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Abstract Successful problem solving relies on the availability of suitable mental representations of the task domain. Especially for more complex problems, there might be a wide variety of possible problem representations, and it might even be beneficial to change them during problem solving. In a first part, we argue that investigating the dynamics of understanding in terms of dynamically changing problem representations is an underexplored aspect of problem solving research, and that most classic tasks even preclude the opportunity of such dynamics to occur. Continuing this theoretical discussion, as an illustrative example of a task designed for the exploration of such representational dynamics, the second part of the paper discusses a novel, complex spatial transformation and problem solving task. In this task, one is asked to repeatedly mentally cross-fold a sheet of paper, and to predict the resulting sheet geometry without the use of external aids. Through its deliberate openness and difficulty, this task requires finding new and more efficient representations – ranging from kinaesthetic and visuospatial imagery to symbolic notions. We present an overview of the task domain and discuss various ways of representing the domain as well as potential dynamics between them. [ABSTRACT FROM AUTHOR]