Towers of Hanoi and London on a tablet-PC: correlations with other executive tests

We have developed computerised versions on a tablet PC for the popular executive function tests Tower of Hanoi (ToH) and Tower of London (ToL) (Hinz et al., 2007). They simulate the original wooden games in a realistic manner so they can be used at the bedside. In addition to timing each step, the program documents the solution pathway chosen and visualises it in a state graph.

We analysed the two tower puzzles for possible performance differences and compared them with other executive function tests.

62 controls (44 female) from two age groups (20–45 years, mean 29.1; 46–70 years, mean 57.8) had to solve 20 tasks for each Tower in a fixed sequence, each differing in the level of difficulty. The first twelve ToL tasks were Shallice's original tasks (1982). We added a number of 6- and 7-move tasks to increase the level of difficulty. The ToH tasks were comparable in the start and end positions as well as in the optimal solution pathway. Performance was analysed in terms of solution times, initiation times, completion times and moves. Subjects had to solve one puzzle at the beginning and the other at the end of the testing session in a randomised order to see if there is a mutual influence among the puzzles. We also tested short-term and working memory (digit and visual span forward and backward, WMS-R), cognitive flexibility (Trail Making Tests A and B), verbal and design fluency (animals, S-words, 5-Point-Test) and abstract reasoning (Matrices Test, WAIS).

In general, both age groups needed more time for the solution of the ToL in comparison to the ToH and they needed less time to solve the second puzzle. There were significant differences between the two groups in total solution and completion times for almost all tower tasks. Number of moves correlates with completion time for all tasks but not with the initiation time, except for three 6-move tasks of the ToL. There are also significant correlations for total solution and completion times of both puzzles with the TMT A and B, digit span backward, the Matrices Test and the 5-Point-Test.

The correlations of the ToH and ToL with cognitive flexibility, working memory, abstract reasoning and design fluency show that the two puzzles tap different aspects of executive function. This is supported by the observation of performance differences among tasks with very similar solution paths.