What is diagrammatic reasoning?

Diagrammatic reasoning is the ability to follow a process shown as a diagram: you track how inputs are changed by a series of rule-based steps, or work backwards from the result to find what an unknown step does. In tests it usually appears as flowcharts where rows of shapes pass through operator boxes.

It is a form of inductive and procedural reasoning: you infer a rule from examples, then apply it precisely in sequence. Employers use it for roles that involve systems, processes or code, because it measures how reliably someone can hold several transformation rules in mind at once.

By What's Your IQ · Published 3 Oct 2026 · Updated 3 Oct 2026

Format: Flowcharts of operator boxes acting on shapes, letters or numbers
Question types: Find the output, find the operator, multi-box chains
Typical employer test: 15–30 items in 15–25 minutes
Measures: Rule inference, sequential processing, working memory
This test: 10 flowcharts, 12 minutes, free, instant explanations

The six operators

Every box in the test does one of these. Learn the tell-tale sign of each and hidden boxes become quick to spot.

ReverseOrder flips end to end.

Tell-tale:the whole row reads backwards; the middle swaps too.

ShiftFirst shape moves to the end.

Tell-tale:every shape moves one place left; nothing changes appearance.

Flip fillSolid ↔ outline, all shapes.

Tell-tale:order and shapes stay put; only fill changes.

Swap endsFirst and last trade places.

Tell-tale:the middle shapes don't move at all.

Drop firstRemoves the first shape.

Tell-tale:the row gets shorter by one.

Next shape○ → □ → △ → ☆ → ○

Tell-tale:positions and fills stay; every shape changes kind.

Cracking a hidden box

Compare what went in with what came out, one property at a time.

1CountSame number of shapes in and out, so it isn't Drop first.4 → 4 · rule out Drop
2ShapesSame four kinds appear, so it isn't Next shape.○□△☆ kept · rule out Next shape
3PositionsThe circle and star traded ends; the middle two stayed put.ends swapped · Swap ends?
4FillsEvery fill flipped too. One box can't do both, so a two-box chart would be Swap ends + Flip fill.fills changed · second operator

Take the test

10 flowcharts · 12 minutes · operator key always visible

Find the output5 flowchartsFind the box3 flowchartsTwo boxes2 flowcharts

Flowchart 1 of 10Find the output

00:00

What comes out of the flowchart?

Reverse

KEY

ReverseOrder flips end to end.

ShiftFirst shape moves to the end.

Flip fillSolid ↔ outline, all shapes.

Swap endsFirst and last trade places.

Drop firstRemoves the first shape.

Next shape○ → □ → △ → ☆ → ○

0/10Learn the six tell-tales, then try again.Weakest: find the output (0/5) · 29854919:35

Find the output0/5Find the box0/3Two boxes0/2

Flowchart 1 · Find the outputAnswer B · you chose nothingApply Reverse: order flips end to end.

Flowchart 2 · Find the outputAnswer D · you chose nothingApply Flip fill: solid ↔ outline, all shapes.

Flowchart 3 · Find the outputAnswer A · you chose nothingApply Shift, then Flip fill: first shape moves to the end. Then solid ↔ outline, all shapes.

Flowchart 4 · Find the outputAnswer C · you chose nothingApply Next shape: ○ → □ → △ → ☆ → ○

Flowchart 5 · Find the boxAnswer B · you chose nothingCompare in and out: The middle shapes don't move at all. That's Swap ends.

Flowchart 6 · Find the boxAnswer A · you chose nothingCompare in and out: The row gets shorter by one. That's Drop first.

Flowchart 7 · Find the boxAnswer D · you chose nothingCompare in and out: Positions and fills stay; every shape changes kind. That's Next shape.

Flowchart 8 · Two boxesAnswer C · you chose nothingCompare in and out: Order and shapes stay put; only fill changes. That's Flip fill.

Flowchart 9 · Find the outputAnswer A · you chose nothingApply Drop first, then Reverse: removes the first shape. Then order flips end to end.

Flowchart 10 · Two boxesAnswer B · you chose nothingCompare in and out: Positions and fills stay; every shape changes kind. That's Next shape.

WHERE POINTS GO

Five slips that cost easy marks

Most wrong answers in flowchart tests come from tracking, not reasoning. These are the habits that stop them.

1Applying boxes in the wrong orderReverse then shift is not shift then reverse. Follow the arrows, not the order you read the key.

2Tracking in your headWrite the row down after every box. Four symbols is already too many to hold reliably.

3Forgetting fillsShapes and positions grab attention; a fill flip is easy to miss on the final check.

4Assuming one box when there are twoIf in and out differ in two ways, look for two operators rather than an exotic one.

5Not using the optionsOn 'find the box' questions, run each option on the input. It's often faster than deducing.

Keep going

Abstract reasoningRules hidden in shapes, without the flowchart.Open

Logical reasoningIf-then rules and clue puzzles.Open

Matrix reasoning gameEndless 3×3 shape puzzles to train on.Open

References

Larkin, J. H., & Simon, H. A. (1987). Why a diagram is (sometimes) worth ten thousand words. Cognitive Science, 11(1), 65–100.
Klauer, K. J., & Phye, G. D. (2008). Inductive reasoning: A training approach. Review of Educational Research, 78(1), 85–123.
Carpenter, P. A., Just, M. A., & Shell, P. (1990). What one intelligence test measures: A theoretical account of the processing in the Raven Progressive Matrices Test. Psychological Review, 97(3), 404–431.