TEST

Tower of Hanoi (ToH)

Planning, working memory, and procedural learning

Digital version of the classic subgoal-based problem-solving task. With four subtests (3 and 4 disks, two attempts each), it makes it possible to separate initial planning from procedural learning, a critical dissociation for dysexecutive profiles.

Request a demo

View SPAIn battery

4

SUBTESTS (3 and 4 disks, x2)

7

OPTIMAL SOLUTION (3 disks)

15

OPTIMAL SOLUTION (4 disks)

Δ

LEARNING ATTEMPT 1 vs. 2

WHAT THE TEST IS

The classic paradigm for assessing strategic thinking

Despite having more than a century of history, the Tower of Hanoi remains one of the most widely used neuropsychological tests for assessing planning, working memory, and subgoal-based problem solving. It requires keeping a rule active (not placing larger disks on smaller ones), anticipating consequences, and sequencing moves toward a goal.

Digital administration introduces a fundamental advance: repeating each configuration twice. This makes it possible to calculate a procedural learning index that distinguishes, for example, poor planning with preserved learning (typical of moderate TBI) from a deficit that remains even after practice (more characteristic of schizophrenia or dementias). Sensitive to frontal, basal ganglia, and cerebellar dysfunction.

HOW IT IS ADMINISTERED

Move the disks while respecting the size rule

Three vertical rods and a set of disks of decreasing sizes in an initial position. The user must move all the disks to the target rod while preserving the pyramid (large at the bottom, small at the top). Single rule: never place a larger disk on top of a smaller one.

Administration consists of up to 4 subtests: ToH 3 disks, ToH 4 disks, ToH 3 disks (repetition), and ToH 4 disks (repetition). The professional decides which ones to administer; the comparison between the first and second attempt provides the procedural learning index. Interaction is by tapping: tap the disk to be moved, then the destination rod.

WHAT THE TEST MEASURES

Indicators and their interpretation

Each subtest provides time, number of moves, and errors. Its true clinical power lies in the comparison between attempts to estimate procedural learning.

Number of moves

Total number of moves made, compared with the optimal minimum (7 for 3 disks, 15 for 4 disks). A direct measure of planning efficiency.

Close to optimal: effective planning.
Far above optimal: trial and error, executive deficit, reversals due to working memory failure.

Total time

Seconds from the first move to completion. Integrates planning, processing, and execution speed.

High time + many moves: executive inefficiency.
High time + optimal: careful reflectiveness, acceptable.

Mean time between moves

Continuous cognitive latency: how much the user thinks between moves. Makes it possible to distinguish reflectiveness from impulsivity or indecision.

High: deliberate planning or hesitation.
Low + errors: impulsivity.
Low + optimal: internalized plan.

Size errors

Attempts to place a larger disk on a smaller one. Reflect failures in inhibitory control, rule maintenance, or monitoring.

0–1: rule respected.
Many errors: executive deficit, especially if repeated after feedback.

Procedural learning (3p)

Difference in moves between the first and second attempt with 3 disks. An exclusive metric of this digital version.

Large positive Δ: robust learning (typical of mild TBI, mild MS).
Δ close to 0: does not extract a strategy from the first attempt.

Procedural learning (4p)

Equivalent difference with 4 disks. More sensitive to impairment, since greater complexity makes the planning/learning dissociation evident.

Marked improvement: preserved procedural learning.
Negative Δ: worsening (fatigue, frustration, or severe impairment).

REFERENCES

Bibliography

Goldberg, T. E., Saint-Cyr, J. A., & Weinberger, D. R. (1990). Assessment of procedural learning and problem solving in schizophrenic patients by Tower of Hanoi type tasks. Journal of Neuropsychiatry and Clinical Neurosciences, 2(2), 165–173.
Welsh, M. C., Satterlee-Cartmell, T., & Stine, M. (1999). Towers of Hanoi and London: Contribution of working memory and inhibition to performance. Brain and Cognition, 41(2), 231–242.
Knapp, F., & Morton, J. B. (2017). Examining the relations between performance on the Tower of Hanoi and executive functions. Journal of the International Neuropsychological Society.
Bull, R., Espy, K. A., & Senn, T. E. (2004). A comparison of performance on the Towers of London and Hanoi. Journal of Child Psychology and Psychiatry, 45(4), 743–754.
Strauss, E., Sherman, E. M. S., & Spreen, O. (2006). A compendium of neuropsychological tests (3rd ed.). Oxford University Press.