# Sum of a set

Number Theory Level pending

Let $$A$$ be a set of the first $$n$$ natural numbers $$1,2,3,...,n$$. Given a subset $$B$$ of $$A$$, we call $$sum$$ $$of$$ $$B$$ to the sum of the elements of $$B$$. For instance, if $$B = \left\{ 3,4,6\right\}$$, then the sum of $$B$$ is equal to $$3+4+6=13.$$ The set $$A$$ is going to be split up in 12 disjoint not empty subsets with the same $$sum$$. Find the minimum natural number $$n$$ that satisfies the condition.

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