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Normal AB MAA names with sets of integers

Source: AIME II 2024 Problem 6

February 8, 2024
AMCAIMEAIME II

Problem Statement

Alice chooses a set AA of positive integers. Then Bob lists all finite nonempty sets BB of positive integers with the property that the maximum element of BB belongs to AA. Bob's list has 20242024 sets. Find the sum of the elements of AA
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