Direct and adjoint plane geometry diffusion solutions are combined to provide an inverse method for determining multigroup cross sections and diffusion coefficients; for the equations to work, one group constant for each group must be known. The equations are linear and independent of the slab thickness and require that only the fluxes on the boundaries be measured for a set of experiments with known ingoing currents. The accuracy of the method has been numerically checked using analytical solutions. Another application of the method is to determine the relative concentration of one or more isotopes in a mixture of isotopes whose microscopic cross sections are known.