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A new and simple winner-take-all neural subnetwork suitable for VLSI CMOS implementation is proposed. The subnetwork is used for the real-time solving of minimax optimisation problems. In particular, the Letter shows how to solve, in real time, an over-determined system of linear equations by using the Chebyshev Linfinity norm criterion and a neural network approach. The validity and performance of the network have been checked by extensive computer simulation of different minimax optimisation problems.