🧊 Spatial & Figure Reasoning: Your Magic Eye Adventure!
Imagine you have a superpower to see things from every direction — even when they’re hiding! That’s what spatial reasoning is all about.
🎯 What’s This All About?
Think of yourself as a detective with X-ray vision. You can see:
- What’s INSIDE a wrapped gift box 🎁
- What a LEGO creation looks like from every angle
- Patterns that others miss!
This is Non-Verbal Reasoning — solving puzzles without words, using only your eyes and brain!
🎲 1. Cube Problems
The Story
Imagine a Rubik’s Cube. Each side has a different color or pattern. Now, if I spin it around, can you still tell which side is which?
What Is It?
A cube has 6 faces (like a dice). In cube problems, you see a flat drawing of a cube and need to figure out:
- Which face is opposite to which?
- What happens when you rotate it?
🧊 The Magic Rule
Opposite faces NEVER touch each other!
Think of your head:
- Your face is opposite to the back of your head
- Your left ear is opposite to your right ear
- The top of your head is opposite to your chin
Simple Example
[1]
[2][3][4][5]
[6]
This is an unfolded cube (like opening a cardboard box flat).
- Face 1 is opposite to Face 6
- Face 2 is opposite to Face 4
- Face 3 is opposite to Face 5
When you fold it back into a cube, opposite faces never share an edge!
🎯 Quick Trick
In a cross-shaped unfolding:
- The TOP face is opposite to the one 2 squares DOWN
- The LEFT face is opposite to the one 2 squares RIGHT
🎨 2. Painted Cube Problems
The Story
Imagine dipping a white sugar cube into a bucket of red paint. Now cut it into smaller cubes. Some tiny cubes have paint on 3 sides, some on 2, some on 1, and some have NO paint at all (they were hiding inside!).
The Magic Formula 🪄
If you cut a cube into n×n×n smaller cubes:
| Paint on… | Where are they? | How many? |
|---|---|---|
| 3 faces | Corner cubes | Always 8 |
| 2 faces | Edge cubes (not corners) | 12 × (n-2) |
| 1 face | Face cubes (in the middle of each side) | 6 × (n-2)² |
| 0 faces | Hidden inside | (n-2)³ |
Example: A 3×3×3 Painted Cube
Cut into 27 tiny cubes:
- 8 cubes have 3 painted faces (corners)
- 12 cubes have 2 painted faces (edges)
- 6 cubes have 1 painted face (center of each side)
- 1 cube has 0 painted faces (the hidden one in the very middle!)
Check: 8 + 12 + 6 + 1 = 27 ✓
🧠 Think About It
The bigger the cube, the more “hiding” cubes inside with no paint!
🎲 3. Dice Problems
The Story
A dice is just a special cube where opposite faces add up to 7!
1 is opposite to 6 (1+6=7)
2 is opposite to 5 (2+5=7)
3 is opposite to 4 (3+4=7)
The Standard Dice Rule
On a standard dice, if you place it with 1 on top and 2 facing you:
- 3 is on your RIGHT
- 4 is on your LEFT
- 5 is behind
- 6 is at the bottom
Dice Problem Types
Type 1: Find the Opposite Given two views of the same dice, figure out what’s opposite to what.
Type 2: Which Dice is Different? Spot the dice that doesn’t follow the same pattern.
Type 3: Dice Rotation If I roll a dice forward twice, what number is on top now?
Example Problem
A dice shows:
- Position 1: Top=3, Front=1, Right=2
- Position 2: Top=1, Front=5, Right=3
What is opposite to 2?
Solution: In Position 1, 2 is on the right. In Position 2, 5 is the front (and 6 would be at the back, opposite to 1). Following the rotations… 2 is opposite to 5!
🏗️ 4. 2D to 3D Visualization
The Story
Ever built something with paper? A flat piece of paper (2D) folds into a box (3D). This is 2D to 3D magic!
What You Need to Know
Nets → 3D Shapes A “net” is a flat pattern that folds into a 3D shape.
graph TD A["Flat Net"] -->|Fold| B["3D Cube"] C["Paper Star"] -->|Fold| D["3D Star"]
Common 3D Shapes and Their Nets
| Shape | Faces | What it looks like flat |
|---|---|---|
| Cube | 6 squares | Cross or T-shape |
| Pyramid | 4 triangles + 1 square | Star with square center |
| Cylinder | 2 circles + 1 rectangle | Two circles above a rectangle |
The Folding Trick 🎁
When looking at a net, imagine:
- Pick one face to be the “base” (bottom)
- Fold the connected faces UP
- Check: Do edges that touch in 3D connect in the 2D net?
Example
Which net folds into a cube?
