Diagrammatic Reasoning Test

How the diagrams work

Each lettered operator represents a visual transformation. Infer what the operator does from its example. An operator's meaning is fixed within that question, while the same letter can represent a different transformation in another question.

For shape-step transformations, use this fixed shape order: ○ → □ → △ → ⬡ → ○. A reverse step follows the same cycle backward. For dot-step transformations, use this fixed dot order: 1 → 2 → 3 → 1.

Some questions use one figure. Others use a row of three or four figures. Row operators can move objects, reverse or swap positions, change every object's fill, or apply the same colour or shape across the row.

Question types

• Operator Inference: infer one operator, then apply it to a new figure.
• Inverse Reasoning: work backward to identify the input that would produce a shown output.
• Transformation Chains: apply two or three inferred operators from left to right.
• Multi-Object Chains: apply inferred position and attribute transformations to a row of figures.
• Missing Operator: determine which demonstrated operator uniquely completes a chain.
• Flow Logic: apply the first operator, evaluate the condition, then follow the correct branch.

Difficulty

Easy focuses on single-figure operator inference and inverse reasoning. Medium adds two-step chains and three-object rows. Hard adds longer chains, four-object rows, more operator interactions, and flow logic. Harder output questions can include five answer choices.

Timing and scoring

Timed mode gives 45 seconds per question on average as one overall test clock. The clock pauses while the tab is hidden and during answer feedback. Each correct answer earns one point; unanswered questions receive no point.