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The dynamics of search, impasse, and representational change provide a coherent explanation of difficulty in the nine-dot problem

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Abstract

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.

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Notes

  1. It does not follow that reaching impasse on a problem automatically produces a representational change (i.e. insight), since this is not always the case (Jones, 2003). Equally, whether insight is achieved and if so how quickly it is achieved depends on multiple factors, such as the difficulty of a change to the problem representation and how large the problem space is (Knoblich et al., 1999; Kershaw et al., 2013).

  2. This point was raised by an anonymous reviewer.

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Acknowledgments

This research was made possible by a grant from the German Research Foundation (DFG) KN-489/6–2.

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Authors and Affiliations

  1. Parmenides Center for the Study of Thinking, Parmenides Foundation, Kirchplatz 1, 82049, Pullach by Munich, Germany

    Michael Öllinger

  2. Ludwig-Maximilians-University, Munich, Germany

    Michael Öllinger

  3. Nottingham Trent University, Nottingham, UK

    Gary Jones

  4. Central European University, Budapest, Hungary

    Günther Knoblich

Authors
  1. Michael Öllinger
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  2. Gary Jones
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  3. Günther Knoblich
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Correspondence to Michael Öllinger.

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Öllinger, M., Jones, G. & Knoblich, G. The dynamics of search, impasse, and representational change provide a coherent explanation of difficulty in the nine-dot problem. Psychological Research 78, 266–275 (2014). https://doi.org/10.1007/s00426-013-0494-8

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  • DOI: https://doi.org/10.1007/s00426-013-0494-8

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