Net A: Net B:
[_][_] [_][_][_][_]
[_][_] [_]
[_][_] [_]
Answer: Neither! Net A has too many faces overlapping. Net B would work if arranged correctly. A cube net must have exactly 6 squares with proper connections.
🔍 5. Rule Detection
The Story
You’re a pattern detective! Look at a series of shapes. Something is changing… What’s the secret rule?
Common Rules to Spot
| Rule Type | What Changes | Example |
|---|---|---|
| Rotation | Shape spins | Arrow turns 45° each time |
| Addition | More elements added | 1 dot → 2 dots → 3 dots |
| Subtraction | Elements removed | 5 circles → 4 circles → 3 circles |
| Color flip | Black ↔ White | ⚫→⚪→⚫→⚪ |
| Size change | Gets bigger/smaller | Small → Medium → Large |
| Position shift | Moves location | Left → Center → Right |
Multi-Rule Detection
Sometimes 2 or 3 rules work together!
Example:
Figure 1: Small black triangle pointing UP
Figure 2: Medium black triangle pointing RIGHT
Figure 3: Large black triangle pointing DOWN
Figure 4: ???
Rules Found:
- Size: Small → Medium → Large → (Back to Small?)
- Rotation: Turns 90° clockwise each time
Answer: Small black triangle pointing LEFT
Detective Tips 🔎
- Look at EACH element separately
- Check rotation first (most common)
- Count elements (addition/subtraction)
- Compare colors
- Measure sizes
- Track positions
🔗 6. Figure Analogy
The Story
“Dog is to puppy as cat is to _____?”
Figure analogy works the same way, but with shapes instead of words!
The Format
A : B :: C : ? (A is to B as C is to what?)
Common Transformations
| Change | Example |
|---|---|
| Rotate | Square turns into a diamond |
| Mirror/Flip | Left-facing arrow becomes right-facing |
| Invert colors | Black star becomes white star |
| Add parts | Triangle gets an extra line |
| Scale | Small circle becomes large circle |
| Split | One shape becomes two |
| Merge | Two shapes become one |
Solving Steps
graph TD A["Look at A"] --> B["Look at B"] B --> C["Find the change: A→B"] C --> D["Apply same change to C"] D --> E[That's your answer!]
Example
[▲] : [▼] :: [◄] : [?]
Step 1: Triangle pointing UP becomes triangle pointing DOWN Step 2: Rule = Flip upside down (180° rotation) Step 3: Apply to left arrow → Gets flipped → Right arrow Answer: [►]
🗂️ 7. Figure Classification
The Story
Imagine sorting your toys into boxes. All cars go in one box, all dolls in another. Figure classification is sorting shapes into groups based on what they have in common!
How It Works
You see 5 figures. Find the odd one out OR group similar ones together.
Common Classification Rules
| Basis | What to Look For |
|---|---|
| Number of sides | All triangles vs. one square |
| Open vs. Closed | Complete shapes vs. incomplete |
| Number of elements | 3 dots vs. 4 dots |
| Symmetry | Symmetric shapes vs. asymmetric |
| Curves vs. Straight | All curved vs. one angular |
| Direction | All facing left vs. one facing right |
Example
Find the odd one out:
A: ★ (5 points)
B: ⬡ (6 sides)
C: △ (3 sides)
D: ⬠ (5 sides)
E: ○ (no sides/infinite)
Answer: E (Circle) — It’s the only shape with no straight sides. Or you could say A (Star) — It’s the only shape with points sticking out!
Note: Sometimes multiple answers can be correct with different reasoning!
Classification Strategy
- Count sides/elements
- Look for symmetry
- Check direction/orientation
- Notice patterns (dots, lines, curves)
- Observe colors (if any)
🎯 Quick Summary
| Topic | Key Point |
|---|---|
| Cube Problems | Opposite faces never touch |
| Painted Cubes | Corner=3, Edge=2, Face=1, Inside=0 |
| Dice Problems | Opposite faces sum to 7 |
| 2D to 3D | Nets fold into shapes |
| Rule Detection | Find what changes step by step |
| Figure Analogy | A:B = C:? (Apply same change) |
| Classification | Find the odd one out by one rule |
🚀 Your Superpower Unlocked!
You now have spatial vision superpowers! You can:
- ✅ See inside cubes without cutting them
- ✅ Count painted faces like a pro
- ✅ Predict dice positions after rolling
- ✅ Unfold 3D shapes in your mind
- ✅ Spot hidden patterns others miss
- ✅ Complete shape puzzles with confidence
- ✅ Group figures like a sorting wizard
Remember: Every puzzle is just a pattern waiting to be discovered. Keep your detective eyes sharp, and no spatial puzzle can stump you!
Happy Puzzling! 🧩