This paper proposes a theoretical framework of distributed representations and a methodology of representational analysis for studying distributed cognitive tasks—tasks that require processing information across the internal mind and external environment. The key idea is that distributed representations involve both internal and external components, which together represent the abstract structure of the task. Representational analysis involves decomposing hierarchical tasks into levels to examine their properties independently. The framework is applied to the Tower of Hanoi (TOH) problem, which is analyzed to understand how different representations affect cognitive behavior. The paper discusses the representational effect, where different isomorphic representations of the same structure can lead to different cognitive behaviors. For example, Arabic numerals are more efficient than Roman numerals for multiplication. The TOH problem is used to illustrate how internal and external representations interact. The study shows that the nature of external representations is crucial, as they can be embedded in physical configurations or cultural knowledge. The paper also explores the hierarchical structure of the TOH problem, identifying four levels: problem space structures, rule representations, dimensional representations, and object representations. Each level has abstract structures that can be implemented by different representations. The study uses the TOH to examine how different representations affect problem-solving behavior. In Experiment 1A, the effect of internal rules on problem-solving was studied. The results showed that the number of rules influenced problem difficulty, with more rules sometimes making the problem easier. In Experiment 1B, the effect of external rules was examined, and the results indicated that external rules could make problems easier. Experiment 2 further explored how the distribution of rules between internal and external representations affected problem-solving, showing that more external rules led to easier problems. The study concludes that distributed representations and representational analysis are essential for understanding cognitive tasks. The findings highlight the importance of considering both internal and external representations in cognitive tasks and how their distribution affects problem-solving behavior.This paper proposes a theoretical framework of distributed representations and a methodology of representational analysis for studying distributed cognitive tasks—tasks that require processing information across the internal mind and external environment. The key idea is that distributed representations involve both internal and external components, which together represent the abstract structure of the task. Representational analysis involves decomposing hierarchical tasks into levels to examine their properties independently. The framework is applied to the Tower of Hanoi (TOH) problem, which is analyzed to understand how different representations affect cognitive behavior. The paper discusses the representational effect, where different isomorphic representations of the same structure can lead to different cognitive behaviors. For example, Arabic numerals are more efficient than Roman numerals for multiplication. The TOH problem is used to illustrate how internal and external representations interact. The study shows that the nature of external representations is crucial, as they can be embedded in physical configurations or cultural knowledge. The paper also explores the hierarchical structure of the TOH problem, identifying four levels: problem space structures, rule representations, dimensional representations, and object representations. Each level has abstract structures that can be implemented by different representations. The study uses the TOH to examine how different representations affect problem-solving behavior. In Experiment 1A, the effect of internal rules on problem-solving was studied. The results showed that the number of rules influenced problem difficulty, with more rules sometimes making the problem easier. In Experiment 1B, the effect of external rules was examined, and the results indicated that external rules could make problems easier. Experiment 2 further explored how the distribution of rules between internal and external representations affected problem-solving, showing that more external rules led to easier problems. The study concludes that distributed representations and representational analysis are essential for understanding cognitive tasks. The findings highlight the importance of considering both internal and external representations in cognitive tasks and how their distribution affects problem-solving behavior.