We present a novel Tantalum oxide based Memristor Cellular Neural Network (M-CellNN) configuration comprising only two cells, devised to tackle multiple logic challenges with the same architecture. The distinguishing feature of this setup lies in its adaptable nature, wherein the type of logic gate implemented (AND, OR, or XOR) is exclusively dictated by the initial states of the memristors. The memristors' malleable state, modifiable via current flow, facilitates dynamic manipulation, allowing for the adjustment of initial conditions and consequently, a shift in the circuit's functionality. To optimize the parameters of this dynamic system, contemporary machine learning techniques, particularly gradient descent optimization, was employed. Through a detailed case study, we illustrate the potential of harnessing intricate circuit dynamics to broaden the range of problems solvable with a predefined number of neurons. This in-vestigation not only underscores the importance of adaptability in logical circuits but also showcases the effectiveness of memristive elements in augmenting problem-solving capabilities. Notably, this study represents the first demonstration of the reconfigurable implementation of various logic gates using an existing memristor model, specifically a tantalum oxide memristor.