Type 4 Questions: Which Completes the Set?

Type 4 questions present you with an incomplete grid of shapes (typically a 2×2 arrangement with one cell missing) and ask you to select the shape that correctly completes the set. This format requires you to identify rules that operate across rows AND columns simultaneously — a more demanding task than the linear sequences of Type 3.

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How Type 4 Questions Are Structured

Feature	Detail
What you see	A grid of shapes (usually 2×2, sometimes 2×3) with one cell empty
What you must find	The shape that fills the empty cell
Answer options	4 choices (A, B, C, D)
Key skill	Identifying rules across rows AND columns

The 2×2 Grid Layout

┌─────────┬─────────┐
│  Box 1  │  Box 2  │
├─────────┼─────────┤
│  Box 3  │    ?    │
└─────────┴─────────┘

The missing cell is typically in the bottom-right, though it can be in any position.

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Strategy: Row Rules vs Column Rules

The fundamental approach to Type 4 is to check for rules in two directions:

Row Rules

Look across each row. What is the relationship between the shapes in the same row?

Common row rules:

• Each row contains the same three shape types (one of each)
• Each row contains one of each colour (black, white, grey)
• The shapes in a row have a mathematical relationship (e.g., sides add up to a total)
• The second shape is a transformation of the first (rotated, reflected, colour-inverted)

Column Rules

Look down each column. What is the relationship between the shapes in the same column?

Common column rules:

• Each column contains the same shape type but in different sizes
• Each column has shapes that increase in the number of sides
• The shapes in a column share a common colour

The Answer Must Satisfy Both

The correct answer is the one that satisfies both the row rule and the column rule. This dual constraint is what makes Type 4 distinctive and is your most powerful tool: if two answer options satisfy the row rule, check them against the column rule to determine which is correct.

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Worked Example 1: Simple Grid Completion

The Grid

┌──────────────────┬──────────────────┐
│  Black triangle  │  Black square    │
├──────────────────┼──────────────────┤
│  White triangle  │       ?          │
└──────────────────┴──────────────────┘

Row Analysis

• Row 1: Black triangle, Black square → both are black, shapes differ
• Row 2: White triangle, ? → if the pattern holds, both should be white, shapes should differ

Column Analysis

• Column 1: Black triangle, White triangle → same shape (triangle), colour changes from black to white
• Column 2: Black square, ? → same shape (square) expected, colour should change from black to white

Prediction

The missing shape should be a white square — it satisfies:

• Row 2 pattern: white shapes, different from triangle ✓
• Column 2 pattern: square, changing from black to white ✓

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Worked Example 2: More Complex Grid

The Grid (2×3 with bottom-right missing)

┌─────────────────┬─────────────────┬─────────────────┐
│  1 black circle │  2 white circles│  3 grey circles  │
├─────────────────┼─────────────────┼─────────────────┤
│ 1 black triangle│ 2 white triangles│       ?          │
└─────────────────┴─────────────────┴─────────────────┘

Row Analysis

• Row 1: 1 black circle → 2 white circles → 3 grey circles
  • Number increases: 1, 2, 3
  • Colour changes: black, white, grey
  • Shape stays the same: circles
• Row 2: 1 black triangle → 2 white triangles → ?
  • Number should be: 3
  • Colour should be: grey
  • Shape should stay: triangles

Column Analysis

• Column 1: 1 black circle → 1 black triangle → same count (1), same colour (black), shape changes
• Column 2: 2 white circles → 2 white triangles → same count (2), same colour (white), shape changes
• Column 3: 3 grey circles → ? → should have count 3, colour grey, shape = triangle

Prediction

3 grey triangles — satisfies both row and column rules.

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Diagonal Rules (Less Common but Important)

Some grids also have patterns along the diagonals. In a 3×3 grid:

┌───┬───┬───┐
│ A │ B │ C │
├───┼───┼───┤
│ D │ E │ F │
├───┼───┼───┤
│ G │ H │ ? │
└───┴───┴───┘