[The whole and its parts: solution logic of the 9-point problem]

The ill-defined nine-dot problem is reanalysed to provide a new theoretical perspective for this old problem. In particular, the theory shows how the functional fixedness of the dots can be overcome and the correct solution obtained by a process of logic. The perspective develops ideas from holistic and gestalt psychology, and shows how an entity defines its parts by demanding particular functions and how the parts in turn define the entity by the functions they serve. One central result for problem solving is the partition of processes into processes of composition and decomposition, thus leading to a theoretical foundation for the rule-governed process of planning backwards that contains both top-down and bottom-up processes. The theory is exemplified by providing a detailed account of the solution of the problem.