Free abstract reasoning test

What abstract reasoning is

Abstract reasoning is working out a rule from examples when the material is new to you: no vocabulary to recall, no formula to apply, just a pattern and a gap. Raymond Cattell called this fluid intelligence, reasoning with novel material, as opposed to crystallized intelligence, the knowledge you build up over time (Wikipedia: Fluid and crystallized intelligence). Our explainer on abstract reasoning covers the theory in depth. This page is the practical side: the test above, how matrix puzzles work, and how to get better at them.

In the Cattell-Horn-Carroll (CHC) model, fluid reasoning (Gf) is one of the broad abilities, alongside comprehension-knowledge (Gc), visual processing (Gv), short-term working memory (Gwm) and processing speed (Gs) (McGrew et al., 2023). Above those broad abilities sits general intelligence, the “g” factor Charles Spearman proposed in 1904 (Wikipedia: g factor). Kevin McGrew calls inductive reasoning, inferring a rule from cases, the primary indicator of both Gf and g (McGrew, 2023). Matrix puzzles are inductive reasoning in its purest visual form.

Researchers have looked closely at what people do while solving them. Carpenter, Just and Shell studied solvers of Raven's Progressive Matrices through their spoken reasoning, eye movements and errors (Carpenter, Just & Shell, 1990). Everyone used the same incremental strategy: encode a few tiles, induce a regularity, check it, move on. What separated higher from lower scorers was mainly the ability to induce abstract relations and to keep many problem-solving goals in working memory at once. That fits other evidence: across 14 data sets with more than 3,100 young adults, working memory capacity and fluid reasoning correlated at a median of .72 (Kane et al., 2005).

Matrix difficulty follows from that. It depends on the type of rule, which affects how hard the correspondences are to spot, and on the number of rules, which affects how many goals you have to juggle (Lozano, Embretson & Revuelta, 2025). Carpenter's analysis named five rules found in Raven's items: constant in a row, quantitative pairwise progression, figure addition or subtraction, distribution of three values, and distribution of two values. Constant in a row is the easiest to induce and distribution of two values the hardest.

Matrices are good measures of general ability but not perfect ones. Many experts have considered the Advanced Progressive Matrices the best single measure of general intelligence (Lozano, Embretson & Revuelta, 2025), yet across several large samples Raven's shared about 50% of its variance with g, about 10% with a separate fluid factor, and had about 25% reliable variance specific to the test itself (Gignac, 2015). Gignac concluded that it is not a pure measure of g. In plain terms: matrices tell you a lot about reasoning, and one matrix test is still one test.

How abstract reasoning is measured

Clinical IQ batteries measure it as fluid reasoning. The WAIS-5 has five primary index scales, one of which is Fluid Reasoning, built from the Matrix Reasoning and Figure Weights subtests (Pearson: WAIS-5 overview), and Matrix Reasoning is one of the seven subtests in its Full Scale IQ (Winter et al. 2024). In the older WAIS-IV, Matrix Reasoning sat in the Perceptual Reasoning index next to Block Design and Visual Puzzles (Pearson Introducing the WAIS-IV). The children's WISC-V reports a Fluid Reasoning index (Pearson: WISC-V), and Matrix Reasoning is one of its ten primary subtests (Becker et al. 2024). The Stanford-Binet 5 lists Fluid Reasoning first among its five factors (PRO-ED: SB5).

Stand-alone matrix tests go further. Raven's Progressive Matrices, first published in 1938, is the best known (Wikipedia: Raven's Progressive Matrices). The Standard Progressive Matrices has 60 items in five sets of twelve (Bilker et al., 2012), and the Advanced Progressive Matrices has 48 in two sets (Srivastava et al., 2023). Each Advanced item is a 3 by 3 grid with the bottom-right entry missing (Lozano, Embretson & Revuelta, 2025), exactly the layout you just used. The current Raven's 2 draws its digital forms from an item bank of over 300 items (Univ. of Oslo: Raven's 2 listing). The Cattell Culture Fair test has a matrices subtest among its four (Zahra et al., 2022).

School ability tests use matrices too. Every NNAT3 item shows a pattern with a missing section and five options; the easiest show one large rectangle with a piece missing, and harder ones use 2-by-2, 2-by-3 or 3-by-3 arrays (NNAT3 Manual A to D). In CogAT Figure Matrices, students work out the relationship between the first two elements of a 2 x 2 matrix, apply it to the third, and pick the figure that completes it (Riverside Nonverbal Battery help). Gifted and talented centers use the KBIT-2 Matrices subtest on its own as a measure of nonverbal fluid reasoning (Pearson KBIT-2 Revised comparison).

At work, the PI Cognitive Assessment reports an Abstract Reasoning subscore next to Verbal and Numeric (Predictive Index: Cognitive Assessment). And British Mensa's online test includes a non-verbal diagrammatic fluid reasoning test (British Mensa: online IQ test); see the Mensa admission test page for how qualifying works. For the wider picture, types of IQ tests compares the main batteries.

