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Three rows, three columns, two things changing at once. The worked solution is below — and so is an honest account of what solving it does and does not tell you about yourself.
Matrix reasoning is the item format most people picture when they picture an IQ test: a grid with one cell missing and a row of candidate answers underneath. It is popular with test designers because it needs no vocabulary, no arithmetic and no cultural knowledge — only the ability to work out what rule is generating the pattern.
Here is one you can solve in text. Read the grid, then stop and try it before scrolling on.
Each cell of a three-by-three grid contains one shape, and inside that shape are some dots.
The candidate answers are: a triangle with 1 dot, a triangle with 2 dots, a circle with 1 dot, a square with 1 dot, a triangle with 4 dots. Which one belongs in the missing cell?
Two features vary independently, so there are two rules and both have to hold.
The shape rule is the easy one. Every cell in the top row is a circle, every cell in the middle row is a square, every cell in the bottom row is a triangle. Shape is constant along each row. The missing cell is in the bottom row, so it is a triangle. That single step eliminates the circle and the square from the options.
The dot rule takes one more moment. Look at the rows: the top row runs 1, 2, 3. The middle row runs 3, 1, 2. The bottom row runs 2, 3, and the unknown. Each row uses the numbers 1, 2 and 3 exactly once — so the missing value must be 1, because 2 and 3 are already used in that row.
Check it against the columns, because a good item is consistent both ways. The first column reads 1, 3, 2. The second reads 2, 1, 3. The third reads 3, 2, and the unknown — and 1 is the only value not yet used in that column. Both rules agree.
The answer is a triangle with 1 dot. The grid is a small Latin square: three values, each appearing exactly once in every row and every column, with a second independent feature layered on top of it.
A matrix item is not asking whether you can spot a pattern. It is asking whether you can state one precisely enough to test it.
Honestly: not much on its own. A single item measures almost nothing. Real matrix tests use many items of graded difficulty, because performance on any one of them is heavily influenced by whether you happened to see the rule quickly, and that varies from item to item even within one person.
What is worth taking from it is the method. Naming the rule before looking at the options is the single most useful habit on this item type, because the options are written by someone who knows which partial solutions are tempting. Solving half the puzzle and then choosing the answer that fits the half you solved is the most common way to lose an item you were capable of getting.
And the honest caveat about practice: doing a lot of these makes you better at these. That gain is real, it is worth having if you are about to sit an assessment that uses this format, and it is narrower than the phrase “brain training” implies. The evidence that practice on a specific task transfers to general reasoning is much weaker than the evidence that it improves the task you practised.
If you want to know where your reasoning stands rather than how you did on one puzzle, the measurement has to be built for it: many items, graded difficulty, a named scale, a percentile against a defined reference sample, and a confidence range — because a single sitting produces an estimate, not a fixed property.
Find your IQ score now! →A triangle with 1 dot. Shape is constant along each row, so the bottom row is triangles. The dot counts form a Latin square in which each row and each column uses 1, 2 and 3 exactly once, and 1 is the only value left for that position in both its row and its column.
Matrix reasoning is one of the better-studied item formats for what psychologists call fluid reasoning — solving novel problems without relying on stored knowledge. A single item measures very little; a full test with many graded items measures that specific ability reasonably well, and is one component of a broader assessment rather than the whole of it.
It raises your score on this item type, which is a genuine advantage if you are about to sit a test that uses it. Evidence that practice on a specific task transfers to general reasoning ability is considerably weaker than evidence that it improves the practised task itself.
Corrections: spotted an error? Email corrections@iqmetrics.org and we will update this story and note the change here.
The correlation between them is one of the sturdier findings in cognitive psychology. How strong it is, and what it implies about training either one, is where the agreement stops.
On the scale most modern tests use, 120 sits around the 91st percentile. Change the scale and the same number moves. Add the measurement error every test carries and it stops being a point at all.
Our IIF-certified assessment reports your score with its scale, percentile and confidence range — and a breakdown of the cognitive domains behind it.
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