A discrete mathematics problem by Alejandro Castillo

Discrete Mathematics Level 4

Given a set \(A\) has \(n\) elements, namely \( \{1,2,3, \ldots , n \} \). If you want to divide this set in 12 subsets (no empty) such that the sum of each subset of \(A\) is the same, what is the smallest possible value of \(n\)?