How to Solve Matrix IQ Questions, Step by Step

Matrix puzzles look intimidating: a grid of shapes, one empty square, and five options that all seem plausible. But they are built from a small set of rules, and once you know them and have a method, most puzzles stop being guesswork.

This guide gives you the method first, then walks through each rule with an interactive example you can try. Every wrong option is explained, because understanding why an answer is wrong is how you get faster.

What is a matrix IQ question?

A matrix question shows a grid, usually three by three, with one cell missing. The shapes in the grid change according to hidden rules. Your job is to work out the rules and choose the option that completes the pattern.

The format was made famous by Raven's Progressive Matrices, developed in the mid-1930s by the British psychologist John C. Raven, working with Lionel Penrose, and first published in 1938. Matrix puzzles are now part of the Wechsler intelligence scales and most online reasoning tests, including ours. They are popular because they need no reading or arithmetic, so they test reasoning rather than schooling.

How do you solve matrix questions? The four-step method

1. Look at one feature at a time. Shape, number, size, colour or shading, direction and position can each follow their own rule. Trying to see everything at once is the most common reason people get stuck.
2. Find the rule along the top row. What stays the same? What changes, and by how much?
3. Check it in the other rows and down the columns. A real rule works everywhere. If it fails in row two, it was not the rule.
4. Picture the missing cell before you look at the options. Decide what it must contain, then find the option that matches.

Step 4 matters more than it sounds. In eye-tracking studies, people who score higher tend to spend more of their time studying the grid and look at the options later. People who score lower tend to flick back and forth between the grid and the options, trying each one in turn (Vigneau and colleagues, 2006). Researchers call the first approach constructive matching and the second response elimination. The link is correlational, but building the answer first also protects you from options designed to look almost right.

What rules do matrix puzzles use?

In a well-known analysis of Raven's Advanced Progressive Matrices, Carpenter, Just and Shell (1990) found that nearly every item could be described by five kinds of rule:

Rule	What it looks like
Constant in a row	One feature stays the same along a row
Quantitative progression	A feature changes by the same step from cell to cell: more shapes, bigger, darker, turned further
Figure addition or subtraction	The third cell combines or removes what is in the first two
Distribution of three values	Three values each appear once in every row, like a sudoku
Distribution of two values	Two values appear in each row, and the third cell is blank for that feature

Harder puzzles do not use new kinds of rule. They stack more rules on top of each other, so you have to track several at once. That is why working memory and keeping track of your goals matter so much on the hardest items. Here is each rule in turn.

Rule 1: Constant in a row

The simplest rule: something does not change along a row. Here two constants cross each other, one along the rows and one down the columns.

Rule 2: Progression

A feature changes by the same amount from one cell to the next. The number of shapes goes up by one, the size grows by one step, or the shading gets darker. Often one feature progresses along the rows and another down the columns.

Rotation is a kind of progression too: the shape turns by the same angle at each step. Track the direction it points in, cell by cell.

Rule 3: Adding or removing figures

The third cell is made by combining the first two. On printed tests this is often lines or shapes laid on top of each other. In a subtraction version, anything that appears in both of the first two cells disappears. Our version uses counts, but the logic is identical.

Rule 4: One of each (distribution of three)

Nothing changes step by step. Instead, the same three values are shared out across every row, each appearing once, like a sudoku. These puzzles look random until you list what each row already contains.

The trick: write down, or say to yourself, what the incomplete row already has. The missing cell is whatever is left over, for every feature.

Rule 5: The blank counts (distribution of two)

This is usually the hardest rule to spot, because part of it is invisible. Each row contains two of something and one empty space, so "nothing" is one of the values you are tracking.

How do wrong answer options trick you?

The options in a well-made matrix test are not random. Most wrong answers are the right answer with one rule broken:

• A copy of a neighbouring cell. It fits the row or the column, but not both.
• One feature right, one wrong. Right shape, wrong colour; right count, wrong size.
• An overshoot. The progression goes one step too far.
• A near miss. Everything matches except a small detail, such as shading or direction.

This is why choosing by elimination is risky. If you go straight to the options, a distractor that matches the feature you noticed first will look correct. If you have already decided what the answer must be, the near misses are easy to reject.

What should you do when you cannot see the rule?

• Switch features. If you have been staring at shape, look only at colour, then only at number.
• Read the columns instead of the rows. Some puzzles are built vertically or even along the diagonals.
• Look for a one-of-each pattern. If nothing seems to change steadily, check whether each row contains the same set of values.
• Count the blanks. If some cells seem to be missing a feature, the blank may be part of the rule.
• Move on. On a timed test, every minute spent stuck is time taken from questions you could answer. Choose the most likely option and come back if there is time.

On a test like ours, with 25 questions in 12 minutes, the average is just under 30 seconds per question. Early items take much less, which leaves more time for the hard ones at the end. Our guide to how long an IQ test takes compares the timing of other tests.

Can you get better at matrix reasoning?

You can get better at matrix tests, mainly by learning the format. Research on retesting finds that scores on the same kind of test rise by roughly 5 IQ points on a second attempt, then level off after the third (Scharfen, Peters and Holling, 2018). Studies also show that people change strategy as items get harder, often switching from building the answer to eliminating options (Gonthier and Roulin, 2020). Knowing the five rules and sticking to the four-step method helps you keep the better strategy for longer.

What practice does not do is raise your underlying reasoning ability in a few days. It removes the penalty for being unfamiliar with the format, which makes your score fairer. Heavy drilling can push it higher than your ability, which makes it less meaningful. See how to prepare for an IQ test for what helps and what does not.

Common questions

What is matrix reasoning?

Matrix reasoning is the ability to work out the rules behind a pattern and apply them to complete it. It is a core part of fluid intelligence: solving problems you have never seen before, without relying on knowledge.

Is matrix reasoning the same as Raven's matrices?

Raven's Progressive Matrices is one specific, published test made of matrix puzzles. Matrix reasoning is the general skill and question type. Many tests, including the Wechsler scales and our own, use Raven-style matrix items without being the Raven's test.

What if two options seem to fit?

Go back to the grid and check every feature, one at a time, in both the row and the column. The correct answer satisfies every rule. The other usually breaks one detail, such as colour, size or direction.

Should I check rows or columns first?

Rows first, because most puzzles are built that way, then confirm with the columns. If the rows make no sense, try the columns, then the diagonals.

Where can I practise more?

Try our IQ test questions and answers, the hard IQ test questions explained and the pattern recognition test.