Math the Magic

Find the next number in the sequence

5 12 24 36 ?




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There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
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The day before the 1996 U.S. presidential election, the NYT Crossword contained the clue “Lead story in tomorrow’s newspaper,” the puzzle was built so that both electoral outcomes were correct answers, requiring 7 other clues to have dual responses.