In this work, we describe a logic device in which an act of computation is associated with finding a path connecting input and output ports. The device is based on an active ring circuit comprising electric and magnetic parts. The electric part includes an amplifier, a phase shifter, and an attenuator. The magnetic part is a multi-port magnetic matrix comprising delay lines and frequency filters. Signals propagating on different paths may accumulate different phase shifts. Auto-oscillations occur in the circuit when the magnetic and electric parts match each other to meet the resonance amplitude and phase conditions. The system naturally searches for a resonance path that depends on the position of the electric phase shifter and amplification level. The path is detected by the set of power sensors. The proposed logic device can be used for solving a variety of computational problems. We present the results of numerical modeling illustrating prime factorization and finding the shortest path connected selected points on the mesh. We also present experimental data on the proof-of-the-concept experiment for the two-path device. The magnetic part consists of two waveguides made of single-crystal yttrium iron garnet Y3Fe2(FeO4)3 (YIG) films. Different phase shifts per delay line are achieved by adjusting the magnitude and direction of the bias magnetic field. The auto-oscillation signal changes the propagation path in the magnetic matrix depending on the position of the outer electric phase shifter. The power difference between the active and passive paths exceeds 40 dBm at room temperature. The described logic devices are robust, deterministic, and operate at room temperature. The number of possible paths increases factorial with the size of the mesh. It may be possible to encode information in paths and retrieve it using the external phase shifters and attenuators. Potentially, combinatorial logic devices may compete with quantum computers in functional throughput. Physical limits and constraints are also discussed.