Selfish shellfish

A subset of \(\{1,2,\ldots, 12\}\) is said to be selfish if it contains its size as an element. How many subsets of \(\{1,2,\ldots 12\}\) have the property that both the subset and its complement is selfish?

Details and assumptions

As an explicit example, the set \(\{3,6,9\}\) is selfish because it contains 3 elements, and contains the element 3.

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