Influence of instructions on performance in the Tower of Hanoi and Tower of London puzzles

The Tower of Hanoi (ToH) and Tower of London (ToL) are well-established problem-solving tasks that explore cognitive skills presumably mediated by the frontal cortex. We have developed computerized versions of ToH and ToL and use these to tap planning and problem solving skills (Hinz et al. 2007). Certain instructions appear to favour approaches to problem solving such as “hill climbing“ at the cost of planning ahead.

We specifically addressed the question whether a “planning“ instruction (“find the perfect/shortest solution before beginning the moves“) leads to more efficient performance. Subjects were specifically told to start only when they felt certain to be able solve the task in the explicitly stated minimal number of moves that define a perfect solution. We analysed ToH and ToL performance under this instruction in comparison to an “unlimited“ instruction to solve the problems irrespective of the number of moves.

67 healthy participants successively completed 20 ToH and 20 ToL tasks with difficulty graded according to minimum number of moves required (2 tasks each with 2 and 3 moves, 4 tasks each with 4, 5, 6, and 7 moves). Performance measures (mean solution time, mean initiation time, mean completion time, total moves) of 38 subjects (22 to 38 years: 27,8±3,9; 20 females) who had received the “planning“ instruction were compared with those of 29 subjects (20 to 37 years: 27,2±5,0; 16 females) under the “unlimited moves“ instruction. The “planning“ instruction group had predominantly a high level of education (10 to 21 years: 16,71±2.54). The time-limited instruction group had mainly a medium level of education (12 to 18: 13,79±1,74). There were no significant group differences with respect to additional psychometric measures such as verbal and visual memory span. The “planning“ instruction group showed a significantly longer initiation time than the “unlimited moves“ instruction group and required significantly fewer moves only in two 6-moves ToL tasks, one 7-moves ToL task and a single 5-moves ToH task (p<0.05). There were no significant group differences for other tasks.

Unsurprisingly, the “planning“ instruction caused a longer initiation time devoted to that activity. Since it did not generally improve performance, however, the act of planning ahead does not necessarily cause greater solution efficiency. The nature of mental preplanning in the ToL and ToH task is therefore questionable.