Details of the quantitative techniques successfully applied to artificial rock mixtures distributed for the third Clay Minerals Society Reynolds Cup (RC) contest are presented. Participants each received three samples, two containing 17 minerals each and a third containing ten minerals. The true composition of the samples was unknown to all participants during the contest period. The results submitted were ranked by summing the deviations from the actual compositions (bias). The top three finishers used mainly X-ray diffraction (XRD) for identification and quantification. The winner obtained an average bias of 11.3% per sample by using an internal standard and modified single-line reference intensity ratio (RIR) method based on pure mineral standards. Full-pattern fitting by genetic algorithm was used to measure the integrated intensity of the diagnostic single-line reflections chosen for quantification. Elemental-composition optimization was used separately to constrain phase concentrations that were uncertain because the reference mineral standards were lacking or not ideal. Cation exchange capacity, oriented-sample XRD analysis, and thermogravimetric analysis were also used as supplementary techniques. The second-place finisher obtained an average bias of 13.9%, also by using an RIR method, but without an added internal standard and with intensity measured by whole-pattern fitting. The third-place finisher, who obtained an average bias of 15.3%, used the Rietveld method for quantification and identification of minor phases (using difference plots). This participant also used scanning electron microscopy (with X-ray microanalysis) to identify minor components and verify the composition of structures used in Rietveld analysis. As in the previous contests, successful quantification appears to be more dependent on analyst experience than on the analytical technique or software used.