# Impossible Decagon

Geometry Level 5

Let $$D$$ be the set of all of the multisets containing 10 positive integers such that these integers cannot be the side lengths of a decagon. If $$A$$ is a set in $$D$$ and $$S(A)$$ is the sum of the elements of $$A$$, find the smallest value that $$S(A)$$ can have.

A multiset is an unordered collection of elements that may repeat; compare this with a set, which may not repeat elements, or with a sequence, which is ordered.

Bonus: Can you generalize this for the $$n$$-gon?

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