The ten grids above come from the same engine as the Abstract Reasoning section of the full IQ Octopus test. The first three use a step rule with a row value (a count or size that steps along each row, while each row keeps its own shape). The middle four use distribution of three: three values that each appear once in every row and every column. The last three use line overlays, where the third tile keeps only the lines that appear in exactly one of the first two. Some grids run their rules down the columns instead of across the rows.

Worked examples: easy, medium and hard

The easy grid stacks two simple rules and a constant. One attribute is fixed for each row, another steps the same way along every row, and a third never changes. Read the first row, say all three out loud, then build the missing tile from the third row's value and the third step.

The medium grid has no progression at all, which is what trips people up. Look for a set of three values that each appear once in every row and every column, in shuffled order. Here two attributes are distributed that way, so check which value of each is missing from the bottom row and from the right-hand column.

The hard grid is made of lines, not shapes. Treat each tile as a list of edges and corner ticks. Compare the first two tiles in a row: lines they share cancel out, and lines that appear in only one of them carry over to the third. Confirm that on a complete row before you build the answer.

Common mistakes on matrix puzzles

• Stopping at the first rule. You spot that the count goes up and pick the first option with the right count. On a two-rule grid, several options have that count; only one also has the right shape or fill.
• Ignoring what stays the same. A constant, like every tile being solid, is still a rule, and the easiest kind in Carpenter's list. Options that change it are wrong.
• Forcing a progression. If three values appear once per row in shuffled order, there is no “next” value. It is a distribution of three, and the missing tile simply has the value its row and column do not have yet.
• Reading only rows. Some grids are built down the columns. If the rows look random, turn your attention ninety degrees before you guess.
• Adding instead of cancelling on line overlays. The third tile is not the first two stacked together. A line drawn in both of the first two tiles disappears.
• Looking at the options first. Each wrong option is close to the answer on purpose. Scanning them before you have a description plants doubt and makes near-misses look right.
• Spending 30 seconds on one rule. If one attribute will not resolve, move to another. Two solid rules usually eliminate enough options to choose; a blank always scores zero.

How to practice abstract reasoning

A plan that works with the free puzzle library and the other mini tests:

1. Learn the method once. Read the matrix reasoning guide, which walks through each rule type with diagrams.
2. Work untimed first. Do five of the easy matrix puzzles with no clock. Before you look at the options, write the missing tile in words, such as “two small solid stars.”
3. Drill the rule that has no progression. The medium matrix puzzles are distribution-of-three grids. Do them until you check rows and columns for missing values without thinking.
4. Take on line overlays. The hard matrix puzzles use the cancel-out rule. Go edge by edge; speed comes later.
5. Add the clock. Give yourself 30 seconds per grid, the limit on this test, using the full matrix library, where every puzzle has a worked answer.
6. Widen the formats. Try the Raven's matrices practice test, which leans hard, and the inductive reasoning test, which mixes matrices with sequences and odd-one-out sets.
7. Stop when the gains stop. Once your score on fresh grids levels off, more drilling of the same format adds little.

Be honest with yourself about what this does. Rule learning is real: within a single matrix test, items using the pairwise progression and figure addition or subtraction rules got easier as people went along (Lozano, Embretson & Revuelta, 2025). Retaking a cognitive test raises scores by about a quarter of a standard deviation on average, more on the same form (Hausknecht et al., 2007), and a meta-analysis of 174 samples found average gains of 0.33 SD at the second sitting, 0.50 by the third, and no further gains after that (Scharfen, Peters & Holling, 2018). That is familiarity with the format, which is fair preparation, not a change in underlying ability.

Broader training is more mixed. A meta-analysis of 74 inductive reasoning training experiments with nearly 3,600 children confirmed gains in fluid intelligence and classroom learning (Klauer & Phye, 2008), with an average corrected effect on intelligence tests of d = .52, as reported by a 2022 paper (Pásztor et al., 2022). Brain training is weaker. A 2008 study reported that working memory training transferred to fluid intelligence tests (Jaeggi et al., 2008), but a randomized, placebo-controlled follow-up found no transfer to any of the cognitive ability tests (Redick et al., 2013), and reviews of chess, music and working memory training conclude that far transfer rarely occurs (Sala & Gobet, 2017).

Abstract reasoning on the full IQ Octopus test

The full test has 25 items in five sections: Pattern Recognition (5), Abstract Reasoning (9), Spatial Reasoning (5), Quantitative Reasoning (3) and Logical Reasoning (3). Abstract Reasoning is the largest section, and it uses the same 3x3 matrix format you just practiced, across a wider range of difficulty, with grids that can stack more rules than any item here. Every item is generated fresh for each attempt, so there is no answer key to learn.

Your score above is a count out of ten, nothing more. A real IQ is a deviation score that compares you with people your own age on a scale with a mean of 100 and a standard deviation of 15 (Wikipedia: Intelligence quotient), and ten practice items with no reference sample cannot place you on it. The full test scores all 25 answers with a Rasch model and reports an estimated IQ with a confidence range. When you want that, take the full IQ test.