🔍 Figure Patterns and Analysis
Your Secret Superpower for Seeing Hidden Shapes!
The Story of the Shape Detective 🕵️
Imagine you’re a Shape Detective. Your job? Finding hidden shapes, spotting patterns, and solving visual puzzles that others can’t see!
Think of it like a game of hide-and-seek with shapes. Sometimes shapes hide inside other shapes. Sometimes they follow a secret dance pattern. Your mission is to crack the code!
Why does this matter? Companies, schools, and competitive exams love testing this skill because it shows how well you can think without words. It’s pure brain power! 🧠
1. Embedded Figures 🎯
Finding the Shape That’s Playing Hide-and-Seek
The Simple Idea: An embedded figure is a small shape hiding inside a bigger, messy shape. Your job? Find where the little shape is hiding!
Real-Life Example 🌳
You’re looking at a big tree. Can you find the triangle shapes in the spaces between branches? That’s embedded figure spotting!
How It Works
Question Shape: Complex Figure:
△ ╔═══════╗
║ △ ╱╲ ║
║╱╲ ╲╱╲ ║
╚═══════╝
Answer: The triangle is hidden in the top-left!
🔑 Quick Tips
- Trace the edges of your target shape with your finger
- Ignore extra lines - they’re just distractions
- Check rotation - the shape might be tilted!
- Same size, same proportions - the hidden shape is identical
Example Problem
Find this shape: A simple square (□)
Inside this figure:
╱╲
╱ ╲
╱ □ ╲
╱╲ ╱╲
╱ ╲ ╱ ╲
Answer: The square is in the center of the triangular pattern!
2. Figure Completion ✏️
Finishing the Picture Puzzle
The Simple Idea: You get a shape with a missing piece. Your job? Find which piece fits perfectly!
Real-Life Example 🧩
It’s exactly like putting the last piece of a jigsaw puzzle. The piece must fit perfectly - same bumps, same curves!
How It Works
Given Figure: Options:
┌─────────┐ A: ╲╱ B: ─┐
│ ? │ C: ╱╲ D: └─
│ ╱ │
└─────────┘
The ? area needs a piece that continues the ╱ line!
Answer: Option C (╱╲) completes the pattern
🔑 Quick Tips
- Look at the edges - lines must connect smoothly
- Check the angles - corners must match
- Follow the pattern - if there’s a design, continue it
- Rotate mentally - sometimes pieces are rotated
Example Problem
Complete this figure:
┌──────┐
│ ● ● │
│ ╲╱ │
│ ? │
└──────┘
What goes in ?
- A: ●
- B: ╲
- C: ╱╲
- D: ●●
Answer: D (●●) - The pattern shows pairs of dots with a V between them, so we need another pair!
3. Counting Figures 🔢
How Many Shapes Are Hiding Here?
The Simple Idea: Count ALL the shapes in a figure - including the ones made by combining smaller shapes!
Real-Life Example 🍕
When you cut a pizza into 4 slices, you have:
- 4 individual slices (triangles)
- 2 half-pizzas (combining 2 slices each)
- 1 full pizza (combining all 4)
- Total: 7 shapes from just 4 cuts!
The Counting Method
Simple Triangle Grid:
△
╱╲
△──△
╱╲ ╱╲
△──△──△
Small triangles: 4 (pointing up)
Medium triangles: 3 (made of 4 small ones)
Large triangle: 1 (the whole thing)
TOTAL TRIANGLES = 9
🔑 Counting Rules
- Start small - count the tiniest shapes first
- Combine pairs - count shapes made of 2 small ones
- Combine groups - count shapes made of 3, 4, 5… small ones
- Don’t forget the whole - the entire figure counts too!
Counting Squares Example
┌─┬─┐
├─┼─┤
└─┴─┘
1×1 squares: 4 (the small ones)
2×2 squares: 1 (the big one)
TOTAL SQUARES = 5
Formula Hint 💡
For a square grid of n×n small squares: Total squares = n² + (n-1)² + (n-2)² + … + 1²
For 2×2: 4 + 1 = 5 squares ✓
4. Pattern Recognition in Figures 🎨
Cracking the Visual Code
The Simple Idea: Shapes follow rules - they might rotate, flip, change size, or change color in a pattern. Your job? Find the rule!
Real-Life Example 🌙
The moon follows a pattern: new moon → crescent → half → full → half → crescent → new. Once you know the pattern, you can predict what comes next!
Common Pattern Types
A. Rotation Patterns 🔄
Step 1 Step 2 Step 3 Step 4
│ ─ │ ─
● ● ● ●
Pattern: The line rotates 90° clockwise each step
B. Flip Patterns ↔️
Step 1 Step 2 Step 3 Step 4
◢ ◣ ◢ ◣
Pattern: The triangle flips left-right each step
C. Addition Patterns ➕
Step 1 Step 2 Step 3 Step 4
● ● ● ● ● ● ● ● ● ●
Pattern: Add one dot each step
D. Color/Shade Patterns 🎭
Step 1 Step 2 Step 3 Step 4
■ □ ■ □
Pattern: Alternates between filled and empty
🔑 Pattern-Finding Strategy
- Compare neighbors - what changed between step 1 and 2?
