The Golden Mango was part of a prank that the Stoll Brothers played on Aphrodite's Cabin mentioned in their interview in The Demigod Files.
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The mango, spray-painted with gold and left for the cabin while they were at archery practice, bore the phrase "For the hottest." The Aphrodite cabin started fighting over it meaninglessly over the proper recipient of the mango. After they realize their mistake, they got revenge on the Stoll brothers by applying Permanent Makeup to Travis Stoll, and cursing Connor Stoll so that all of his clothes would be two sizes too small.
The trick is a reference to the mythological Judgement of Paris, the event that set-in motion the Trojan War. Eris, the goddess of chaos, was not invited to the wedding of divine Thetis and Peleus because her presence would have cursed the happy event. Enraged, she exacted revenge by throwing her golden Apple of Discord into the assembly. On it was written the Greek phrase Kallisti, or "to the fairest one," and all the goddesses present began to fight over the proper owner of the apple. Eventually the contest was narrowed to Hera, Athena, and Aphrodite. The duty to judge fell to Zeusbut knowing his decision would cause chaos among the gods he chose the mortal prince Paris to make the decision instead.
Paris, prince of Troy, was brought to Olympus to choose between the three goddesses, but each was so peerless in beauty that he couldn't make a judgement. Therefore, each offered Paris a bribe. Hera, as Queen of the Gods, could have made him king of the mortal world. Athena, goddess of wisdom, bribed him with great wisdom and skill in warfare. Aphrodite, however, offered him the love of the most beautiful woman in the world. Hearing that, Paris instantly chose Aphrodite as the fairest goddess, earning him the hatred of Hera and Athena. His prize was the gorgeous Helen, incidentally a married woman. Her husband was Meneleus, king of Sparta, who would lead an alliance of Greek forces against the city of Troy to reclaim her.