Matrix reasoning practice, one rule at a time
Matrix puzzles look like a test of raw brainpower, but nearly all of them are built from five rules. Pick a rule, solve as many fresh puzzles as you like, and see the rule explained after every answer.
7 practice sets · unlimited puzzles · practice items, not real test questions · reviewed October 2026
Rule 1 of 7: Constant in a row
easy
One feature stays the same along each row, another down each column. Which cell is missing?
?
The five rules behind matrix puzzles
In 1990 Patricia Carpenter, Marcel Just and Peter Shell took Raven's Advanced Progressive Matrices apart item by item. Almost every puzzle was built from five kinds of rule, alone or stacked. Harder items did not use stranger rules. They used more of them at once, and the people who scored highest were the ones who could find several rules and keep track of them without losing the thread.
That finding is why this trainer splits practice by rule. Two of the seven sets are variations: turning by a fixed step is a progression of angle, and the last set stacks two rules.
| Rule (Carpenter et al.) | What happens | How to spot it | Practice set |
|---|---|---|---|
| Constant in a row | One feature stays the same along a row (or down a column) | Cover all but one feature: which never changes? | 1. Constant in a row |
| Quantitative progression | A feature grows, shrinks or turns by a fixed step | Count, measure or turn: is the step the same each time? | 2. Progression, 3. Turning by a fixed step |
| Figure addition or subtraction | Two cells combine, or one is taken from the other, to make the third | Lay the first two cells on top of each other | 4. Adding figures |
| Distribution of three values | Each row holds the same three values, in a different order | Ask what each row is still missing | 5. One of each |
| Distribution of two values | Two values per row, and the third is blank | Treat "nothing" as a value | 6. The blank counts |
| Several rules at once | Two or more of the above in one item | Solve one feature at a time, then combine | 7. Two rules at once |
A method that works on any matrix
- 01
Name the features before you reason
Shape, colour, number, size, angle, position, shading. Say them to yourself. Most wrong answers come from watching one feature and missing another. - 02
Test one feature at a time, rows first
For each feature, ask: does it stay the same, step, combine or rotate through a set of values along the row? Then check the columns agree. - 03
Predict the missing cell before you look at the options
Eye-tracking studies of Raven's tests (Vigneau and colleagues, 2006) found that higher scorers spent longer on the grid and built the answer first, while lower scorers bounced between the options and the grid. - 04
Use the options to check, not to guess
Several options are built to match one rule and break another. If two survive, there is a second rule you have not found yet. - 05
Practise one rule until it is automatic, then mix
When you spot a rule without effort, your working memory is free for the next one. That is what the hardest items demand.
Does practising matrices raise your IQ?
It raises your score on matrix tests. It does not do much for the ability underneath, and it is worth knowing the difference before you start.
- Practice effects are real and modest. A meta-analysis of 107 samples and over 134,000 people (Hausknecht and colleagues, 2007) found an average retest gain of about 0.26 standard deviations: roughly 4 IQ points, or moving from the 50th to about the 60th percentile.
- They level off fast. A larger 2018 meta-analysis (Scharfen, Peters and Holling) found no further gains after the third time people took a test.
- They are not gains in general ability. Across 64 test-retest studies, te Nijenhuis and colleagues (2007) found the biggest gains on the parts of tests that measure general ability least.
So use practice for what it is good at: removing the surprise, so a timed test measures how you reason rather than whether you had seen the format before. That matters most before an employer's abstract reasoning test, where the format is new to most candidates.
Where you will meet matrix puzzles
| Test | Who takes it | Our guide |
|---|---|---|
| Raven's Progressive Matrices | Research, schools and some employers | Raven's guide |
| Wechsler scales (WAIS, WISC): Matrix Reasoning subtest | Clinical and educational assessments | WAIS index scores |
| Cattell Culture Fair test | Mensa and other societies, research | Cattell Culture Fair test |
| Employer abstract and inductive reasoning tests | Graduate and professional job applicants | Abstract reasoning test |
| Online IQ tests, including ours | Anyone curious | Visual IQ test |
Frequently asked questions
What is matrix reasoning?
Finding the rule in a grid of shapes and using it to fill the gap. It is the core item type in Raven's Progressive Matrices and a subtest of its own on the Wechsler scales, because it measures reasoning with new information while needing almost no language or school knowledge.
How do you solve matrix puzzles?
Name the features (shape, colour, number, size, angle), test each one along the rows and down the columns, and work out the missing cell before you look at the options. Then use the options to check your answer. Almost every item uses one or more of five rule types, which is why practising rule by rule works.
Does practising matrices raise your IQ?
It raises your score on matrix tests, mostly because the rule types become familiar. A meta-analysis of 107 samples found an average retest gain of about a quarter of a standard deviation, roughly 4 IQ points. Studies that look at what those gains are made of find they are not gains in general ability.
Are these the real Raven's questions?
No. Raven's items are copyrighted and only given by qualified testers. These puzzles are generated by our own code from the published rule types, so you can practise the reasoning without seeing any real test item.
How many puzzles should I do?
Until you get two or three right in a row for a rule, then move on. Gains from repeated practice level off quickly: in a 2018 meta-analysis, scores stopped rising after the third time people took a test.
Is there a time limit?
Not here: the trainer is for learning the rules. Real tests are timed (about 40 minutes for Raven's Advanced set, 12 minutes for our IQ test), so once the rules are familiar, practise under a clock.
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Ready for puzzles you have not been taught?
The IQ test mixes these rules with spatial, sequence and analogy items, easy to hard, with a 12-minute clock.
Take the IQ test
25 questions · about 12 minutes
Sources
- Carpenter, P. A., Just, M. A., & Shell, P. (1990). What one intelligence test measures: A theoretical account of the processing in the Raven Progressive Matrices Test. Psychological Review, 97(3), 404-431.
- Hausknecht, J. P., Halpert, J. A., Di Paolo, N. T., & Moriarty Gerrard, M. O. (2007). Retesting in selection: A meta-analysis of coaching and practice effects for tests of cognitive ability. Journal of Applied Psychology, 92(2), 373-385.
- Scharfen, J., Peters, J. M., & Holling, H. (2018). Retest effects in cognitive ability tests: A meta-analysis. Intelligence, 67, 44-66.
- te Nijenhuis, J., van Vianen, A. E. M., & van der Flier, H. (2007). Score gains on g-loaded tests: No g. Intelligence, 35(3), 283-300.
- Vigneau, F., Caissie, A. F., & Bors, D. A. (2006). Eye-movement analysis demonstrates strategic influences on intelligence. Intelligence, 34(3), 261-272.
Puzzles are generated by LifeScore code from the published rule types; none is a real test item. By LifeScore Editorial Team · Reviewed October 2026