In this paper a methodology is described to estimate multigroup neutron source distributions which must be added into a subcritical system to drive it to a steady state prescribed power distribution. This work has been motivated by the principle of operation of the ADS (Accelerator Driven System) reactors, which have subcritical cores stabilized by the action of external sources. We use the energy multigroup two-dimensional neutron transport equation in the discrete ordinates formulation (S N ) and the equation which is adjoint to it, whose solution is interpreted here as a distribution measuring the importance of the angular flux of neutrons to a linear functional. These equations are correlated through a reciprocity relation, leading to a relationship between the interior sources of neutrons and the power produced by unit length of height of the domain. A coarse-mesh numerical method of the spectral nodal class, referred to as adjoint response matrix constant-nodal method, is applied to numerically solve the adjoint S N equations. Numerical experiments are performed to analyze the accuracy of the present methodology so as to illustrate its potential practical applications.