What are Number Series, Cube & Dice? These are reasoning ability topics testing pattern recognition. Number series involves finding missing numbers in sequences. Cube questions test spatial ability with cube nets and folding. Dice questions involve understanding dice patterns and positions.

2
4
6
?
10

Find the missing number in the series. Pattern: Even numbers increasing by 2

A
B
C
D
E
F
G
H
I

Cube net visualization - which faces are opposite when folded?

Pro Tip – The 3-Step Series Solving Method!

1. Check Differences: Find differences between consecutive numbers
2. Look for Patterns: Check arithmetic, geometric, or special patterns
3. Verify: Apply pattern to entire series to confirm
Visit SKY Practice for 400+ Series, Cube & Dice questions with detailed solutions.

1. Number Series Basics

What is a Number Series? A sequence of numbers following a specific pattern. Your task is to identify the pattern and find the missing number or next number in the series.

Understanding Series Formats

Types of Number Series in SSC CGL

SSC tests number series in various formats: simple arithmetic, geometric, mixed patterns, and special series.

Arithmetic Series

  • Constant difference between terms
  • Example: 2, 4, 6, 8, 10 (+2 each)
  • Increasing or decreasing
  • Can have variable differences
  • Common in SSC exams
  • Easy to identify
Example: 5, 10, 15, 20, ?
Pattern: +5 each time. Next: 25

Geometric Series

  • Constant ratio between terms
  • Example: 2, 4, 8, 16, 32 (Γ—2 each)
  • Multiplication/division pattern
  • Can be fractions/decimals
  • Less common than arithmetic
  • Watch for large jumps
Example: 3, 6, 12, 24, ?
Pattern: Γ—2 each time. Next: 48

Mixed Patterns

  • Combination of operations
  • Example: +2, Γ—2, +2, Γ—2
  • Alternating patterns
  • Multiple step operations
  • Common in advanced questions
  • Requires careful analysis
Example: 2, 4, 8, 10, 20, ?
Pattern: Γ—2, +2, Γ—2, +2. Next: 22

Special Series

  • Square numbers: 1, 4, 9, 16
  • Cube numbers: 1, 8, 27, 64
  • Fibonacci: 1, 1, 2, 3, 5, 8
  • Prime numbers: 2, 3, 5, 7, 11
  • Pattern based on position
  • Complex mathematical patterns
Example: 1, 4, 9, 16, ?
Pattern: Square numbers. Next: 25 (5Β²)

SSC Shortcut: Series Pattern Identification

Check differences first: Subtract consecutive numbers

Check ratios next: Divide consecutive numbers if differences not constant

Look for alternating patterns: Odd/even positions may have different patterns

Check squares/cubes: See if numbers are perfect squares or cubes

Check prime numbers: Series of prime numbers

Look for Fibonacci pattern: Each term = sum of previous two

Solved Example: Basic Number Series

Q: Find the missing number: 2, 4, 6, ?, 10, 12
Step 1: Analyze the series
Given: 2, 4, 6, ?, 10, 12
Observe: Numbers are increasing

Step 2: Check differences
4 - 2 = 2
6 - 4 = 2
Difference seems constant: +2

Step 3: Apply pattern
If pattern is +2:
2 (+2)β†’ 4
4 (+2)β†’ 6
6 (+2)β†’ 8 (missing number)
8 (+2)β†’ 10
10 (+2)β†’ 12 βœ“

Step 4: Verify entire series
Series: 2, 4, 6, 8, 10, 12
All differences = 2 βœ“

Step 5: Check alternative patterns
Could it be even numbers? 2,4,6,8,10,12 βœ“
Could it be multiples of 2? 2,4,6,8,10,12 βœ“
Both confirm 8 as missing number

Step 6: Write final answer
Missing number = 8

Pattern identification:
This is a simple arithmetic progression with common difference = 2
Formula: an = 2n where n=1,2,3...
Or: an = an-1 + 2

Final Answer: 8

2. Number Series Patterns & Techniques

Advanced Patterns: SSC often uses complex patterns that require multiple steps to identify.

Common Series Patterns

Frequency of Series Types in SSC CGL

Based on analysis of previous 5 years' papers, these are the most common series patterns.

