Executive Function
Tower of Hanoi
Also called: Towers of Hanoi, Tower of Hanoi puzzle, disk-transfer task
Measure planning by the moves over the minimum a person needs to move towers of three, four and five disks to another peg.
6-10 minUntimed
Free to start: 10 free participants per account, then $0.99 per participant for academic research, or any yearly plan. Preview any test free after you sign up.
- Papers, 2021 to 2025
- 106
- Evidence grade
- C
- Registered clinical studies
- 34
What it measures
A planning task with three pegs and a tower of disks of different sizes. Participants move the tower from the left peg to the right peg, one disk at a time and never onto a smaller disk, with three, four and five disks. Scores give the moves over the minimum, the time to the first move, puzzles solved and refused moves.
Constructs
- Planning
- Problem solving
- Goal and subgoal management
- Executive function
Research uses
- Executive function research
- Frontal lobe and neurological research
- Aging and development research
- Within-study group comparison
How the paradigm works
The Tower of Hanoi is a planning puzzle that Edouard Lucas published in 1883. Simon (1975) and Kotovsky, Hayes and Simon (1985) made it a standard task for studying how people solve problems, and Goel and Grafman (1995) used it to study planning after frontal lobe lesions. Three pegs stand in a row, and a tower of disks of different sizes sits on the left peg, the largest at the bottom. Participants move the whole tower to the right peg. Only the top disk of a peg can move, one disk at a time, and a disk can never go onto a smaller disk. Participants click or tap a peg to pick up its top disk and then another peg to put it down. A move the rules do not allow is refused with a message and counted. The goal is shown beside the board.
More about the paradigm
The test runs one puzzle for each tower size from 3 disks up to the largest the researcher sets, 5 as standard, smallest first. The fewest possible moves are 7, 15 and 31, which is 2 to the power of the number of disks, minus 1. Each puzzle shows its fewest moves and ends when the tower reaches the right peg, after three times its fewest moves (21, 45 and 93), or after 2, 3 and 5 minutes. A practice puzzle with 2 disks comes first, with feedback.
The primary score is the number of moves over the minimum, summed over the puzzles; an unsolved puzzle counts as using its full move limit. The second is the time to the first move, from the board appearing to picking up the first disk. Scores also give moves over the minimum for each tower size, puzzles solved, puzzles solved in the fewest moves, total time, refused moves and timeouts. Each puzzle is checked by replaying its recorded moves. Scores support research and do not diagnose.
Scores from a few puzzles vary from one session to the next: the test-retest correlation was about .5 in children (Bishop et al., 2001), and Welsh and Huizinga (2001) raised internal consistency to .77 with a set of 22 problems.
Scores
- Moves over the Minimummoves
- Moves above the fewest possible, summed over the puzzles. An unsolved puzzle counts as using its full move limit.
- Lower is better
- Time to First Movems
- Mean time from the board appearing to picking up the first disk. A first move under 100 ms is left out.
- Informational
- Moves over the Minimum, 3 Disksmoves
- Moves above the fewest possible on the 3-disk tower.
- Lower is better
- Moves over the Minimum, 4 Disksmoves
- Moves above the fewest possible on the 4-disk tower.
- Lower is better
- Moves over the Minimum, 5 Disksmoves
- Moves above the fewest possible on the 5-disk tower.
- Lower is better
- Puzzles Solvedcount
- Towers moved to the right peg within the move and time limits.
- Higher is better
- Solved in the Fewest Movescount
- Puzzles solved with no extra moves.
- Higher is better
- Total Timems
- Time from each board appearing to its end, added over the puzzles.
- Informational
- Refused Movescount
- Attempts to put a disk on a smaller disk. The task refuses these moves.
- Lower is better
- Timeoutscount
- Puzzles ended by their time limit.
- Lower is better
- Puzzles without a Movecount
- Puzzles that ended before any move was made.
- Any invalidates the session
- Anticipationscount
- First moves under 100 ms after the board appeared.
- Lower is better
- Completed Puzzlescount
- Puzzles with a readable, replayed move log.
- Fewer than planned invalidates the session
- Planned Puzzlescount
- Puzzles in the session's plan.
- Set by the settings
Use and evidence
106 papers from 2021 to 2025 name this task in their title or abstract, down 18% compared with 2016 to 2020. That ranks it 180 of 395 test families in our census. See the counts for every test.
