Shape and Arrangement Puzzles are an important part of Non-Verbal Reasoning and Logical Reasoning. These questions test a candidate's ability to understand figures, identify patterns, visualize rotations and reflections, count geometric shapes, and determine the correct arrangement of objects.
Such questions are useful for Bihar STET, BPSC, SSC, Banking, Railway, CTET, Police, Defence and other competitive examinations.
1. What are Shape and Arrangement Puzzles?
Shape and Arrangement Puzzles are reasoning questions in which information is represented through:
Geometrical shapes
Figures
Symbols
Objects
Patterns
Positions
Arrangements
Sequences
The candidate has to identify the relationship between figures or determine the correct position, sequence, missing shape, or arrangement.
Example
Suppose a sequence contains:
▲ → ■ → ● → ▲ → ■ → ?
The pattern repeats after three shapes:
▲ → ■ → ●
Therefore, the missing shape is:
●
2. Major Types of Shape and Arrangement Puzzles
Important types include:
Figure Series
Figure Analogy
Figure Classification
Odd Figure Out
Figure Matrix
Pattern Completion
Embedded Figures
Mirror Images
Water Images
Figure Rotation
Figure Reflection
Counting Figures
Shape Arrangement
Paper Folding
Figure Formation
Spatial Arrangement
Shape-Based Coding
Matchstick Puzzles
Cube and Dice Arrangements
Hidden Figure Problems
3. Figure Series
In a figure series, several figures are arranged in a particular order.
The candidate must determine:
The next figure
The missing figure
The pattern
The transformation
Common Patterns
Figures may change according to:
Rotation
Addition
Removal
Movement
Size
Shading
Number of elements
Direction
Example
▲ → ▶ → ▼ → ◀ → ?
The triangle rotates 90° clockwise each time.
Therefore, the next figure is:
▲
4. Figure Analogy
Figure analogy questions follow a relationship such as:
A : B :: C : ?
The transformation from A to B must be applied to C.
Possible transformations include:
Rotation
Reflection
Addition
Removal
Shading
Change of shape
Change of position
Solving Method
Compare Figure A and B.
Identify the exact transformation.
Apply the same transformation to Figure C.
Select the matching figure.
5. Figure Classification
In figure classification, several figures are given.
Usually, three or four figures follow a common rule while one figure does not.
The task is to identify the different figure.
Check
Compare:
Number of shapes
Direction
Rotation
Symmetry
Shading
Position
Internal elements
6. Odd Figure Out
The Odd Figure Out problem asks you to identify the figure that does not belong to the group.
Example
Suppose four figures contain:
Triangle
Square
Circle
Triangle
If three figures have the same number of sides or follow a common pattern and one does not, the different figure is the answer.
7. Figure Matrix
A figure matrix generally contains figures arranged in rows and columns.
One position is missing.
The candidate must identify the rule operating across:
Rows
Columns
Diagonals
Common Rules
Addition of shapes
Rotation
Alternation
Increasing number of elements
Shading
Combination of previous figures
Tip
Check the row pattern first, then the column pattern.
8. Pattern Completion
A figure may contain a partially completed design.
The candidate must select the figure that correctly completes it.
Look for:
Lines
Curves
Symmetry
Direction
Shape continuity
Repeated patterns
Important Rule
Don't look at the complete figure randomly. Break it into smaller sections.
9. Embedded Figures
An embedded figure question contains a small target figure hidden inside a larger complicated figure.
The task is to locate the target figure.
Solving Technique
Focus on:
Shape boundaries
Angles
Number of sides
Relative positions
Ignore unnecessary lines.
Important Point
The hidden figure may be:
Rotated
Overlapped
Inverted
Partially surrounded by other lines
10. Mirror Image
A mirror image is the reflection of an object in a mirror.
For a standard vertical mirror:
Left becomes right.
Right becomes left.
Top remains top.
Bottom remains bottom.
Example
ABC | Mirror
The order of letters appears reversed in the mirror.
Important Tip
For a vertical mirror:
Horizontal position changes, vertical position remains the same.
11. Water Image
A water image is the reflection of an object in a horizontal surface such as water.
For a water image:
Top becomes bottom.
Bottom becomes top.
Left remains left.
Right remains right.
Memory Trick
Mirror → Left/Right changes
Water → Top/Bottom changes
12. Mirror Image vs Water Image
| Mirror Image | Water Image |
|---|---|
| Left-right reversal | Top-bottom reversal |
| Vertical mirror | Horizontal reflection |
| Top generally remains top | Left generally remains left |
| Bottom generally remains bottom | Right generally remains right |
This distinction is frequently tested in reasoning examinations.
13. Rotation of Shapes
Rotation means turning a figure around a fixed point.
