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The Tower of Hanoi is a simple mathematical puzzle often employed for the assessment of problem-solving and in the evaluation of frontal lobe deficits. The task allows researchers to observe the participant’s moves and problem-solving ability, which reflect the individual’s ability to solve simple real-world problems.

The Qolty Mobile Assessments utilizes the Apple ResearchKit™ framework  to define a large number of predefined tasks in six broad categories: motor activities, fitness, cognition, voice, audio, and hand dexterity. We utilize these functions for your use in your study, making it easy to capture objectively reported data from your patients.

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Introduction

Cognitive control of behavior relies on a set of cognitive functions called executive functions. These functions are controlled by the frontal lobe of the brain which is involved with motivation, planning, social behavior, and speech production. Executive functions are divided into organization functions (information gathering and structuring) and regulation functions (behavioral responses based on the surroundings).

The Tower of Hanoi is a simple mathematical puzzle often employed for the assessment of problem-solving and in the evaluation of frontal lobe deficits. The task allows researchers to observe the participant’s moves and problem-solving ability, which reflect the individual’s ability to solve simple real-world problems. Deficits in problem-solving ability can have a serious impact on the quality of life of an individual and can also be a sign of impending disorders.

Methods

Conventionally, the Tower of Hanoi task uses three pegs and a set number of disk (usually 3) stacked in increasing order of size on the starting peg. The participant must move the disks, one by one, from the start peg to the destination peg using the buffer peg as an aid. The participant has an additional constraint during the task; a larger disk cannot be placed on a smaller disk. The participant must try to solve the puzzle in the minimum possible steps.

This task can be carried out using more number of disks or pegs to change the difficulty of the task. A derivative of the Tower of Hanoi is the Tower of London task which employs a similar problem-solving requirement.

Active Task: Tower of Hanoi

Apple’s ResearchKit uses the Tower of Hanoi active task to measure the participant’s problem-solving skill by measuring the number of moves. The puzzle is presented through a user-friendly interface on the individual’s iPhone and is solved by moving the entire stack to the highlighted platform. The task ends when the user has solved the puzzle or has conceded defeat.

Tower of Hanoi task instructions

  1. Hold the device or place it on a surface for optimal game performance.
  2. Begin the task.
  3. Move the stack to the highlighted platform in the minimum number of moves.
  4. Solve the puzzle successfully or concede the task.
  5. Task completed.

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Applications

Alzheimer’s disease

Balachandar et al., 2015 evaluated the age-related cognitive decline using the Tower of Hanoi task. 24 patients with mild Alzheimer’s were assessed for their planning capabilities. The task was carried out using a varying number of disk (2 to 5 disks). The patients showed extreme difficulty in completing the task and showed significantly poorer performance as the disk numbers were increased.

Post-Traumatic Stress Disorder

Yang et al., 2017 assessed the often-neglected neurocognitive functioning in cancer patients with PTSD. The executive function assessment was performed using 3 and 4 disks Tower of Hanoi. In comparison to healthy controls, a significant difference in performance was observed.

Emotional Intelligence

Arefnasab et al., 2012 compared the problem-solving capabilities of individuals with high emotional intelligence with those having low emotional intelligence. The study employed a four disks version of the task without the constraint “no larger disk should be placed on smaller disk.” The subjects were also not given any time constraints. A significant performance difference was found between the two groups, with the high emotional intelligence group making lesser errors and requiring lesser time for the task.

Schizophrenia

Goldberg et al., 1990 used 3 and 4 disks version of the Tower of Hanoi to assess learning and problem-solving capabilities in schizophrenic patients. In comparison to the control group, schizophrenic patients performed significantly worse. However, performance on the 4 disks Tower of Hanoi task was slightly better than in the 3 disks version in schizophrenic patients suggesting the ability to acquire a procedure and greater preservation of basal ganglia function.

Cerebellar Atrophy

Grafman et al., 1992 evaluated the performance of 12 patients with cerebellar atrophy using the 5 disks Tower of Hanoi task. Their performance was compared to healthy controls. Analysis of the scoring revealed that patients with cerebral atrophy performed significantly worse in the task. The patients solved fewer trials of the task and showed more tendency in making illegal moves.

Results and Data Analysis

Data collected from the Tower of Hanoi task include the total time taken to solve, the number of moves to solve, and the number of rule violations. Other aspects such as impulsivity to perform the task, eye movements and other observable behaviors can also be recorded by an examiner conducting the task.

The following graph depicts sample scores of controls versus schizophrenic patients in a 3 disks Tower of Hanoi task (Goldberg et al., 1990).

The following sample graph compares the total time taken by the controls and Alzheimer’s disease patients to complete 3 and 4 disks version Tower of Hanoi (Balachandar et al., 2015).

Strengths and Limitations

Strengths

The Tower of Hanoi is a simple mathematical puzzle that can easily assess the problem-solving capabilities of an individual. It is a widely used tool for the evaluation of planning and working memory abilities. The Tower of Hanoi puzzle is sensitive to prefrontal damage and dysfunction. The puzzles difficulty level can easily be increased or decreased with additional disks or pegs respectively.

Limitations

The Tower of Hanoi cannot be used standalone to understand and assess executive functions of the brain. It can be difficult to employ in individuals unable to cooperate with the process. Other factors such as sleep, anxiety, may also affect the performance.

Summary

  • Executive functions impact cognitive control and are controlled by the frontal lobe.
  • Executive functions are divided into organization functions (information gathering and structuring) and regulation functions (behavioral responses based on the surroundings).
  • The Tower of Hanoi is a mathematical puzzle involving pegs and different sized disks.
  • The puzzle is solved by moving the disk one by one from the start peg to the target peg keeping in mind not to place a larger disk over a smaller disk.
  • The Tower of Hanoi puzzle is often employed to assess frontal lobe deficits and executive function dysfunction.
  • The difficulty of the puzzle can be increased by adding additional disks.
  • The Tower of London is another puzzle similar in design and principle to the Tower of Hanoi.

References

Arefnasab Z, Zare H, Babamahmoodi A (2012). Emotional intelligence and problem solving strategy: comparative study based on “tower of hanoi” test. Iran J Psychiatry Behav Sci. 6(2):62-8.

Balachandar R, Tripathi R, Bharath S, Kumar K (2015). Classic Tower of Hanoi, Planning Skills, and the Indian Elderly. East Asian Arch Psychiatry. 25(3):108-14.

Goldberg TE, Saint-Cyr JA, Weinberger DR (1990). Assessment of procedural learning and problem solving in schizophrenic patients by Tower of Hanoi type tasks. J Neuropsychiatry Clin Neurosci. 2(2):165-73.

Grafman J, Litvan I, Massaquoi S, Stewart M, Sirigu A, Hallett M (1992). Cognitive planning deficit in patients with cerebellar atrophy. Neurology. 42(8):1493-6.

Ritter, S. (2014). Apples Research Kit Development Framework for iPhone Apps Enables Innovative Approaches to Medical Research Data Collection. Journal of Clinical Trials, 05(02). doi:10.4172/2167-0870.1000e120

Yang J, Guo J, Jiang X (2017). Executive function in cancer patients with posttraumatic stress disorder. Int J Psychiatry Med. 52(2):137-146. doi: 10.1177/0091217417720898.