By using ill-structured problems and examining problem- solving processes, this study was conducted to explore the nature of solving complex, multistep problems, focusing on how prior knowledge, problem-solving process utilization, and analogical problem solving are related to success. Twenty-four college students qualified to participate by virtue of 100% performance on the Test for Requisite Mathematical Knowledge. Stimulus problems were from "The Adventures of Jasper Woodbury," a video- based problem-solving series. Subjects worked independently to reach problem solutions and explained how they arrived at the solution. Two to four weeks later, subjects watched a second scenario with an analogous problem. Protocols were produced from the subjects' audio and video taped responses. Prior mathematical knowledge as defined in this study was necessary, but not solely sufficient for solving the two problems. Highly successful subjects spent more time on the problems than subjects in other levels, and minimally successful subjects spent the most time setting long-range plans and the least time setting immediate plans. It appears that the experience of dealing with the initial problem may have shaped how problem-solving processes were used on the later analogous problem. Engagement in the initial problem also appears to increase success on the analogous problem. (Contains 16 references.) (SLD)