Addition and Subtraction Sequences

Addition and subtraction sequences involve the number of elements changing from one box to the next. In an addition sequence, new shapes appear with each step. In a subtraction sequence, shapes disappear. In more complex patterns, both can happen simultaneously — or an element is added while another is removed (replacement).

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Addition Sequences

Simple Addition: One Element Per Step

Sequence:

• Box 1: One black circle
• Box 2: Two black circles
• Box 3: Three black circles
• Box 4: Four black circles

Next: Five black circles.

What to check: Are the new elements identical to the existing ones, or different?

Addition with Position Pattern

Often, the new elements are not just added randomly — they appear in specific positions.

Sequence:

• Box 1: One triangle in the top-left corner
• Box 2: One triangle in the top-left, one triangle in the top-right
• Box 3: One triangle in the top-left, one triangle in the top-right, one triangle in the bottom-right
• Box 4: One triangle in the top-left, one triangle in the top-right, one triangle in the bottom-right, one triangle in the bottom-left

Pattern: Triangles are added one per step, filling corners clockwise starting from top-left.

Next: All four corners are filled. The next step might add a triangle in the centre, or begin a second shape type, or the shading might change.

Addition with Type Variation

Each new element is a different shape type:

Sequence:

• Box 1: One circle
• Box 2: One circle, one triangle
• Box 3: One circle, one triangle, one square
• Box 4: One circle, one triangle, one square, one pentagon

Pattern: Each step adds the shape with the next number of sides (0→3→4→5).

Next: Add a hexagon (6 sides): circle, triangle, square, pentagon, hexagon.

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Subtraction Sequences

Simple Subtraction: One Element Removed Per Step

Sequence:

• Box 1: Five black squares
• Box 2: Four black squares
• Box 3: Three black squares
• Box 4: Two black squares

Next: One black square.

Subtraction with Order

Shapes are removed in a specific order:

Sequence:

• Box 1: Circle, triangle, square, pentagon, hexagon (arranged left to right by side count)
• Box 2: Circle, triangle, square, pentagon (hexagon removed — the rightmost/most-sided)
• Box 3: Circle, triangle, square (pentagon removed)
• Box 4: Circle, triangle (square removed)

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

Next: Triangle removed, leaving only the circle.

Subtraction with Alternation

Sequence:

• Box 1: Six circles in a row (all black)
• Box 2: Five circles (one removed from the right end)
• Box 3: Four circles (one removed from the left end)
• Box 4: Three circles (one removed from the right end)

Pattern: Circles are removed alternately from the right and left ends.

Next: Two circles (one removed from the left end).

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Combined Addition and Subtraction

In the most challenging sequences, elements are both added and removed simultaneously.

Replacement Pattern

Sequence:

• Box 1: Three black circles
• Box 2: Two black circles, one black triangle
• Box 3: One black circle, two black triangles
• Box 4: Three black triangles

Pattern: One circle is replaced by one triangle each step. The total number of shapes remains constant (3).

Next: If the pattern continues, what replaces the triangles? Check the answer options — a new shape type (squares?) might begin replacing triangles.

Addition and Subtraction Simultaneously

Sequence:

• Box 1: Two circles at the top, one triangle at the bottom
• Box 2: Three circles at the top, no triangle (triangle removed, one circle added)
• Wait — that has two changes. Let me reconsider.

A cleaner example: