Tower of Hanoi has become a popular tool in cognitive and neuropsychology to assess a set of behaviors collectively referred to as executive functions. Substantial variability in performance on the Tower of Hanoi (TOH) disk-transfer task among normally functioning young adults, and potential contributions to these individual differences, were examined. In this expanded 60-problem version of the four-disk TOH, the degree to which problem administration (blocked vs. random) and strategy knowledge influenced overall performance and changes in accuracy across problems was examined. Eighty-seven college students were randomly assigned to a Blocked Group (problems given in ascending order of move-length) and a Random Group (problems given in a random order). After administration of the TOH task, participants described their problem solving and these verbal protocols were analyzed with regard to four elements of a strategic approach to problem solving. Problem administration order demonstrated no effect on task performance or on expressed strategy knowledge; however, strategy knowledge did predict performance on the TOH. An expected decrease in performance across trials was observed in the Blocked Group, and an increase in accuracy in the Random group indicated a learning effect. Strategy knowledge did not interact with these changes in performance across the items. These results suggest that external cues do not influence performance on the TOH to the same extent as individual differences in strategy induction relatively early in the problem solving process.