Series Pattern Frequency in SSC CGL

Arithmetic Series 85%
Mixed Patterns 70%
Geometric Series 65%
Square/Cube Series 60%
Alternating Patterns 55%
Prime Numbers 50%
Fibonacci Type 45%

Arithmetic Patterns

β€’ Simple: +2, +3, +4, etc.
β€’ Increasing difference: +2, +4, +6, +8
β€’ Decreasing: -3, -5, -7, -9
β€’ Variable: +2, +3, +2, +3 alternating
β€’ Double step: Add same number twice

Examples:
2,4,6,8 β†’ +2 each
2,5,10,17 β†’ +3,+5,+7 (odd numbers)
100,95,85,70 β†’ -5,-10,-15

Geometric Patterns

β€’ Simple: Γ—2, Γ—3, Γ—0.5
β€’ Increasing ratio: Γ—2, Γ—3, Γ—4
β€’ Decreasing ratio: Γ·2, Γ·3, Γ·4
β€’ Alternating: Γ—2, Γ·2, Γ—2, Γ·2
β€’ Combined: Γ—2 then +1 pattern

Examples:
3,6,12,24 β†’ Γ—2 each
2,6,24,120 β†’ Γ—3,Γ—4,Γ—5
64,32,16,8 β†’ Γ·2 each

Square/Cube Patterns

  • Perfect squares: 1,4,9,16,25
  • Perfect cubes: 1,8,27,64,125
  • Squares with operations
  • Cubes with operations
  • Square roots series
  • Cube roots series
Examples:
1,4,9,16,25 (1Β²,2Β²,3Β²,4Β²,5Β²)
1,8,27,64,125 (1Β³,2Β³,3Β³,4Β³,5Β³)
2,5,10,17,26 (1Β²+1,2Β²+1,3Β²+1...)

Special Patterns

  • Fibonacci: 1,1,2,3,5,8,13
  • Prime numbers: 2,3,5,7,11,13
  • Triangular numbers: 1,3,6,10,15
  • Factorial: 1,2,6,24,120
  • Digital sum patterns
  • Product of digits
Examples:
Fibonacci: 1,1,2,3,5,8 (sum of previous two)
Triangular: 1,3,6,10,15 (1,1+2,1+2+3...)
Factorial: 1,2,6,24 (1!,2!,3!,4!)

1 Difference Method for Series

Step 1: Find first differences (subtract consecutive terms)
D1 = a2 - a1, a3 - a2, a4 - a3, ...

Step 2: If D1 not constant, find second differences
D2 = differences of D1

Step 3: Continue until pattern emerges

Example: 2, 5, 10, 17, 26, ?
D1: 3, 5, 7, 9 (increasing by 2)
D2: 2, 2, 2 (constant)
Next D1: 9+2=11
Next term: 26+11=37

Pattern: an = nΒ² + 1

2 Ratio Method for Series

Step 1: Find ratios (divide consecutive terms)
R1 = a2 Γ· a1, a3 Γ· a2, a4 Γ· a3, ...

Step 2: If R1 constant β†’ geometric series
If R1 not constant, check pattern in ratios

Step 3: For alternating patterns, check odd/even positions separately

Example: 2, 6, 12, 36, 72, ?
Ratios: 6Γ·2=3, 12Γ·6=2, 36Γ·12=3, 72Γ·36=2
Pattern: Γ—3, Γ—2, Γ—3, Γ—2 alternating
Next: 72Γ—3=216

Pattern: Odd positions: Γ—3, Even positions: Γ—2

Solved Example: Complex Series Pattern

Q: Find the missing number: 2, 3, 5, 9, 17, ?
Step 1: Analyze the series
Given: 2, 3, 5, 9, 17, ?
Numbers are increasing but not linearly

Step 2: Check differences
3 - 2 = 1
5 - 3 = 2
9 - 5 = 4
17 - 9 = 8
Differences: 1, 2, 4, 8

Step 3: Analyze differences pattern
Differences: 1, 2, 4, 8
This looks like powers of 2: 2⁰, 2¹, 2², 2³
Or: Γ—2 each time: 1Γ—2=2, 2Γ—2=4, 4Γ—2=8

Step 4: Predict next difference
Next difference should be: 8 Γ— 2 = 16
Or: 2⁴ = 16

