andromeda.