A complementary set of stereochemically controlled approaches to the preparation of twelve diastereomers of the bistetrahydrofurans 11 is described. The key transformation involves a series of nucleophilic displacement reactions within triepoxides 19-the "end-to-end" triepoxide cascade reaction-which leads, presumably via 22 and 23, after acetylation to bistetrahydrofuran tetraacetates 24. The "inside-out" cyclization of 30 exemplifies a useful variation with significant stereochemical consequences. The role of symmetry in these approaches is discussed. A general mathematical analysis for conceptualizing isomer distribution within multistep sequences is presented.