T-TT conversion

\(R_1 = 2 \Omega\), \(R_2 = 3 \Omega\) and \(R_3 = 6 \Omega\) are resistors interconnected with one common node while remained with 3 terminals named 1, 2 and 3 which are not externally connected. The equivalent circuit with same resultant resistances to replace them are resistors named \(R_{12}\), \(R_{23}\) and \(R_{31}\) of which each of them is connected to 2 among 3 terminals of exactly 3 distinct combinations or selections. What is the sum of resistances such that \(R_{12} + R_{23} + R_{31}\)in \(\Omega ?\)

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