Show the numbers
| Year | Papers |
|---|---|
| 2025 | 23 |
| 2024 | 25 |
| 2023 | 22 |
| 2022 | 16 |
| 2021 | 20 |
| 2020 | 19 |
| 2019 | 25 |
| 2018 | 34 |
| 2017 | 25 |
| 2016 | 27 |
| 2015 | 31 |
| 2014 | 23 |
| 2013 | 23 |
| 2012 | 20 |
| 2011 | 22 |
| 2010 | 27 |
| 2009 | 24 |
| 2008 | 20 |
| 2007 | 27 |
| 2006 | 16 |
| 2005 | 19 |
| 2004 | 16 |
| 2003 | 17 |
| 2002 | 22 |
| 2001 | 26 |
| 2000 | 13 |
Use grade C
100 to 299 papers from 2021 to 2025.
Evidence grade C
At least 2 test-retest papers, 30 reliability or validity papers or 3 registered clinical studies.
- Papers on test-retest reliability
- 7
- Papers on reliability or validity
- 42
- Registered clinical studies using it as an outcome
- 34
Note on the counts: includes puzzle and computing papers.
How the grades work
Use: A is 1,000 or more papers from 2021 to 2025, B 300 to 999, C 100 to 299, D 30 to 99 and E fewer than 30. Evidence: A means at least 25 papers report its test-retest reliability and at least 25 registered clinical studies use it as an outcome; B, at least 8 test-retest papers, and either 5 registered clinical studies or 150 reliability or validity papers; C, at least 2 test-retest papers, 30 reliability or validity papers or 3 registered clinical studies; D, little published measurement evidence found. The counts measure use. They include every paper that names the task in its title or abstract. Grades describe the published research on this task, not ConductCognition's version of it.
Source: ConductCognition test census 0.14.0, counted 31 October 2026 from OpenAlex and ClinicalTrials.gov.
Task design
The trial sequence as the test runs in ConductCognition.
- Board
- Three pegs, with the goal shown beside the board.
- Rules
- One disk at a time, only the top disk of a peg, and never a disk on a smaller disk. A move against the rules is refused and counted.
- Moves
- Click or tap a peg to pick up its top disk, then a peg to put it down.
- Puzzles
- One tower each of 3, 4 and 5 disks (standard; the largest can be 3 to 5), smallest first, from the left peg to the right peg. The fewest moves are 7, 15 and 31.
- Limits
- Each puzzle ends at the goal, after three times its fewest moves (21, 45 and 93), or after 2, 3 and 5 minutes.
- Practice
- 1 puzzle with 2 disks, with feedback.
- Input
- Mouse, touch or keyboard.
Quality checks
Each session is marked valid, needs review or invalid, with the reason, before you see its scores.
Scored rows: tower_of_hanoi_puzzle from the scored run, one per tower size. A session missing a planned puzzle, or with a puzzle where no move was made before its time limit, is invalid. A first move under 100 ms is an anticipation: more than max(2, 20%) invalidate, and any is flagged.
Why these rules
There is no correct option to compare with chance, so accuracy is not judged against chance. The primary score sums moves over the minimum across the planned puzzles, so a session that misses one cannot be compared with others. Making no move at all on a puzzle is not an attempt and signals non-engagement. A first move under 100 ms cannot come from looking at the board.
Running this test
Settings you can change
| Setting | Standard | Allowed |
|---|---|---|
| Largest tower (disks) | 5 | 3 to 5 |
Yearly plans can change settings within these limits. Free and pay-as-you-go studies use the standard settings.
Need a setting this test does not have?
Devices and languages
- Untimed test: runs on desktops, laptops, tablets and phones. Participant devices
- Languages: English, Spanish, French, German, Italian, Portuguese (Brazil), Chinese (Simplified) and Japanese.
- Available on: Every plan, including the free plan.
- Recruiting online? See the setup guides for Prolific, Sona Systems, CloudResearch Connect and Qualtrics.
Cite and describe
Participants completed the Tower of Hanoi task in a web browser (ConductCognition task version 1.0.0, scoring version 1.0.0; Simon, 1975; Kotovsky, Hayes & Simon, 1985), with the standard settings (largest tower (disks): 5). The main score was moves over the minimum (moves above the fewest possible, summed over the puzzles).
