How to Solve Matrix Reasoning Questions: Rows, Columns, and Rules (Practice Inside)

The biggest trap in matrix reasoning is staring at eight answer choices before you know what the missing box should contain. Solve the pattern first; use the choices second.

Matrix reasoning questions usually show a grid of shapes with one cell missing. Your job is to infer the rule — or combination of rules — that links the rows and columns, then choose the option that completes the matrix.

The fastest way to improve is not to memorize dozens of obscure puzzle tricks. It is to use a repeatable process: identify the changing features, isolate the rules, predict the missing cell, then verify the prediction against the answer choices.

You can try that process immediately with Cognitive Train's embedded Matrix Reasoning Test below, or read the solving method first and come back to it.

Step 1: Inventory What Can Change

Before looking for a rule, list the features that actually vary. Matrix questions commonly manipulate:

• Number — one shape becomes two, two become three, or quantities combine.
• Position — an object moves left, right, clockwise, diagonally, or between corners.
• Orientation — a line or shape rotates or reflects.
• Shape — circles become squares, triangles alternate with diamonds, or forms combine.
• Shading or color — filled, empty, striped, or differently colored elements follow a cycle.
• Size — elements grow, shrink, or alternate between sizes.

This first pass prevents a common mistake: trying to explain the whole picture at once. If three features are changing independently, you may need three small rules rather than one elaborate story.

Step 2: Check Rows and Columns Systematically

Do not bounce randomly around the grid. Compare the first row from left to right. Then the second. Ask whether the same relationship repeats. Next check the columns.

This systematic scan is more than tidy test-taking. In their classic analysis of Raven's Progressive Matrices, Carpenter, Just, and Shell used verbal reports, eye movements, errors, and computational models to study how people solved the problems. A recurring process across solvers was incremental encoding and repeated induction of regularities. Higher-scoring performance was especially associated with inducing abstract relations and managing multiple problem-solving goals.

In plain English: strong solving is often a cycle of look, form a rule, check it, add another rule — not one giant flash of insight.

Step 3: Look for the Simplest Rule That Repeats

Start with simple transformations before inventing complicated ones. Common matrix relationships include:

• Progression: a feature increases, decreases, or moves by a constant step.
• Alternation: A-B-A-B, filled-empty-filled-empty, left-right-left-right.
• Combination: the third cell contains features from the first two.
• Subtraction: shared features disappear, leaving only differences.
• Distribution: each row or column contains one of each shape, position, or shading.
• Transformation: the same rotation, reflection, or movement is applied repeatedly.

The key test is repetition. A rule that explains one row but fails on the next is usually not the rule.

Worked Example: Separate the Rules

Here is a deliberately simple matrix. Each row follows two independent patterns: the number of circles increases from one to three, while shading cycles across the cells.

The useful habit is the separation. You do not need a single verbal rule such as “filled circles grow in a strange alternating way.” Track count and shading independently, then combine them in the missing cell.

Step 4: Construct the Missing Cell Before Looking at the Options

If possible, mentally build the answer first. Researchers often call this a constructive matching strategy: infer the relations in the matrix, construct the expected answer, and then compare that prediction with the choices.

That contrasts with response elimination, where you inspect the answer choices early and repeatedly discard options that violate partial rules.

Both strategies can be used, especially as questions become difficult, but research suggests that strategy matters. In two experiments, Gonthier and Thomassin found that experimentally inducing an effective Raven-solving strategy reduced the relationship between working-memory capacity and performance, while measured strategy use statistically mediated that relationship in a second experiment.

Eye-tracking work by Hayes, Petrov, and Sederberg adds another practical clue: participants whose scanning became more systematic across two Raven sessions tended to improve more. Changes in eye-fixation strategy predicted roughly 30% of the variance in score gains in their sample.

So there is good reason to avoid letting the answer choices run the problem for you.

Step 5: Verify Every Rule Against More Than One Row or Column

Matrix distractors are often designed to satisfy part of the pattern. An option may have the right number of shapes but the wrong rotation. Another may match the row rule but violate the column rule.

Before committing, ask:

• Does my rule explain at least two complete rows or columns?
• If two features change, does my answer satisfy both?
• Am I using the same operation consistently?
• Can I explain why the tempting wrong options fail?

That last question is especially useful. If you cannot say why two plausible options are wrong, you may not have found the full rule yet.

What to Do When There Are Multiple Rules

Harder matrices often layer several relationships. One feature may rotate, another may increase in number, and a third may be distributed so each row contains one of each type.

Do not try to hold the whole puzzle as one visual impression. Write or mentally label the components: rotation: +90°; count: 1-2-3; shading: cycles. Then solve each feature separately.

This is where working memory becomes more relevant. Carpenter and colleagues specifically highlighted management of multiple problem-solving goals as one source of individual differences in Raven performance. If you want to test updating and temporary information management separately from matrix reasoning, Cognitive Train's N-Back Test targets that neighboring skill.

When Elimination Is Actually Useful

Constructing the answer first is a strong default, but elimination is not useless. On very hard items you may identify only part of the rule. In that case, use what you know aggressively.

If the missing cell must contain three objects, remove every two-object option. If orientation must be horizontal, eliminate the vertical choices. Then return to the matrix and search for the feature that separates the survivors.

The important distinction is between using elimination after extracting a real rule and simply comparing choices until one “looks right.” The first reduces the problem; the second invites guessing.

Practice Matrix Reasoning Directly

The best way to use these steps is on actual matrix problems: inventory the features, scan systematically, identify the simplest repeating relations, construct the missing cell, and only then use the choices.

Cognitive Train's full Matrix Reasoning Test gives you a dedicated set of matrix problems. If you want the broader category, the Abstract Reasoning Test and Inductive Reasoning Test extend the same rule-finding idea beyond one format.

For more background, see Progressive Matrices or the wider Pattern Recognition section. Cognitive Train's brain tests collection covers related reasoning, memory, attention, and speed tasks, while the homepage brings together the broader set of cognitive training and brain training tools.