Figure Matrix Puzzles
A three-by-three grid with the bottom-right cell empty. Rules run along the rows and down the columns, and the missing figure has to satisfy both at once. Sixty patterns, unlimited generated puzzles, and the reasoning after every attempt — including why each wrong option is wrong.
Also known as matrix reasoning and progressive matrices — the 3×3 grid with one cell missing.
Two Rules At Right Angles
A figure matrix is a 3×3 grid of figures with the bottom-right cell missing. One rule runs along the rows, another runs down the columns, and both must agree at the missing cell. It is the figure series doubled: read one direction, read the other, and take the figure that satisfies both.
How To Solve Figure Matrix Puzzles
- Read across the first row and name what changes.
- Confirm the same change across the second row.
- Read down the first column and name the second change.
- Apply the row rule and the column rule together at the empty cell.
- Check the answer against both directions before choosing.
The two rules are independent. If your candidate satisfies one direction but not the other, it is wrong — and the explanation will say which direction broke.
| Family | What it covers |
|---|---|
| Row progressions | One rule, running left to right. The columns hold still. |
| Column progressions | One rule, running top to bottom. The rows hold still. |
| Crossed rules | A different attribute moving in each direction — the standard matrix item. |
| Same attribute both ways | One attribute driven along the rows and down the columns at different rates. |
| Latin squares | Every value appears once per row and once per column. Nothing progresses; it distributes. |
| Double rules | Two attributes moving together in the same direction. |
| Triple composites | Three rules spread across both directions. Eliminate; do not predict. |
| Cycle and progression | A latin square in one attribute while another attribute progresses. |
Why Matrices Reward Systematic Readers
Every matrix on this page is generated from the same rule algebra as the series and analogy puzzles, so the moves are the ones you already know — rotation steps, shading advances, count changes — arranged at right angles. Scan rows first, columns second, and the grid closes itself.
Figure Matrix Puzzles Frequently Asked Questions
How is this different from figure series?
A series runs in one direction, so there is one rule set to find. A matrix runs in two, so the missing cell must satisfy its row and its column at the same time. Applying only the rule you noticed first is the classic error.
What is a latin square matrix?
One where each value appears exactly once in every row and once in every column. Nothing progresses — the answer is whichever value the last row and last column have not used yet.
How many puzzles are there?
There is no fixed number. Each puzzle is rebuilt from the short seed in the page address, so the supply is effectively unlimited. Copying the puzzle link saves that exact puzzle permanently.
Can I practise one pattern at a time?
Yes. Pick any pattern from the catalogue above and the board switches to that pattern only, with its own address you can bookmark or hand out.
What is a figure matrix question?
A figure matrix shows a three-by-three grid of figures with one cell — usually the bottom right — left empty. Rules run along the rows and down the columns, and you have to work out both before you can say what belongs in the gap. It is also called a progressive matrix or a matrix reasoning question.
Is it free and does it need an account?
It is completely free and there is no account. Nothing is uploaded; your score is kept only in your own browser.
How do you solve a figure matrix?
Read it as rows first, then as columns, and do not assume both are doing something. Many matrices run a rule one way only, which leaves the other direction looking identical on purpose. If nothing seems to increase or move, check whether each value simply appears once per row and column — that is a distribution pattern, and hunting it for a direction of change will never end.