What do matrix puzzles measure? A short guide to fluid reasoning

A grid of three by three figures, the last cell empty, and eight possible answers below it. You have probably seen a puzzle like this. Matrix puzzles have been used in psychological research since the 1930s, when the British psychologist John C. Raven published the best-known version. They are still among the most common ways to study reasoning. What exactly are they measuring?

Fluid and crystallised abilities

In the 1940s, the psychologist Raymond Cattell began to distinguish between two broad kinds of ability; he set out the theory in detail in a 1963 paper. Crystallised abilities draw on what you have learned – vocabulary, facts, familiar procedures. Fluid abilities are about dealing with something new: spotting relations, forming and testing rules, and solving problems you have not met before.

Matrix puzzles are a typical fluid task. You do not need to know any words or facts. Everything you need is in the picture; the challenge is to find the structure hidden in it.

The rules inside a matrix

In 1990, Patricia Carpenter, Marcel Just and Peter Shell published a detailed analysis of how people solve matrix problems. They studied the puzzles themselves, people’s eye movements and their spoken reasoning, and wrote computer programs that simulated good and less good solvers.

One of their findings was that most items are built from a small set of rule types – five in their analysis. Simplified, four of them are:

• Constant in a row – a feature stays the same across a row, for example all figures in a row are triangles.
• Progression – a feature changes step by step, for example one more dot in each cell, or a figure turning 90° each time.
• Distribution of three values – three different values each appear once in every row, like a small Sudoku.
• Figure addition or subtraction – the third figure is made by combining the first two, or by removing one from the other.

A single puzzle can combine several rules, each applying to a different feature – shape, number, fill, size or orientation.

Why some matrices are so much harder

If the rule types are simple, why do some puzzles feel nearly impossible? Carpenter and colleagues found that difficulty rose mainly with the number of rules a solver had to discover and keep track of at the same time, and with how abstract the correspondence between figures was.

This links matrix reasoning closely to working memory and to what the researchers called goal management: breaking a problem into sub-goals, solving them one by one, and keeping the intermediate results in mind. Better solvers were not using fundamentally different tricks – they were better at spotting abstract relations and at holding several sub-goals and partial solutions in mind at once.

How to approach a matrix puzzle

Based on what we know about good solvers, a few habits help:

1. Look at one feature at a time. Ask separately: what happens to the shape? The number? The fill? The orientation?
2. Check rows first, then columns. Many rules run along rows; some run down columns.
3. Describe the rule in words. “Each row has one empty, one solid and one striped figure” is easier to check than a vague impression.
4. Predict before you look at the options. Decide what the missing cell should look like, then find it.
5. Verify every rule. Wrong options are usually built by breaking exactly one rule. If an option looks right, check it against each rule you found.

What this does not mean

• Matrices are not a complete measure of intelligence. They capture an important kind of reasoning, but not verbal ability, knowledge, creativity or practical skills.
• They are not perfectly culture-free. Although they need no language, they assume familiarity with abstract shapes, grids and the idea of a test. A review of decades of data by John Raven, son of the test’s creator, documented how norms varied between cultural and social groups and shifted over time.
• Scores are not fixed. Practice with the format improves performance on it. And the largest generational gains in test scores during the 20th century – the Flynn effect – were seen on exactly this kind of task, which shows how sensitive such scores are to environment and experience.

How IQ Arion builds its matrices

The pattern questions in IQ Arion are generated by a program from rule types like the ones above: constant values, progressions, distributions of three values, and adding or subtracting lines. Wrong options are created by breaking one rule of the correct answer. A separate solver then checks every option against the rules, and a question is only used if exactly one option fits.

The best way to understand matrix puzzles is to try a few. Our free short test includes two of them – one easier, one harder.