Find all integers $ n \ge 2 $ for which it is possible to divide any triangle $ T $ in triangles $ T_1, T_2, \cdots, T_n $ and choose medians $ m_1, m_2, \cdots, m_n $, one in each of these triangles, so that these $ n $ medians have equal length.
Source: Peru Ibero TST 2018
Tags: combinatorics
Find all integers $ n \ge 2 $ for which it is possible to divide any triangle $ T $ in triangles $ T_1, T_2, \cdots, T_n $ and choose medians $ m_1, m_2, \cdots, m_n $, one in each of these triangles, so that these $ n $ medians have equal length.