The focus of this study is on the role of achievement goals in students' persistence. The authors administered 5 puzzles to 96 college students: 4 unsolvable and 1 relatively easy (acting as a hope probe). They examined whether and how persistence may deteriorate as a function of failing the puzzles, as well as whether and how persistence may rebound after an event of success. Time spent engaging in the task comprised the dependent variable persistence (representing a behavioral aspect of engagement). Results suggested that mastery-oriented students persisted significantly longer compared with performance approach-oriented, performance avoidance-oriented, and amotivated students across failure trials. However, performance approach-oriented students were more likely to rebound after experiencing success. Qualitative data provided insights into the affective processes that accompanied engagement with the task. (Contains 3 tables, 1 footnote, and 2 figures.)