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Counting sets that contain their cardinality

Source: Moldova TST Problem 8

April 1, 2015
combinatoricscountingSubsets

Problem Statement

Consider a positive integer nn and A={1,2,...,n}A = \{ 1,2,...,n \}. Call a subset X⊆AX \subseteq A perfect if ∣X∣∈X|X| \in X. Call a perfect subset XX minimal if it doesn't contain another perfect subset. Find the number of minimal subsets of AA.
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