Reasoning
Number Sequence Task
Also called: number series task, number series completion, series completion task, numerical induction task
Measure inductive reasoning: participants find the rule behind a row of numbers and type the next one, on 16 rows made for this test, easier to harder.
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
- 18
- Evidence grade
- D
- Registered clinical studies
- 1
What it measures
Measures inductive reasoning with numbers. Participants see 16 rows of numbers that each follow a rule, such as adding the same amount or two rows taking turns, and type the number that comes next, with 45 seconds per row by default. The rows were made for this test and run from easier to harder. The main score is the number of rows completed correctly. The rows use no words.
Constructs
- Inductive reasoning
- Fluid reasoning
- Numerical pattern detection
Research uses
- Fluid intelligence and individual-differences research
- Cognitive aging research
- Within-study group comparison
How the paradigm works
Number series completion is a classic measure of inductive reasoning, inferring a rule from examples: the participant finds the rule behind a row of numbers and gives the next one (LeFevre and Bisanz 1986). Solving takes four steps: finding how neighbouring numbers relate, finding the period, completing the pattern and extending it (Simon and Kotovsky 1963; Kotovsky and Simon 1973; Holzman, Pellegrino and Glaser 1983). These steps and knowledge of arithmetic explained over 70% of the differences in difficulty between problems (Holzman, Pellegrino and Glaser 1983), and strong and weak solvers differed in recognizing familiar sequences and in calculating quickly (LeFevre and Bisanz 1986). In automatic item generators, the kind of rule predicts difficulty: rows taking turns, groups of repeated numbers and patterns in the steps make rows harder (Loe, Sun, Simonfy and Doebler 2018), and rules that need two operations are the hardest (Sun, Liu and Luo 2019).
More about the paradigm
This test has 16 rows made for it by code from stated rules, 4 in each of four bands from easier to harder: one constant relation; repeated numbers, two rows taking turns, a growing step and the sum of the two numbers before; two operations in turn, two rows of different kinds, a doubling step and a step up and down; a faster-growing step, three rows taking turns, a growing factor and two rows taking turns with a growing step in one. Every number is a whole number from 1 to 999, the rows use digits only and are the same in every language, and no two answers are the same. The session's seed orders the rows within each band. Each row shows 4 to 9 numbers and a blank for the next one, which the participant types and sends with Enter or Submit within 45 seconds by default (30 to 90 as a setting), with a bar for the time left. One practice row has feedback; the test has none. Letter series are not included, because the order of the alphabet is not learned the same way in all eight languages.
The main score is the number of rows completed correctly. Each band has its own count, and wrong answers, time-outs, blank answers and the median time of correct answers are also reported. Scores support research and do not diagnose.
Scores
- Rows Correctcount
- Rows answered with the next number of their rule, out of 16.
- Higher means more rows completed correctly
- Band 1 Rows Correctcount
- Rows correct among the 4 easiest, each with one constant relation.
- Higher means more correct answers; most adults complete these
- Band 2 Rows Correctcount
- Rows correct among the 4 of the second band.
- Higher means more correct answers
- Band 3 Rows Correctcount
- Rows correct among the 4 of the third band.
- Higher means more correct answers
- Band 4 Rows Correctcount
- Rows correct among the 4 hardest.
- Higher means more correct answers
- Wrong Answerscount
- Rows answered with another number or with no number in the answer.
- Higher means more errors
- Time-Outscount
- Rows where the time ran out before an answer was sent. Text left in the box is saved and not scored.
- Higher means more rows unanswered in time
- Blank Answerscount
- Rows sent with an empty box.
- Lower means more rows were attempted
- Median Time to a Correct Answerms
- Median time from a row's appearance to a correct answer, leaving out answers under 100 ms.
- Lower means faster correct answers
- Answers Under 100 mscount
- Answers sent within 100 ms of the row appearing.
- Expected to be 0
- Rows Answeredcount
- Rows answered, right or wrong, before the time ran out.
- A session with fewer than 4 is invalid
- Rows Showncount
- Rows presented in the scored run.
- 16 in a completed run
- Largest Same Answer Countcount
- The largest number of rows given one identical answer.
- 6 or more is flagged for review
Use and evidence
18 papers from 2021 to 2025 name this task in their title or abstract. That ranks it 333 of 395 test families in our census. See the counts for every test.
Show the numbers
| Year | Papers |
|---|---|
| 2025 | 6 |
| 2024 | 2 |
| 2023 | 3 |
| 2022 | 2 |
| 2021 | 5 |
| 2020 | 2 |
| 2019 | 4 |
| 2018 | 1 |
| 2017 | 0 |
| 2016 | 1 |
| 2015 | 2 |
| 2014 | 1 |
| 2013 | 2 |
| 2012 | 0 |
| 2011 | 1 |
| 2010 | 0 |
| 2009 | 0 |
| 2008 | 2 |
| 2007 | 0 |
| 2006 | 0 |
| 2005 | 0 |
| 2004 | 0 |
| 2003 | 0 |
| 2002 | 1 |
| 2001 | 2 |
| 2000 | 0 |
Use grade E
Fewer than 30 papers from 2021 to 2025.
Evidence grade D
Little published measurement evidence found.
