This paper is an extension to what the author had already done in [1] and [2]. In this paper we will see one solution to the XOR problem using minimum configuration MLP an ANN model. The proposed solution is proved mathematically in this paper. The problem of non-linear separability is addressed in the paper. The Architectural Graph representation of the proposed model is placed and also an equivalent Signal Flow Graph is represented to show how the proof the proposed solution. The non-linear Activation function used for the hidden layer minimum configuration MLP is Logistic function. (C) 2015 The Authors. Published by Elsevier B.V.