Computer simulations of a simple model of a reversible diffusion-influenced reaction are used to test various approximate theoretical treatments. The model is a random walk in continuous time of N particles on a one-dimensional lattice. The particles can be trapped reversibly at the origin. They move independently, except that only one particle at a time can occupy the origin. The theory is formulated in general terms using master equations for the probability distribution of occupancy numbers of different lattice sites. The general theoretical problem is not solved, although some exact consequences are presented. Several approximation schemes are described and tested by comparison with the simulations.