Understanding problem solving or planning has been a shared challenge for both AI and cognitive science since the birth of both fields. We explore the extent to which modern planners from the field of AI can account for human performance on the Tower of London (TOL) task, a close relative of the Tower of Hanoi problem that has been extensively studied by psychologists. We characterize the task using the Planning Domain Definition Language (PDDL) and evaluate an adaptive online planner and a family of well-known planners, including online planners, optimal planners and satisficing planners. Each planner is evaluated based on its ability to predict the actions and planning times of participants in a new behavioral experiment. Our results suggest that participants use a range of strategies but that an adaptive lookahead planner provides the best overall account of both human actions and human planning times. This finding is consistent with the view that humans differ from standard AI planners by integrating a mechanism for evidence accumulation.