Progressive Change Rules

Progressive change rules are unique because they involve a feature that changes systematically across the boxes in a set — each box shows a different stage in a progression. While most Type 1 rules involve a feature that is constant across all boxes, progressive rules involve a feature that varies predictably. They blur the line between Type 1 and Type 2 questions and require a different analytical approach.

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How Progressive Change Rules Work in Type 1

In a standard Type 1 question, the boxes in Set A are not ordered — they simply all satisfy the same rule. In a progressive-change question, the boxes are implicitly ordered, and a feature increases, decreases, or cycles across them.

Important clarification: In Type 1 questions, the boxes are typically not presented in a meaningful order. However, the underlying rule can still involve a progressive element if the feature varies within a range rather than being constant. For example, "the number of shapes increases by 1 from the first to the last box" requires you to notice the progression even if the boxes are not explicitly labelled as a sequence.

More commonly, progressive change rules appear in the relationship between Set A and Set B, or as the core mechanism in Type 2 (sequence) questions. This lesson covers both contexts.

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Category 1: Increasing Count

A countable feature increases across the boxes.

Worked Example: Increasing Number of Shapes

Set A (arranged left to right):

• Box 1: 1 shape
• Box 2: 2 shapes
• Box 3: 3 shapes
• Box 4: 4 shapes
• Box 5: 5 shapes
• Box 6: 6 shapes

Rule: The number of shapes increases by 1 from each box to the next.

In a Type 1 context, the test designer might present these boxes in shuffled order. Your job is to recognise that the shape counts (1, 2, 3, 4, 5, 6) form a progression. A test shape with 3 shapes fits the set (it could be one of the intermediate stages). A test shape with 8 shapes does not fit because 8 exceeds the maximum in the progression.

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Category 2: Decreasing or Cycling Feature

Decreasing Size

Sequence:

• Box 1: Very large triangle
• Box 2: Large triangle
• Box 3: Medium triangle
• Box 4: Small triangle

Next: Very small triangle, or if the sizes cycle: very large again.

Cycling Shading

Sequence:

• Box 1: Black shape
• Box 2: Grey shape
• Box 3: White shape
• Box 4: Black shape (cycle restarts)

Next: Grey shape.

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Category 3: Progressive Addition

A new element is added at each step while previous elements remain.

Worked Example

Sequence:

• Box 1: One circle in the top-left
• Box 2: One circle in the top-left + one circle in the top-right
• Box 3: One circle in the top-left + one circle in the top-right + one circle in the bottom-right
• Box 4: One circle in the top-left + one circle in the top-right + one circle in the bottom-right + one circle in the bottom-left

Rule: A circle is added in the next clockwise corner at each step. All previous circles remain.

What comes next? All four corners are filled. The progression might:

• Stop (if it is exactly a 4-step sequence)
• Begin adding circles in new positions (edges, centre)
• Start removing circles (reversal)

Tip: Look at how many steps remain to determine which continuation is most likely.

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Category 4: Progressive Subtraction

An element is removed at each step.

Worked Example

Sequence:

• Box 1: Five shapes — circle, triangle, square, pentagon, hexagon
• Box 2: Four shapes — circle, triangle, square, pentagon (hexagon removed)
• Box 3: Three shapes — circle, triangle, square (pentagon removed)
• Box 4: Two shapes — circle, triangle (square removed)

Next: One shape — circle (triangle removed).

Pattern: The shape with the most sides is removed at each step.

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Category 5: Progressive Rotation

A shape rotates by a consistent angle at each step. (This was covered in the Rotation lesson but is included here for completeness as it is the most common progressive change.)

Key Angles to Check