Common rotations:
45°
90°
180°
270°
360°
Example
A figure rotated by:
90° clockwise + 90° clockwise
becomes:
180° clockwise
Shortcut
Track one distinctive part of the figure, such as:
Arrow
Dot
Line
Shaded section
This makes rotation questions easier.
14. Clockwise and Anticlockwise Rotation
Clockwise
The figure rotates in the same direction as the movement of clock hands.
↑ → ↓ → ←
Anticlockwise
↑ → ← → ↓
When solving questions, identify the direction before counting the number of rotations.
15. Symmetry
A figure is symmetrical when one part corresponds to another part in a particular reflection.
Types
Vertical symmetry
Horizontal symmetry
Rotational symmetry
Example
A square has:
Vertical symmetry
Horizontal symmetry
Diagonal symmetry
Rotational symmetry
16. Counting Figures
Counting figure questions ask candidates to determine the number of geometric figures hidden inside a larger figure.
Common questions involve:
Triangles
Squares
Rectangles
Circles
Lines
Polygons
Important Technique
Do not count only the smallest shapes.
Count:
Small figures
Medium figures
Large figures
Combined figures
17. Counting Triangles
For triangle-counting problems:
Step 1
Count the smallest triangles.
Step 2
Combine adjacent triangles to form larger triangles.
Step 3
Look for triangles formed by multiple sections.
Step 4
Check inverted triangles.
Step 5
Check the complete outer triangle.
18. Counting Squares
When counting squares, check:
Small squares
Medium squares
Large squares
Rotated squares
Do not assume every four-sided figure is a square.
A square must have:
Four equal sides
Four right angles
19. Shape Arrangement
Shape arrangement problems ask candidates to arrange figures according to given conditions.
Conditions may involve:
Position
Direction
Size
Color/shading
Distance
Adjacency
Sequence
Example
If:
Circle is left of square.
Triangle is right of square.
Then:
Circle → Square → Triangle
20. Spatial Arrangement
Spatial reasoning tests the ability to understand the position of objects in space.
Questions may involve:
Above/below
Left/right
Front/behind
Near/far
Inside/outside
Rotation
Movement
Tip
Create a small diagram instead of solving everything mentally.
21. Shape Sequence
A shape sequence follows a particular pattern.
For example:
○ → △ → □ → ○ → △ → ?
The pattern is:
Circle → Triangle → Square
Therefore, the answer is:
Square
22. Addition and Removal Pattern
Some figure sequences work by adding or removing one element at every step.
Example:
1 line → 2 lines → 3 lines → 4 lines → ?
The next figure should contain:
5 lines
23. Movement-Based Pattern
A shape may move around a fixed position.
Example:
Top → Right → Bottom → Left → Top
The object is rotating around a center.
Tip
Track the position of one object rather than comparing the entire figure.
24. Shading Pattern
Some questions change the shaded area or alternate between:
Black
White
Dotted
Striped
Example:
Black → White → Black → White → ?
Answer:
Black
25. Matchstick Shape Puzzles
Matchstick puzzles use sticks to create geometric figures.
Questions may ask you to:
Move one stick
Remove one stick
Add one stick
Create a new shape
Correct an equation
Important Strategy
Look for:
Symmetry
Shared sides
Rotation
Overlapping lines
26. Paper Folding and Cutting
In paper-folding questions:
A paper is folded.
A hole or cut is made.
The paper is unfolded.
The candidate identifies the final pattern.
Key Principle
Every fold creates a corresponding reflection of the cut.
Therefore, mentally reverse each fold in the correct order.
27. Figure Formation
In figure formation problems, several pieces are provided.
The candidate must determine which pieces can form a particular target figure.
Technique
Check:
Angles
Side lengths
Curves
Orientation
Matching boundaries
28. Cube and Dice Arrangement
Cube-based puzzles involve:
Opposite faces
Adjacent faces
Common faces
Rotations
Different views
Important Rule for a Standard Die
Opposite faces of a standard die usually add up to:
7
For example:
1 ↔ 6
2 ↔ 5
3 ↔ 4
However, always follow the specific die arrangement provided in the question if it differs from the standard orientation.
29. Shape-Based Coding
In these questions, shapes represent numbers, letters, or operations.
Example:
▲ = 2
● = 5
■ = 3
Then:
▲ + ● = 2 + 5 = 7
The key is to identify the coding rule first.
30. General Strategy for Shape Puzzles
Follow these steps:
Step 1: Observe
Look carefully at all figures.
Step 2: Identify the Changing Element
Check whether the following changes:
Direction
Position
Size
Number
Shading
Shape
Step 3: Find the Rule
Look for repetition, rotation, addition, subtraction or reflection.
Step 4: Apply the Rule
Apply the identified rule to the missing figure.
Step 5: Verify
Check the answer against the entire sequence or arrangement.
