Explorative behavioural analysis of the Tower of London puzzle: influence of structural parameters and iso-problems

The Tower of London (ToL) puzzle, a testing method to assess planning and problem solving abilities, has been employed in many variants and with a variety of tasks and performance measures so that a comparison across studies is hardly possible. In the present study we used a computerized ToL on an easy-to-handle tablet PC and followed the physical appearance, instructions given, and the selection of tasks according to Shallice's original version. We added tasks with 6, 7, and 8 moves that allow a further investigation of specific configurations, summing up to 22 tasks in total. With the goal of providing normative data of nonclinical controls we tested 81 healthy subjects (40 young participants, aged 20–45 years, and 41 older subjects, aged 46–70 years). A broad set of performance measures was employed, including the Total Moves that subjects required, the Efficiency Value, the Solution Time needed for solving a given problem along with its distinction of Initiation Time and Completion Time. Our analysis revealed that younger subjects were significantly faster in solving a given task. However, as there was no significant difference in the Mean Initiation Time, it seems reasonable that older subjects only needed more time to execute the movements (Completion Time). We found that the Number of Perfectly Solved Tasks is positively correlated with the Mean Initiation Time and negatively correlated with the Mean Completion Time, which strengthens the idea that a longer mental preplanning, in contrast to an “online“ planning, has an impact on the accuracy of the solution. An investigation of the moves and times showed that, in general, tasks with a higher minimum number of moves are less likely to be solved perfectly and require a longer Solution Time. Since we found performance differences between tasks even with the same number of minimum moves, we suggested that structural parameters, determined by the specific start and ending configuration of the task, also play an important role. Furthermore, we investigated yet little studied isomorphic problems, i.e. tasks which share an identical sequence of ball moves to solve but differ in the colour of the balls which are transformed (Berg & Byrd, 2002; Faber et al., 2007). Our findings supports the suggestion that subjects are not aware of the similarity of such iso-problems but problem solvers' performance significantly improves with experience, which is different from a general learning effect.