Figure Patterns
Subject: Mental Ability | Frequency: 1-2 questions per APPSC paper | Time: 45-60 sec/question
Introduction
Figure pattern questions present a sequence of figures with a visual pattern; you must predict the next figure or find the odd one out. APPSC commonly tests rotation-based series and pattern completion. This is purely a visual pattern recognition skill that improves with repetition — practice is the only shortcut.
Core Method
- Observe the sequence — study all given figures carefully
- Identify what changes between figures:
- Position (rotation, shift)
- Shape (addition, deletion, transformation)
- Shading (filled, empty, half-filled)
- Size (increasing, decreasing)
- Count (number of elements)
- Determine the rule — what pattern governs the change?
- Apply the rule to predict the next figure
- Match with options — select the closest match
- Verify — ensure the rule holds for ALL given figures, not just two
Common Patterns
Rotation Patterns
| Pattern | Description |
|---|---|
| Clockwise rotation | Figure rotates 45, 90, or other angles CW |
| Anticlockwise rotation | Figure rotates CCW |
| Alternating rotation | CW then ACW alternately |
Element Changes
| Pattern | Description |
|---|---|
| Addition | One new element added each step |
| Deletion | One element removed each step |
| Replacement | Element changes to different type |
| Movement | Element shifts to different position |
Shading Patterns
| Pattern | Description |
|---|---|
| Progressive fill | Sections fill one by one |
| Alternating shade | Black <-> White alternating |
| Cyclic shading | Shading rotates through sections |
Counting Patterns
| Pattern | Description |
|---|---|
| Increasing count | Lines, dots, shapes increase (1,2,3...) |
| Decreasing count | Elements decrease |
| Constant count | Same total, just rearranged |
Worked Examples — Easy
Q1: Figures show a triangle rotating 90 degrees clockwise each step. Currently pointing right. What's next?
- Up → Right → Down → Left (90 degrees CW cycle)
- Currently pointing right → next: pointing down
Q2: Series shows: 1 dot, 2 dots, 3 dots, 4 dots, ?
- Pattern: +1 dot per step
- Answer: 5 dots
Q3: Square with a shaded quadrant moving clockwise: top-left, top-right, bottom-right, ?
- Shading moves one quadrant clockwise each step
- Answer: bottom-left shaded
Worked Examples — Medium
Q4: Pentagon with one marked side. Mark moves one side clockwise each step. Where after 4 steps from top?
- Top → upper-right → lower-right → lower-left → upper-left
- Answer: upper-left
Q5: Circle with 1 line, triangle with 2 lines, square with 3 lines, pentagon with ?
- Shapes: increasing sides (circle, 3, 4, 5)
- Lines: 1, 2, 3, ?
- Answer: Pentagon with 4 lines
Q6: Matrix: Row 1: circle, triangle, square. Row 2: triangle, square, circle. Row 3: square, circle, ?
- Each row contains all three shapes in different positions
- Row 3 needs the missing shape: triangle
Worked Examples — Hard
Q7: Arrow right + dot above → Arrow down + dot right → Arrow left + dot below → ?
- Arrow rotates 90 degrees CW each step
- Dot position follows: above → right → below → left
- Answer: Arrow up + dot on left
Q8: Fig 1: outer circle + inner triangle. Fig 2: outer square + inner circle. Fig 3: outer triangle + inner square. Fig 4: ?
- Outer shapes: circle → square → triangle → circle (cycle)
- Inner shapes: triangle → circle → square → triangle (cycle)
- Inner shape becomes outer shape of next figure
- Answer: Outer circle + inner triangle (cycle repeats)
Q9: 3x3 grid has a checkerboard pattern with one cell missing.
- Rule: If (row + column) is even = one color; if odd = other color
- Identify the missing cell's row and column, apply the rule
- Answer: Determined by the (row+column) parity rule
Shortcuts & Tricks
| Shortcut | When to Use |
|---|---|
| Track ONE element | Don't track everything; focus on the most distinctive element |
| Rotation = count turns | 90 degrees CW = right turn; track cumulative rotation |
| Matrix: row + column check | In 3x3 matrices, each row and column usually has all variants |
| Elimination first | Rule out 2-3 options on one feature, then verify the remaining |
| Count sides/lines | Many patterns are based on incrementing geometric properties |
| Overlay mentally | For embedded figures, mentally place the target on the complex figure |
Common Mistakes
- Tracking too many elements — focus on one changing element first, then verify others
- Ignoring rotation direction — CW and ACW rotations look similar but produce different results
- Missing subtle shading — half-shaded vs fully shaded sections are easy to confuse
- Wrong elimination — eliminating a correct option based on superficial check
- Not checking all given figures — pattern must hold for the ENTIRE sequence, not just the last 2
Exam Strategy
- Practice figure series daily — this is a visual skill that improves with repetition
- APPSC keeps difficulty at medium
- Focus on rotation-based series and pattern completion — these are the most common
- Time: 45-60 seconds per question
- For figure series: identify the ONE most prominent change first, then verify with secondary changes
Practice Questions
- Arrow pointing East rotates 90 degrees ACW each step. After 3 steps? → E→N→W→S (South)
- Series: 2 sides, 3 sides, 4 sides, 5 sides, ? → 6 sides (hexagon)
- Dot moves: top-left, top-right, bottom-right, bottom-left, ? → top-left (cycle repeats)
- Shaded section in circle: 1/4, 2/4, 3/4, ? → 4/4 (fully shaded)
- Matrix with all shapes used: Row has circle and square, missing? → triangle
Key Terms / Formulas
| Term | Meaning |
|---|---|
| Rotation | Figure turns by a fixed angle each step |
| CW / ACW | Clockwise / Anticlockwise |
| Progressive fill | Sections fill sequentially |
| Embedded figure | A simple figure hidden within a complex figure |
| Pattern completion | Fill a missing piece in a larger pattern |
| Figure matrix | 3x3 grid where each row/column follows a rule |