ConductCognition versions: task version 1.0.0, scoring version 1.0.0. Every export records the versions each session used, for a methods section.
- Simon, H. A. (1975). The functional equivalence of problem solving skills. Cognitive Psychology, 7(2), 268-288. https://doi.org/10.1016/0010-0285(75)90012-2
- Kotovsky, K., Hayes, J. R., & Simon, H. A. (1985). Why are some problems hard? Evidence from Tower of Hanoi. Cognitive Psychology, 17(2), 248-294. https://doi.org/10.1016/0010-0285(85)90009-XProblem difficulty in the Tower of Hanoi.
- Goel, V., & Grafman, J. (1995). Are the frontal lobes implicated in "planning" functions? Interpreting data from the Tower of Hanoi. Neuropsychologia, 33(5), 623-642. https://doi.org/10.1016/0028-3932(95)90866-PPlanning after prefrontal lesions.
- Humes, G. E., Welsh, M. C., Retzlaff, P., & Cookson, N. (1997). Towers of Hanoi and London: Reliability and validity of two executive function tasks. Assessment, 4(3), 249-257. https://doi.org/10.1177/107319119700400305Reliability, and the correlation with the Tower of London.
- Welsh, M. C., & Huizinga, M. (2001). The development and preliminary validation of the Tower of Hanoi-revised. Assessment, 8(2), 167-176. https://doi.org/10.1177/107319110100800205A longer problem set with higher reliability.
- Bishop, D. V. M., Aamodt-Leeper, G., Creswell, C., McGurk, R., & Skuse, D. H. (2001). Individual differences in cognitive planning on the Tower of Hanoi task: Neuropsychological maturity or measurement error? Journal of Child Psychology and Psychiatry, 42(4), 551-556. https://doi.org/10.1111/1469-7610.00749Test-retest reliability in children.
- Durand, G. (2018). Influence of allelic variations in relation to norepinephrine and mineralocorticoid receptors on psychopathic traits: A pilot study. PeerJ, 6, e4528. https://doi.org/10.7717/peerj.4528Moves and times of adults on a 5-disk tower.
Source papers
- Simon HA (1975). The functional equivalence of problem solving skills. Cognitive Psychology, 7(2):268-288.Paradigm source, Adults
- Durand G (2018). Influence of allelic variations in relation to norepinephrine and mineralocorticoid receptors on psychopathic traits: a pilot study. PeerJ, 6:e4528.N 57, Adults, mean age 34.5
Questions
How long does the Tower of Hanoi take?
About 6 to 10 minutes, as listed in the test library.
What device does a participant need?
Untimed test: runs on desktops, laptops, tablets and phones. The browser must be Chrome, Edge, Firefox or Safari.
What scores does it produce?
Moves over the Minimum, Time to First Move, Moves over the Minimum, 3 Disks, Moves over the Minimum, 4 Disks, Moves over the Minimum, 5 Disks, Puzzles Solved, Solved in the Fewest Moves, Total Time, Refused Moves, Timeouts, Puzzles without a Move, Anticipations, Completed Puzzles and Planned Puzzles. Each session is also marked valid, needs review or invalid, with the reason.
How widely is the Tower of Hanoi used in research?
106 papers from 2021 to 2025 name it in their title or abstract, down 18% compared with 2016 to 2020. That ranks it 180 of 395 test families in the ConductCognition test census (use grade C). Source: ConductCognition test census 0.14.0, counted 31 October 2026 from OpenAlex and ClinicalTrials.gov.
How much reliability evidence does the Tower of Hanoi have?
In the published research, 7 papers report its test-retest reliability and 34 registered clinical studies use it as an outcome (evidence grade C in the ConductCognition test census).
Which settings can a researcher change?
Largest tower (disks) (3 to 5). Settings can be changed on yearly plans; free and pay-as-you-go studies use the standard settings.
Which languages can participants use?
Participants can take this test in English, Spanish, French, German, Italian, Portuguese (Brazil), Chinese (Simplified) and Japanese. English is on every plan, and the other languages come with yearly plans. Have a native speaker read the machine-translated text before launch.
Is this a clinical test?
No. ConductCognition is for research use only. It runs, scores and exports the test; clinical interpretation is outside the platform.
Every test: the full test list.
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