Figure Matrix

Master figure matrix problems for RRB exam preparation with comprehensive concepts and practice problems.

Basic Concepts

What is Figure Matrix?

Definition

• 3×3 Grid: Matrix with 9 figures (8 given, 1 missing)
• Pattern Recognition: Identify logical relationships
• Missing Figure: Find the figure that completes the pattern
• Visual Logic: Based on shape, size, position, orientation

Types of Patterns

• Row Pattern: Relationship across rows
• Column Pattern: Relationship down columns
• Diagonal Pattern: Relationship along diagonals
• Overall Pattern: Pattern covering entire matrix

Pattern Categories

Shape-based Patterns

• Shape Addition: Shapes combine to form new shapes
• Shape Subtraction: Shapes remove parts from each other
• Shape Transformation: One shape converts to another
• Shape Counting: Number of shapes follows pattern

Position-based Patterns

• Rotation: Figures rotate by fixed angles
• Reflection: Figures mirror across axis
• Movement: Elements move in specific direction
• Alignment: Elements align in specific way

Size-based Patterns

• Gradation: Size increases/decreases progressively
• Alternation: Sizes alternate between two values
• Proportional: Size ratio remains constant
• Relative: Size changes relative to position

Common Patterns

Row-wise Patterns

Arithmetic Operations

• Addition: Left + Middle = Right
• Subtraction: Left - Middle = Right
• Combination: Features from both figures combine

Sequential Changes

• Stepwise Change: Each figure changes by fixed amount
• Progressive Change: Gradual transformation
• Alternating Pattern: Two patterns alternate

Column-wise Patterns

Vertical Relationships

• Top to Middle: Specific transformation
• Middle to Bottom: Continuation of transformation
• Top to Bottom: Combined transformation

Position Logic

• Stacking: Elements stack vertically
• Alignment: Vertical alignment patterns
• Distribution: Elements distribute vertically

Problem-Solving Approach

Step-by-Step Method

Step 1: Analyze Rows

1. Compare first and second figures in each row
2. Identify transformation pattern
3. Verify if third figure follows pattern
4. Check if pattern is consistent across rows

Step 2: Analyze Columns

1. Compare top and middle figures in each column
2. Identify vertical relationship
3. Verify if bottom figure follows pattern
4. Check consistency across columns

Step 3: Check Diagonals

1. Analyze diagonal relationships
2. Look for reflection patterns
3. Check for rotation patterns
4. Verify symmetry

Step 4: Eliminate Options

1. Rule out clearly wrong options
2. Compare remaining options with pattern
3. Select best matching option
4. Verify answer fits complete matrix

Common Transformations

Shape Operations

• Union: Combine all elements
• Intersection: Keep common elements
• Difference: Remove overlapping parts
• Superimposition: Overlap with transparency

Position Changes

• Rotation: 90°, 180°, 270° clockwise/anticlockwise
• Reflection: Horizontal, vertical, diagonal
• Translation: Movement in specific direction
• Scaling: Enlargement or reduction

Practice Problems

Question 1

[ ] [ ] [ ]
[ ] [ ] [ ]
[ ] [?] [ ]

In the matrix above, each row shows a rotation pattern. If the first figure is a triangle pointing up, and it rotates 90° clockwise in each step, what should be in the missing position?

Question 2

[○] [△] [□]
[△] [□] [○]
[□] [?] [△]

Find the missing figure in the matrix above.

Question 3

In a 3×3 matrix, the pattern is: (Row 1) Circle + Square = Circle with Square inside, (Row 2) Triangle + Circle = Triangle with Circle inside. What should be in Row 3: Square + Triangle = ?

Question 4

[▲] [▲] [△]
[●] [○] [○]
[■] [?] [□]

Find the missing figure following the pattern.

Question 5

Matrix pattern: First column shows 1 line, second column shows 2 lines, third column shows 3 lines. Each row increases line count by 1. What should be in the missing position?

Question 6

[◇] [◇] [○]
[○] [◇] [◇]
[◇] [?] [○]

Find the missing figure in the alternating pattern matrix.

Question 7

Pattern: Figures in first row increase in size by 50%, second row decreases by 25%. What should be the size pattern in third row?

Question 8

[+ ] [× ] [○]
[− ] [+ ] [×]
[÷ ] [?] [+ ]

Find the missing symbol in the mathematical operation pattern.

Question 9

Matrix shows arrows pointing in different directions. Row 1: North, East, South. Row 2: East, South, West. Row 3: South, West, ? What’s the missing direction?

Question 10

Pattern: First column has shaded shapes, second column has partially shaded, third column has fully shaded. Each row shows progression of shading. What should be in the missing position?

Advanced Patterns

Complex Transformations

• Multiple Operations: Combination of rotation + reflection
• Conditional Logic: Different operations based on position
• Progressive Complexity: Patterns get more complex

Hidden Patterns

• Count-based: Number of elements follows arithmetic progression
• Position-based: Position determines transformation
• Relationship-based: Figures relate to their neighbors

Quick Tips

Pattern Recognition

1. Start Simple: Look for obvious patterns first
2. Check Consistency: Pattern should work for all rows/columns
3. Consider Options: Sometimes only one option fits
4. Think 3D: Some problems involve 3D visualization

Common Mistakes

1. Overthinking: Don’t create overly complex patterns
2. Missing Options: Don’t forget to check all answer choices
3. Incomplete Analysis: Check both rows and columns
4. Assumption: Don’t assume pattern without verification

Time Management

1. Quick Scan: Take 30 seconds to identify obvious patterns
2. Systematic Approach: Use step-by-step method
3. Elimination: Rule out wrong options quickly
4. Move On: Don’t spend more than 2-3 minutes per question

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