31. Common Shortcuts
Shortcut 1: Track One Element
If a figure is complicated, track one:
Dot
Arrow
Shaded region
Small triangle
Shortcut 2: Check Rotation First
Many figure-series questions are based on 90°, 180° or 270° rotation.
Shortcut 3: Count Elements
Count:
Lines
Dots
Shapes
Shaded portions
Shortcut 4: Look for Alternation
Patterns often alternate:
A B A B A B
or
A B C A B C
Shortcut 5: Check Rows and Columns
For matrix questions, examine both directions.
32. Common Mistakes
Avoid these mistakes:
Assuming a pattern too early
Ignoring rotation
Confusing mirror and water images
Counting only small figures
Ignoring hidden figures
Not checking all rows/columns
Treating clockwise as anticlockwise
Focusing on unnecessary lines
33. 50 Important MCQs on Shape and Arrangement Puzzles
Q1. Shape and Arrangement Puzzles mainly test:
A. Vocabulary
B. Visual and spatial reasoning
C. Grammar
D. General knowledge
Answer: B
Q2. In a figure series, the next figure is generally determined by:
A. Random selection
B. An underlying pattern
C. Alphabetical order
D. Numerical value only
Answer: B
Q3. In a vertical mirror image, which direction is generally reversed?
A. Top-bottom
B. Left-right
C. Diagonal only
D. None
Answer: B
Q4. In a water image, which direction is generally reversed?
A. Left-right
B. Top-bottom
C. Front-back only
D. None
Answer: B
Q5. A figure rotated by 180° is:
A. Unchanged in orientation
B. Half-turned
C. Quarter-turned
D. Reflected
Answer: B
Q6. A 90° clockwise rotation means the figure turns:
A. One quarter turn clockwise
B. Half turn
C. Full turn
D. Three-quarter turn anticlockwise
Answer: A
Q7. A 360° rotation produces:
A. A mirror image
B. The original orientation
C. An opposite image
D. A water image
Answer: B
Q8. Which is commonly used to identify a pattern in figure series?
A. Rotation
B. Shading
C. Addition/removal
D. All of these
Answer: D
Q9. Which type of question contains a hidden target figure?
A. Embedded figure
B. Number series
C. Coding-decoding
D. Blood relation
Answer: A
Q10. A figure matrix generally contains:
A. Only words
B. Figures arranged in rows and columns
C. Only numbers
D. Paragraphs
Answer: B
Q11. In an analogy question A : B :: C : ?, the relationship between:
A. A and C is important
B. A and B is applied to C
C. B and C is ignored
D. All figures are unrelated
Answer: B
Q12. Which technique is useful in counting figures?
A. Count small and larger combined figures
B. Count only the largest figure
C. Ignore overlapping figures
D. Count randomly
Answer: A
Q13. Which figure has four equal sides and four right angles?
A. Triangle
B. Square
C. Circle
D. Pentagon
Answer: B
Q14. Which shape has three sides?
A. Square
B. Triangle
C. Pentagon
D. Hexagon
Answer: B
Q15. A pentagon has:
A. 4 sides
B. 5 sides
C. 6 sides
D. 7 sides
Answer: B
Q16. A hexagon has:
A. 5 sides
B. 6 sides
C. 7 sides
D. 8 sides
Answer: B
Q17. If a pattern is ▲, ■, ●, ▲, ■, ?, the missing shape is:
A. ▲
B. ■
C. ●
D. ◆
Answer: C
Q18. If a shape rotates 90° clockwise four times, the final orientation is:
A. 90°
B. 180°
C. 270°
D. Same as original
Answer: D
Q19. Which transformation reverses left and right?
A. Vertical mirror reflection
B. Horizontal reflection
C. Rotation only
D. Translation
Answer: A
Q20. Which transformation reverses top and bottom?
A. Vertical reflection
B. Horizontal reflection
C. Translation
D. Enlargement
Answer: B
Q21. The odd figure out is identified by finding:
A. The common pattern
B. The different pattern
C. The largest figure only
D. The smallest figure only
Answer: B
Q22. A figure with equal corresponding halves demonstrates:
A. Symmetry
B. Rotation only
C. Translation
D. Coding
Answer: A
Q23. A figure can have:
A. Only vertical symmetry
B. Only horizontal symmetry
C. Both vertical and horizontal symmetry
D. No symmetry ever
Answer: C
Q24. Which is a common pattern in shape sequences?
A. Rotation
B. Movement
C. Shading
D. All of these
Answer: D
Q25. In a spatial arrangement question, the best method is often:
A. Draw a rough diagram
B. Ignore positions
C. Guess immediately
D. Memorize the answer
Answer: A
Q26. If a circle is left of a square and a triangle is right of the square, the arrangement is:
A. Triangle – Square – Circle
B. Circle – Square – Triangle
C. Square – Circle – Triangle
D. Circle – Triangle – Square
Answer: B
Q27. If an arrow points upward and rotates 90° clockwise, it points:
A. Left
B. Right
C. Down
D. Up
Answer: B
Q28. If an arrow points right and rotates 180°, it points:
A. Up
B. Down
C. Left
D. Right
Answer: C
Q29. Which puzzle requires identifying a figure hidden within another figure?
