Matrix Reasoning Strategies: Elimination, Axis Logic, and Rule Tracking

The answer choices can help you solve a matrix — or quietly hijack your reasoning. The useful skill is knowing when to ignore them, when to use them, and how to keep several rules from getting tangled together.

Matrix reasoning strategies are different from matrix rules. A rule describes what the puzzle is doing: rotation, progression, distribution, addition, subtraction, and so on. A strategy describes how you search for that rule and how you decide among the answers.

That distinction matters because two people can understand the same kinds of patterns but approach a problem very differently. One studies the matrix until a likely answer is mentally constructed. Another jumps repeatedly between the grid and the choices, eliminating options as partial clues appear.

The strongest approach is flexible. Extract as much structure as you can from the matrix first, then let the answer choices help.

Strategy 1: Construct the Answer Before You Shop the Choices

When the matrix is manageable, try to solve it before inspecting the alternatives in detail. This is often called constructive matching: infer the relationships, build a mental description of the missing cell, and then look for the option that matches.

That strategy has a practical advantage. The choices cannot lure you toward a partly correct pattern if you already know that the missing cell should be, for example, “a black triangle rotated 90 degrees with two internal dots.”

Research on Raven's matrices treats constructive matching as one of the major solving strategies. In a study of within-person strategy shifts, Gonthier and Roulin found that participants tended to move away from constructive matching and toward response elimination as items became more difficult. Constructive matching was the more accurate strategy overall, but it was also more demanding on complex items.

A 2024 developmental study by Gonthier and colleagues reached a related conclusion. Constructive matching increased strongly with age from childhood through late adolescence, and strategy use mediated more than half of the age effect on Raven performance in their sample.

Strategy 2: Use Elimination After You Have a Real Constraint

Elimination is not a bad strategy. Premature elimination is.

Suppose you cannot solve the entire matrix, but you are certain the missing shape must contain three elements. Remove every option with one, two, or four. If you also know the orientation must be horizontal, eliminate the vertical options. You have converted an eight-choice puzzle into a smaller problem using genuine information.

This is response elimination: working partly backward from the alternatives. The trap is using the choices before you have extracted any stable rule. Then every attractive answer starts generating its own story.

The 2020 study above is useful because it shows why a blanket “never eliminate” rule would be unrealistic. Participants shifted toward response elimination as difficulty increased. The better lesson is: construct when you can; eliminate when complexity prevents a complete construction.

Strategy 3: Use Axis Logic — Rows First, Then Columns

Axis logic is a practical label here, not a formal research term. It means treating the horizontal and vertical directions as separate sources of evidence instead of scanning the entire 3×3 grid as one picture.

Ask three questions in order:

• What relationship repeats across the completed rows?
• What relationship repeats down the completed columns?
• Does the candidate answer satisfy both?

Sometimes the row rule is enough. Sometimes the column rule is enough. Harder items often make the two axes constrain different features. A row may determine the number of shapes while a column determines their orientation. If you stop after solving only one axis, a distractor can look perfect while still being wrong.

If you want to see the rule families themselves rather than the strategy for finding them, Matrix Reasoning Examples walks through progression, distribution, combination, and constant-feature patterns. The broader How to Solve Matrix Reasoning Questions page gives the full step-by-step workflow.

Strategy 4: Track Each Rule Separately

Once an item contains two or three simultaneous relationships, stop trying to hold the whole thing as one visual impression. Give each rule its own mental line.

For example:

• Shape: circle → triangle → square
• Orientation: +90° each step
• Number: 1 → 2 → 3

Now the missing cell is simply the intersection of three constraints.

This kind of tracking fits the classic analysis by Carpenter, Just, and Shell. Their model described matrix solving as an incremental, reiterative process of encoding and inducing regularities. One important source of individual differences was the ability to dynamically manage multiple problem-solving goals in working memory.

If you want to test updating and temporary rule maintenance separately from matrix reasoning, Cognitive Train's N-Back Test provides a useful cross-check on that neighboring skill.

Strategy 5: Reduce Unnecessary Toggling

Watch what your eyes are doing. If you are bouncing from one matrix cell to answer D, back to the center, then to answer B, then up to another row, you may be letting the alternatives fragment your reasoning.

Eye-tracking research supports the value of more systematic inspection. Hayes, Petrov, and Sederberg tracked participants solving Raven's Advanced Progressive Matrices across two sessions. Changes in scan strategy accounted for about one-third of the variance in score gains in their sample, supporting the idea that improved test performance can partly reflect strategy refinement rather than a broad increase in intelligence.

The practical takeaway is modest but useful: finish one comparison before starting another. Scan a row with a purpose. Check a column with a purpose. Move to the answers when you have something specific to test.

When Should You Switch Strategies?

Easy item: stay with constructive matching. Medium item: construct as much as possible, then use elimination for the unresolved feature. Hard item: accept that you may need to alternate between the matrix and a reduced set of choices.

That flexibility is more realistic than treating one method as universally superior. Gonthier and Roulin found substantial within-person strategy shifts as matrix items became harder. The question is not “which strategy is always best?” It is “which strategy fits the amount of structure I have already extracted?”

Practice the Strategy, Not Just the Answer

Use the embedded Matrix Reasoning Test below with one extra rule for yourself: after each question, notice how you solved it. Did you construct the missing cell? Did you eliminate? Did the row and column axes agree? Did you lose track of a second rule?

That kind of self-check turns practice into more than accumulating correct answers. You start noticing which part of your process breaks first.

A Three-Pass Routine for Timed Questions

Under time pressure, use three passes:

1. Pass 1 — structure: identify the changing features and scan rows/columns.
2. Pass 2 — candidate: construct the most likely missing cell.
3. Pass 3 — choices: eliminate violations and verify the surviving option against both axes.

If Pass 1 produces nothing after a reasonable attempt, move to partial constraints instead of staring indefinitely. A single reliable feature can still remove several distractors.

Try the Full Matrix Reasoning Test

Cognitive Train's full Matrix Reasoning Test lets you practice these strategies across a dedicated set of matrix problems. For nearby rule-finding formats, compare your performance on the Abstract Reasoning Test and Inductive Reasoning Test.

For the wider family of visual-rule problems, browse the Pattern Recognition section or read about Progressive Matrices. Cognitive Train's brain tests collection covers related reasoning, memory, attention, and processing tasks, while the homepage brings together the broader set of brain training and cognitive training tools.