The nine-dot problem is often used to demonstrate and explain mental impasse, creativity, and out of the box thinking. The present study investigated the interplay of a restricted initial search space, the likelihood of invoking a representational change, and the subsequent constraining of an unrestricted search space. In three experimental conditions, participants worked on different versions of the nine-dot problem that hinted at removing particular sources of difficulty from the standard problem. The hints were incremental such that the first suggested a possible route for a solution attempt; the second additionally indicated the dot at which lines meet on the solution path; and the final condition also provided non-dot locations that appear in the solution path. The results showed that in the experimental conditions, representational change is encountered more quickly and problems are solved more often than for the control group. We propose a cognitive model that focuses on general problem solving heuristics and representational change to explain problem difficulty.Keywords: Nine-Dot Problem, Insight, Heuristics, Search, Representational Change Nine-dot problem 3There is growing evidence that an insight to the solution of a problem can be characterized by a representational change (Knoblich, Ohlsson, Haider, & Rhenius, 1999;Ohlsson, 1984aOhlsson, , 1992Öllinger, Jones, & Knoblich, 2008;Thevenot & Oakhill, 2008). This evidence makes it difficult to explain insight problem solving within the classical information-processing account (Newell & Simon, 1972), where problem solving is understood as search within a well-defined problem space (problem representation). The problem space account has no mechanism to implement a representational change for instances when the current search gets stuck, is insufficient, or does not reduce the distance to the desired goal.There are a few accounts that attempt to remedy this omission. One suggestion is to claim that insight problems are nothing special and therefore representational change plays only a marginal role. For such explanations, problem difficulty relates either to the size of the problem space being overly large and preventing exhaustive search (Kaplan & Simon, 1990), or that problem solvers apply inappropriate heuristics when searching the problem space Ormerod, MacGregor, & Chronicle, 2002). Both accounts miss a cognitive process that addresses the change of the search space. In the first, an additional process is necessary that re-focuses on particular areas of the search space by changing the problem representation; in the second an additional cognitive process is required that changes the search space after repeated failures of the problem solving process.Ohlsson (Knoblich et al., 1999;Ohlsson, 1984aOhlsson, , 1984bOhlsson, , 1992) provided a detailed framework that stressed the importance of a representational change for insight problem solving, and identified impasse as a crucial pre-condition. Moreover, Ohlsson (1992) identified at least three ...