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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