AtlasIQHow to solve matrix reasoning problems

IQ explained · 8 min read

How to solve matrix reasoning problems

Figure-matrix rule families with worked examples: progression, distribution, two attributes, rotation and counts, plus a method that works before you look at the options.

In short

A matrix reasoning problem is a 3×3 grid of figures with one cell missing. Every such problem is built from a small set of rule families: one attribute progresses across a row, three shapes are distributed so that each appears once per row and column, two attributes vary independently by row and column, a shape rotates by a fixed angle, or a count changes. The method is to describe what changes along a row and along a column in words, predict the missing cell, then find it among the options.

The method: describe before you look

  • Read the first row left to right. Name what changes: shape, fill, count, rotation, size, position.
  • Read the first column top to bottom. Name what changes there.
  • Check the second row and column to confirm the rule holds.
  • Predict the missing cell in words: for example "the third shape of the row set, filled, count two".
  • Only now look at the options and pick the one matching the description. If two options match, you have missed an attribute.

Looking at the options first invites the most common error: choosing the option that looks most like its neighbours rather than the one the rule requires.

Progression

One attribute moves in steps along a row: fill goes from outline to half to solid, or the count goes one, two, three. The rows are independent copies of the same progression, so the missing cell is the next step in its own row.

Answer

Each row keeps its shape while the fill progresses outline → half → solid across the columns. The missing cell is the solid version of the third row's shape.

Distribution

Three shapes appear so that each row and each column contains every shape exactly once, like a small Latin square. The missing cell is whichever shape is absent from both its row and its column.

Answer

Every row and every column holds each of the three shapes once. The missing cell is the shape that its row and its column both lack.

Two attributes, two directions

The row fixes one attribute and the column fixes another: shape by row, fill by column, for instance. The missing cell combines the row's shape with the column's fill. These problems feel harder because both directions matter, but the method is the same: describe the row, describe the column, combine.

Answer

Shape is fixed by the row and fill by the column, so the missing cell takes the bottom row's shape with the right column's fill.

Rotation and count

A figure turns by a fixed angle per column, usually 45 or 90 degrees, while the row controls another attribute such as fill. The trap is the mirror image: a reflection is never a rotation, and option sets often include one. Count rules change how many copies appear, by row or by column, and are easy to miss when the shapes are small.

Practise with the rule named

The abstract-reasoning and matrix routes on this site generate problems from these exact families and name the family for every item in the answer review, so a missed item tells you which rule to practise rather than just that you missed one.

Sources

Text on this page is original to MyTestAtlas. It explains published standards and definitions; it is not psychological, medical or admissions advice.