A. Embedded figure
B. Analogy
C. Classification
D. Coding
Answer: A
Q30. Which puzzle asks for a missing figure in a sequence?
A. Figure series
B. Blood relation
C. Direction test
D. Alphabet test
Answer: A
Q31. In counting triangles, we should consider:
A. Only smallest triangles
B. Only the outer triangle
C. Small, medium and large combinations
D. Only inverted triangles
Answer: C
Q32. Which of the following is NOT normally a transformation in figure series?
A. Rotation
B. Shading
C. Movement
D. Grammatical tense
Answer: D
Q33. In a water image, the left side generally:
A. Becomes right
B. Remains left
C. Disappears
D. Rotates 90°
Answer: B
Q34. In a mirror image, the top generally:
A. Becomes bottom
B. Remains top
C. Rotates
D. Disappears
Answer: B
Q35. A 90° anticlockwise rotation of an upward arrow makes it point:
A. Right
B. Left
C. Down
D. Up
Answer: B
Q36. A shape sequence follows ▲ → ■ → ● → ▲ → ■ → ?. The missing shape is:
A. ▲
B. ■
C. ●
D. ◆
Answer: C
Q37. In a figure matrix, if every row follows the same rule, the missing figure can be found by:
A. Applying the row rule
B. Guessing
C. Ignoring columns
D. Counting letters
Answer: A
Q38. Which shape has no straight sides?
A. Triangle
B. Square
C. Circle
D. Pentagon
Answer: C
Q39. Which figure generally has the greatest number of sides?
A. Triangle
B. Square
C. Pentagon
D. Hexagon
Answer: D
Q40. Matchstick puzzles mainly involve:
A. Arrangement of lines
B. Vocabulary
C. Grammar
D. Memory recall
Answer: A
Q41. In paper-folding questions, after unfolding:
A. The cut may appear symmetrically at multiple positions
B. The cut disappears
C. Only one side remains
D. The paper becomes circular
Answer: A
Q42. Which is important in embedded figure problems?
A. Orientation
B. Shape boundaries
C. Angles
D. All of these
Answer: D
Q43. If a pattern alternates between black and white, after Black → White → Black → White, the next is:
A. White
B. Black
C. Grey
D. None
Answer: B
Q44. If one line is added at every step, the next figure should have:
A. One fewer line
B. The same number
C. One additional line
D. No lines
Answer: C
Q45. Which is NOT a major type of shape puzzle?
A. Figure analogy
B. Figure matrix
C. Embedded figure
D. Essay writing
Answer: D
Q46. In shape analogy, the transformation from the first figure to the second should be:
A. Ignored
B. Applied to the third figure
C. Applied randomly
D. Applied only to the answer choices
Answer: B
Q47. A square has:
A. 2 sides
B. 3 sides
C. 4 sides
D. 5 sides
Answer: C
Q48. Which shape has five sides?
A. Triangle
B. Square
C. Pentagon
D. Hexagon
Answer: C
Q49. Which is the best first step when solving a complicated figure sequence?
A. Guess the answer
B. Observe the changing elements
C. Ignore the figures
D. Count letters
Answer: B
Q50. The most important skill for shape and arrangement puzzles is:
A. Visualization and logical observation
B. Memorizing vocabulary
C. Writing speed only
D. Spelling
Answer: A
Quick Revision Notes
| Concept | Key Point |
|---|---|
| Figure Series | Find the repeating/transformation pattern |
| Figure Analogy | Apply A→B transformation to C |
| Classification | Find the different figure |
| Embedded Figure | Find hidden target figure |
| Mirror Image | Left ↔ Right |
| Water Image | Top ↔ Bottom |
| Rotation | Figure turns around a point |
| Symmetry | Corresponding parts are balanced/reflected |
| Figure Matrix | Find row/column relationship |
| Counting Figures | Count small + combined figures |
| Paper Folding | Reverse folds after unfolding |
| Matchstick Puzzle | Rearrange/add/remove sticks |
| Spatial Arrangement | Understand relative positions |
Final Exam Tips
For Bihar STET, BPSC, SSC, Banking and Railway exams, practice these topics regularly:
Figure Series → Figure Analogy → Figure Classification → Embedded Figures → Mirror Image → Water Image → Figure Matrix → Counting Figures → Rotation → Paper Folding → Spatial Arrangement
Easy Memory Trick
M-W-R-S-C
M = Mirror
W = Water
R = Rotation
S = Series
C = Counting
These five areas form an important foundation for solving many non-verbal reasoning questions.
