A method, Predictive Array Design, is presented for sampling combinatorial chemistry space and selecting a subarray for synthesis based on the experimental design method of Latin Squares. The method is appropriate for libraries with three sites of variation. Libraries with four sites of variation can be designed using the Graeco-Latin Square. Simulated annealing is used to optimise the physicochemical property profile of the sub-array. The sub-array can be used to make predictions of the activity of compounds in the all combinations array if we assume each monomer has a relatively constant contribution to activity and that the activity of a compound is composed of the sum of the activities of its constitutive monomers.