The generalized maze problem has been considered as an interesting testbed by various researchers in AI and neural networks. The most significant results, from a neural network point of view, were: 1. Simultaneous recurrent networks are necessary if a neural network-based cellular automaton approach to the problem is to be successful.2. These networks can be designed so that convergence to a correct solution is assured.Here, a simple closed-form solution for the critic is shown, making adaptation unnecessary. Furthermore, it is shown that the design converges to the correct solution in only J steps, and the worst case convergence speed for an N x N mesh is derived.