The problem of designing molecules or compounds with desired properties is complex primarily because it is combinatorial. A novel approach is proposed here by resorting to a combinatorial analysis of the problem. It is supposed that the set of functional groups is available and that the intervals of values of the desired properties of the molecule or compound to be designed are known. The desired properties constitute constraints on the integer variables assigned to the functional groups. The feasible region defined by such constraints is determined by an algorithm involving a branching strategy. This algorithm generates those collections of the functional groups that can constitute structurally feasible molecules or compounds satisfying the constraints on the given properties. The efficacy of the approach has been demonstrated with several examples.