- Papers on test-retest reliability
- 1
- Papers on reliability or validity
- 14
- Registered clinical studies using it as an outcome
- 1
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.
- Rows
- 16 made for this test by code from stated rules, 4 in each of 4 bands from easier to harder. Every number is a whole number from 1 to 999, and no two answers are the same.
- Rules
- A constant difference or ratio, repeated numbers, two or three rows taking turns, a step that grows or doubles, two operations in turn, a factor that grows, and each number the sum of the two before.
- Order
- The bands run from easier to harder, and the session's seed orders the rows within each band. Each row shows 4 to 9 numbers.
- Answer
- A typed number, sent with Enter or Submit, in a box that opens the number keypad on phones. 45 seconds per row by default, 30 to 90 as a setting, with a bar for the time left. No feedback.
- Languages
- The rows are digits, the same in every language. Letter series are not used.
- Practice
- 1 row outside the set, with feedback.
- Scores
- Rows correct, overall and in each band; wrong answers, time-outs and blank answers; and the median time of correct answers.
The rows were made for this test; no published number series item, such as those of intelligence test batteries or the ICAR, is used, so published norms do not apply.
Quality checks
Each session is marked valid, needs review or invalid, with the reason, before you see its scores.
Scored rows: number_series_item from the scored run, one typed number per row of numbers before its time limit. Typed answers have no chance level, so accuracy is not judged against chance, and a time-out is a normal result on a hard row. Fewer than 4 rows answered invalidates. A run short of its rows is invalid with fewer than half shown and flagged otherwise. One identical answer on 6 or more rows is flagged for review. Answers under 200 ms on at least half of 4 or more answered rows invalidate. A hidden tab withholds the percentile.
Why these rules
There is no correct option to compare with chance, so accuracy is not judged against chance. A low score is the result the test measures and never invalidates, but with almost nothing answered a low score cannot be told from no effort. The 16 answers all differ, so one answer typed for many rows cannot follow them; it is flagged. An answer under 200 ms is faster than a simple visual reaction, so it cannot reflect the item. Following response-time effort screening for untimed tests (Wise and Kong 2005), the session is invalid only when at least half the answers are that fast. A hidden tab lets the study, delay or response timers run without the participant, so a percentile is withheld after one.
Running this test
Settings you can change
| Setting | Standard | Allowed |
|---|---|---|
| Time per row (seconds) | 45 | 30 to 90 |
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 Number Sequence Task in a web browser (ConductCognition task version 1.0.0, scoring version 1.0.0; Simon & Kotovsky, 1963; Holzman, Pellegrino & Glaser, 1983), with the standard settings (time per row (seconds): 45). The main score was rows correct (rows answered with the next number of their rule, out of 16).
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., & Kotovsky, K. (1963). Human acquisition of concepts for sequential patterns. Psychological Review, 70(6), 534-546. https://doi.org/10.1037/h0043901
- Kotovsky, K., & Simon, H. A. (1973). Empirical tests of a theory of human acquisition of concepts for sequential patterns. Cognitive Psychology, 4(3), 399-424. https://doi.org/10.1016/0010-0285(73)90020-0
- Holzman, T. G., Pellegrino, J. W., & Glaser, R. (1983). Cognitive variables in series completion. Journal of Educational Psychology, 75(4), 603-618. https://doi.org/10.1037/0022-0663.75.4.603
- LeFevre, J.-A., & Bisanz, J. (1986). A cognitive analysis of number-series problems: Sources of individual differences in performance. Memory & Cognition, 14(4), 287-298. https://doi.org/10.3758/BF03202506Individual differences in solving number series.
- Loe, B. S., Sun, L., Simonfy, F., & Doebler, P. (2018). Evaluating an automated number series item generator using linear logistic test models. Journal of Intelligence, 6(2), 20. https://doi.org/10.3390/jintelligence6020020Rules that predict how hard a row is.
- Sun, L., Liu, Y., & Luo, F. (2019). Automatic generation of number series reasoning items of high difficulty. Frontiers in Psychology, 10, 884. https://doi.org/10.3389/fpsyg.2019.00884Rules with two operations as the hardest.
Source papers
- Loe BS, Sun L, Simonfy F, Doebler P (2018). Evaluating an automated number series item generator using linear logistic test models. Journal of Intelligence, 6(2):20.Paradigm source, Adults
Questions
How long does the Number Sequence Task 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?
Rows Correct, Band 1 Rows Correct, Band 2 Rows Correct, Band 3 Rows Correct, Band 4 Rows Correct, Wrong Answers, Time-Outs, Blank Answers, Median Time to a Correct Answer, Answers Under 100 ms, Rows Answered, Rows Shown and Largest Same Answer Count. Each session is also marked valid, needs review or invalid, with the reason.
How widely is the Number Sequence Task used in research?
18 papers from 2021 to 2025 name it in their title or abstract. That ranks it 333 of 395 test families in the ConductCognition test census (use grade E). Source: ConductCognition test census 0.14.0, counted 31 October 2026 from OpenAlex and ClinicalTrials.gov.
How much reliability evidence does the Number Sequence Task have?
In the published research, 1 paper reports its test-retest reliability and 1 registered clinical study uses it as an outcome (evidence grade D in the ConductCognition test census).
Which settings can a researcher change?
Time per row (seconds) (30 to 90). 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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