This paper proposes a theoretical framework and methodology for studying distributed cognitive tasks, which involve processing information across both internal mind representations and external environmental representations. The authors introduce the concept of distributed representations, where the representational system of a task is a set of internal and external representations that together form an abstract structure of the task. The methodology of representational analysis involves decomposing the representation of a hierarchical task into its component levels to independently examine the representational properties at each level. The Tower of Hanoi (TOH) problem is used as a case study to illustrate these principles and methods. Four experiments are designed to examine the representational properties of the TOH, focusing on the interaction between internal and external representations, the nature of external representations, and the impact of rule representations. The results show that problem space structure, rule distribution, and dimensional representations significantly affect problem-solving behavior. Specifically, external rules can simplify problems, and the more rules are distributed externally, the easier the problem becomes. The study also highlights the importance of distinguishing between internal and external representations in understanding complex cognitive tasks.This paper proposes a theoretical framework and methodology for studying distributed cognitive tasks, which involve processing information across both internal mind representations and external environmental representations. The authors introduce the concept of distributed representations, where the representational system of a task is a set of internal and external representations that together form an abstract structure of the task. The methodology of representational analysis involves decomposing the representation of a hierarchical task into its component levels to independently examine the representational properties at each level. The Tower of Hanoi (TOH) problem is used as a case study to illustrate these principles and methods. Four experiments are designed to examine the representational properties of the TOH, focusing on the interaction between internal and external representations, the nature of external representations, and the impact of rule representations. The results show that problem space structure, rule distribution, and dimensional representations significantly affect problem-solving behavior. Specifically, external rules can simplify problems, and the more rules are distributed externally, the easier the problem becomes. The study also highlights the importance of distinguishing between internal and external representations in understanding complex cognitive tasks.