Memristor networks are capable of low-power and massive parallel processing and information storage. Moreover, they have presented the ability to apply for a vast number of intelligent data analysis applications targeting mobile edge devices and low power computing. Beyond the memory and conventional computing architectures, memristors are widely studied in circuits with increased intelligence, capable to tackle with complex problems in a power and area efficient manner, offering viable solutions often arriving from the biological principles of living organisms. In this paper, a memristive circuit exploiting the dynamics of oscillating networks is utilized for the resolution of Sudoku puzzles. More specifically, the proposed circuit design methodology is able of using the advantages of interconnections in a oscillation network and memristor's switching dynamics resulting to logic-solvable puzzle-instances. The reduced complexity of the proposed circuit and its increased scalability constitute its main advantage against previous approaches and the broadly presented SPICE based simulations provide a clear proof of concept of the aforementioned appealing characteristics.