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.
What Belongs In The Empty Cell
A figure matrix is a grid of figures — almost always 3×3 — with one cell left empty. A rule runs along the rows and a second rule runs down the columns, so the missing figure has to satisfy both at once. That double constraint is what separates a matrix from a series, and why a matrix of the same difficulty takes longer to read.
Reading The Grid Across, Then Down
A matrix is not a harder series — it is a series in two directions at once, and that changes the method. The single most common mistake is spotting one rule, applying it, and stopping.
- Read one full row first. Take the top row on its own and ask what changes from left to right. Ignore everything else.
- Then read one full column. Take the left column and ask what changes downwards. This is the step people skip.
- Check both rules on a cell you can see. The middle cell should be explained by one step right and one step down. If it is not, you have the wrong rule.
- Apply both to the empty cell. Two steps right from the bottom-left, or two steps down from the top-right — either route must give the same answer.
- If nothing progresses, count instead. Some grids distribute rather than progress: each value appears once per row and once per column. Then the answer is simply the value the last row and last column have not used.
The two-route check. Because the rules commute, you can reach the missing cell along the bottom row or down the right-hand column and must land in the same place. Doing it both ways takes seconds and catches the "I only applied one rule" error before you commit to an answer.
Progression Versus Distribution
There are two genuinely different things a matrix can be doing, and telling them apart quickly is most of the skill:
- Progression — an attribute moves steadily in a direction. Sides increase to the right, shading advances downwards. Look for the step size.
- Distribution — a latin square — three values are dealt out so each appears once in every row and once in every column. Nothing is increasing at all. Looking for a direction of change here will never find one, which is why these feel impossible until you recognise the shape of them.
Eight of the sixty patterns here are latin squares, and four more combine a latin square with a progression. If a grid resists a progression reading for more than a few seconds, switch and check whether each value appears once per line.
| Progression | Distribution (latin square) | |
|---|---|---|
| What it does | A value steps in a direction | Three values each appear once per row and column |
| Rows look | Different from each other | Like reorderings of each other |
| Hunting for a direction | Finds one | Never terminates — nothing increases |
| Fastest tell | Frame 1 and frame 3 of a row differ in degree | The same three values recur everywhere |
| If a rule runs one way only | The other direction is identical on purpose | Both directions carry the constraint |
The Eight Matrix Rule Families
- 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 in each direction. The standard matrix item.
- Same attribute both ways — one attribute driven along the rows and down the columns at different rates, sometimes fighting each other.
- Latin squares — distribution rather than progression.
- Double rules — two attributes moving together in the same direction.
- Triple composites — three rules spread across both directions.
- Cycle and progression — a latin square in one attribute while another progresses.
Where The Figure Matrix Came From
The matrix is the most widely used shape in all of pattern puzzling, and its modern form dates to the 1930s, when John C. Raven laid figures out in a grid with the last cell missing. The idea that made it stick is simple and slightly devious: put a rule on the rows and a rule on the columns, so the missing cell has to satisfy two constraints at once. That is why a matrix feels harder than a series of the same difficulty — you are not finding a rule, you are finding the intersection of two.
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.