Size-Based Patterns

Size is one of the most visually striking attributes of shapes in AR boxes, yet it is often used as a distractor rather than the actual rule. Learning to recognise when size is genuinely part of the pattern — and when it is irrelevant noise — is a crucial AR skill.

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How Size Appears in UCAT AR

In the UCAT, shapes typically appear in two or three distinct sizes:

Size category	Description
Small	Noticeably smaller than other shapes in the box
Medium	Between small and large (not always present)
Large	Noticeably larger than other shapes in the box

Size is always relative — there is no absolute measurement. A "large" shape is large compared to the other shapes in the same box or across boxes in the set.

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Category 1: Uniform Size Rules

The simplest size-based rule: all shapes in a set are the same size or different sizes.

Worked Example

Set A:

• Box 1: Three small circles
• Box 2: Two small triangles, one small square
• Box 3: One small hexagon, one small pentagon, one small diamond
• Box 4: Four small rectangles
• Box 5: Two small arrows
• Box 6: One small star, two small circles, one small square

Set B:

• Box 1: One large triangle, one small circle
• Box 2: One large square, two small hexagons, one medium pentagon
• Box 3: One large arrow, one large circle, one small triangle
• Box 4: Two medium diamonds, one small rectangle
• Box 5: One large pentagon, one medium circle, one small square
• Box 6: Two large hexagons, one small star

Rule A: All shapes are the same size (all small). Rule B: Shapes are of different sizes (mixed small, medium, large).

Key insight: The rule is not "all shapes are small" but "all shapes are the same size". If Set A had boxes where all shapes were large, the rule would still hold. Check whether the consistency is about a specific size or about uniformity of size.

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Category 2: Size as a Counting Variable

Sometimes the rule involves how many shapes of each size appear.

Common Counting-Size Rules

• "There are always more small shapes than large shapes"
• "There is always exactly one large shape per box"
• "The number of large shapes equals the number of small shapes"
• "There are always exactly two sizes present (never three)"

Worked Example

Set A:

• Box 1: One large circle, one large triangle, three small squares (2 large, 3 small)
• Box 2: One large hexagon, two small circles (1 large, 2 small)
• Box 3: Three large pentagons, four small triangles (3 large, 4 small)
• Box 4: One large diamond, two small rectangles (1 large, 2 small)
• Box 5: Two large arrows, five small circles (2 large, 5 small)
• Box 6: One large star, three small hexagons (1 large, 3 small)

Observation: In every box, the number of small shapes exceeds the number of large shapes. Rule: More small shapes than large shapes.

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Category 3: Size Linked to Another Attribute

Some of the most challenging size-based patterns link size to another feature — typically shape type or colour. These are conditional rules.

Examples of Conditional Size Rules

Rule	How it manifests
"Circles are always large; triangles are always small"	Every box has large circles and small triangles, regardless of other shapes present
"The largest shape is always black"	In each box, the biggest shape is shaded black; other shapes may be any colour
"Shapes in the top row are large; shapes in the bottom row are small"	Size is linked to vertical position
"The number of sides determines size: more sides = larger shape"	Hexagons are large, triangles are small, squares are medium

Worked Example: Size Linked to Colour

Set A:

• Box 1: One large black circle, two small white squares
• Box 2: One large black triangle, one small white pentagon, one small white circle
• Box 3: Two large black hexagons, one small white diamond
• Box 4: One large black arrow, three small white triangles
• Box 5: One large black rectangle, one small white circle, one small white hexagon
• Box 6: Three large black pentagons, two small white squares

Rule: Large shapes are always black. Small shapes are always white. Size and colour are linked.

Test shape: One large white circle, one small black triangle.

• Large shape is white (should be black) → violates the rule.
• Answer: Not Set A. Check Set B or answer Neither.