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Eight applications of the Random-Choice Method (RCM) to the solution of problems in shock and detonation-wave dynamics are presented. It is shown that unlike other numerical methods, the RCM yields sharp-fronted shocks and contact surfaces without resorting to artificial and perhaps erroneous means of predicting their locations. It has been shown by examples that the RCM provides exceptionally high computational accuracy for flows involving planar and spherical shock waves, rarefaction waves and contact surfaces, as well as their interactions. In addition, the RCM can handle flows with detonations and chemical reactions involving the above transition fronts.