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Behavioural Neurology
Volume 25 (2012), Issue 1, Pages 13-22

Graph Theory of Tower Tasks

Andreas M. Hinz1,2

1Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstraße 39, 80333 München, Germany
2Fakultät für Mathematik und Informatik, Fern Universität in Hagen, Lützowstraße 125, 58095 Hagen, Germany

Received 26 December 2011; Accepted 26 December 2011

Copyright © 2012 Hindawi Publishing Corporation and the authors. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The appropriate mathematical model for the problem space of tower transformation tasks is the state graph representing positions of discs or balls and their moves. Graph theoretical quantities like distance, eccentricities or degrees of vertices and symmetries of graphs support the choice of problems, the selection of tasks and the analysis of performance of subjects whose solution paths can be projected onto the graph. The mathematical model is also at the base of a computerized test tool to administer various types of tower tasks.