Abstract: 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.
Keywords: Tower of Hanoi, Tower of London, mathematical model, graph