- Confirm the rule - does the same change happen between 2 and 3?
- Apply the rule - predict what comes next!
5. Figure Series 📊
What Comes Next in the Shape Story?
The Simple Idea: A figure series is like a story told in pictures. Each picture changes a little bit. Your job? Guess the next picture in the story!
Real-Life Example 🚶
Think of a walking animation:
- Left foot forward
- Right foot forward
- Left foot forward
- Right foot forward…
Once you see the pattern, you know what comes next!
Example Series Problem
Box 1 Box 2 Box 3 Box 4 Box 5
┌───┐ ┌───┐ ┌───┐ ┌───┐ ┌───┐
│ ▲ │ │▲ │ │ ▲ │ │ ▲│ │ ? │
│ │ │ │ │ │ │ │ │ │
└───┘ └───┘ └───┘ └───┘ └───┘
What goes in Box 5?
Analysis:
- Box 1: Triangle in CENTER
- Box 2: Triangle on LEFT
- Box 3: Triangle in CENTER
- Box 4: Triangle on RIGHT
- Box 5: Should be CENTER (pattern repeats!)
Answer: Triangle in CENTER ▲
Multi-Element Series
Step 1: ●○ Step 2: ○● Step 3: ●○ Step 4: ?
The dot pair swaps positions each time!
Answer: ○●
🔑 Series-Solving Steps
- List all elements - what shapes are in each box?
- Track each element - how does each shape change?
- Find the rhythm - is it every step? Every 2 steps?
- Predict the future - apply the rule to find the answer!
6. Figure Matrix Problems 🧮
Solving the Grid Puzzle
The Simple Idea: A figure matrix is a 3×3 grid of shapes. Each row follows a rule. Each column follows a rule. One box is missing - find it!
Real-Life Example 📅
Think of a calendar. Every row is a week. Every column is the same day (all Mondays, all Tuesdays). There’s a pattern in both directions!
How Matrix Rules Work
Column 1 Column 2 Column 3
┌─────────┬─────────┬─────────┐
Row 1 │ ● │ ● ● │ ● ● ● │
├─────────┼─────────┼─────────┤
Row 2 │ ■ │ ■ ■ │ ■ ■ ■ │
├─────────┼─────────┼─────────┤
Row 3 │ ▲ │ ▲ ▲ │ ? │
└─────────┴─────────┴─────────┘
Row Rule: Add one shape each column
Column Rule: Different shape each row
Answer: ▲ ▲ ▲ (three triangles)
Common Matrix Patterns
Pattern 1: Rotation Across Row
│ ├ │ ┬ │ ┤ │ Each box rotates 90°
Pattern 2: Addition/Subtraction
│ ● │ ●● │ ●●●│ Adding elements
Pattern 3: Combination
│ ● │ ■ │ ●+■ │ Row 3 = Row 1 + Row 2
🔑 Matrix-Solving Strategy
-
Analyze ROWS first
- What changes from left to right?
-
Analyze COLUMNS second
- What changes from top to bottom?
-
Check DIAGONALS (sometimes)
- Rare but possible pattern location
-
Apply BOTH rules
- The answer must satisfy row AND column patterns!
Complete Example
┌─────┬─────┬─────┐
│ ○ │ □ │ △ │ ← Different shapes
├─────┼─────┼─────┤
│ ◐ │ ◧ │ ◭ │ ← Half-filled
├─────┼─────┼─────┤
│ ● │ ■ │ ? │ ← Fully filled
└─────┴─────┴─────┘
Row Pattern: Circle, Square, Triangle
Column Pattern: Empty → Half → Full
Answer: ▲ (filled triangle)
🎯 Master Strategy for All Figure Problems
The 5-Second Scan
- What type is it? (Embedded? Series? Matrix?)
- How many elements? (Shapes, colors, positions)
- What’s changing? (Rotation? Size? Number?)
- What’s the rule? (Every step? Alternating?)
- Apply and verify!
Common Traps to Avoid ⚠️
- Don’t rush - wrong answers are designed to trick you
- Check ALL rules - matrices have row AND column patterns
- Watch for rotation - shapes might be the same, just tilted
- Count carefully - in counting problems, go systematically
🏆 Your Shape Detective Toolkit
| Problem Type | Key Question | First Step |
|---|---|---|
| Embedded | “Where is it hiding?” | Trace the target shape |
| Completion | “What piece fits?” | Check edge connections |
| Counting | “How many total?” | Start with smallest |
| Pattern | “What’s the rule?” | Compare neighbors |
| Series | “What comes next?” | Track each element |
| Matrix | “What satisfies both?” | Check rows, then columns |
💪 You’ve Got This!
Remember: These puzzles aren’t about being “naturally smart.” They’re about having a system and practicing it!
Every time you solve a figure puzzle:
- Your visual brain gets stronger 🧠
- Your pattern-spotting improves 👁️
- Your confidence grows! 🌟
Now go find those hidden shapes, crack those codes, and become the ultimate Shape Detective! 🕵️♂️✨