This paper advocates a programming methodology using message passing. Efficient programs are derived for fast exponentiation, merging ordered sequences, and path existence determination in a directed graph. The problems have been proposed by John Reynolds as interesting ones to investigate because they. illustrate significant issues in programming. The methodology advocated here is directed toward the production of programs that are intended to execute efficiently in a computing environment with many processors. The absence of the COTO construct does not seem to be constricting in any respect in the development of efficient programs using the programming methodology advocated here.