Step 5: Find missing number
17 + 16 = 33

Step 6: Verify pattern
Series: 2, 3, 5, 9, 17, 33
Check: Each term = previous term + 2^(n-1)
Where n is position of difference
Or: Each term = 2Γ—previous term - 1? Let's check:
2Γ—2-1=3 βœ“, 2Γ—3-1=5 βœ“, 2Γ—5-1=9 βœ“, 2Γ—9-1=17 βœ“, 2Γ—17-1=33 βœ“
Pattern confirmed: an = 2an-1 - 1

Step 7: Alternative pattern recognition
This is also: 2, 2+1=3, 3+2=5, 5+4=9, 9+8=17, 17+16=33
Where added numbers double each time

Step 8: Write final answer
Missing number = 33

Pattern identification:
Multiple patterns work:
1. an = 2an-1 - 1
2. Start with 2, add 1,2,4,8,16... (powers of 2)
3. Formula: an = 2^(n) + 1? Let's test: n=1:2ΒΉ+1=3 βœ— (should be 2)
Actually: an = 2^(n-1) + 1? Test: n=1:2⁰+1=2 βœ“, n=2:2ΒΉ+1=3 βœ“, n=3:2Β²+1=5 βœ“
Yes: an = 2^(n-1) + 1 works!

Final Answer: 33
2
3
5
9
17
?
65
129
257
513

Extended series pattern: 2, 3, 5, 9, 17, 33, 65, 129, 257, 513 (2a-1 pattern)

3. Cube Basics & Folding Concepts

Cube Problems: These test spatial visualization ability - understanding how 2D nets fold into 3D cubes and identifying opposite/adjacent faces.

Cube Fundamentals

Understanding Cube Properties

A cube has 6 faces, 8 vertices, and 12 edges. In cube problems, we focus on face positions and relationships.

Front
Top
Back
Left
Center
Right
Bottom
Hidden
Opposite

Opposite Faces Rule

  • Cube has 3 pairs of opposite faces
  • Opposite faces never touch
  • They are always separated
  • Standard dice: 1↔6, 2↔5, 3↔4
  • In letter cubes: A↔Z, B↔Y, etc.
  • Opposite faces sum to 7 in dice
Rule:
If front = A, back = opposite face
If top = B, bottom = opposite face

Adjacent Faces Rule

  • Adjacent faces share an edge
  • They touch each other
  • Four faces adjacent to any face
  • One face opposite (not adjacent)
  • In nets, adjacent faces share sides
  • Can rotate around edges
Rule:
If A is adjacent to B and C
Then B and C may be adjacent or opposite

Rotation Rules

  • Cube can rotate in 3 dimensions
  • Faces maintain relationships
  • Opposite faces remain opposite
  • Adjacent faces remain adjacent
  • Relative positions change
  • Visualize mental rotation
Example:
Rotate cube 90Β° right:
Front→Right, Right→Back, etc.

Unfolding Rules

  • Cube unfolds into 6 connected squares
  • 11 possible net patterns
  • Opposite faces separated in net
  • Adjacent faces share edges
  • Can refold mentally
  • Practice visualization
Rule:
In net, opposite faces never share edge
They're separated by at least one face

SSC Shortcut: Cube Problem Solving

Identify opposite faces first: Look for faces that can't be adjacent

Use elimination: If A adjacent to B, and B opposite to C, then A adjacent to C

Visualize mentally: Imagine holding and rotating the cube

Draw simple diagrams: Sketch cube with labeled faces

Check all options: Test each option against given conditions

Remember standard dice: 1↔6, 2↔5, 3↔4 (sum=7)

Solved Example: Cube Faces

Q: In a cube, if face A is opposite to face B, and face C is adjacent to both A and B, which face is opposite to C?
Step 1: Understand the cube structure
A cube has 6 faces: Let's label them A, B, C, D, E, F
Given: A opposite B (so A and B are on opposite sides)

Step 2: Visualize the cube
Imagine a cube with A on front, B on back (opposite)
The four side faces are adjacent to both A and B
These are: left, right, top, bottom faces

Step 3: Place C according to condition
C is adjacent to both A and B
This means C must be one of the four side faces
Let's say C is the left face

Step 4: Identify opposite to C
In a cube, each face has one opposite face
If C is left face, its opposite is right face
Let's call the right face D
So C opposite D

Step 5: Generalize the solution
In a cube, if a face is adjacent to two opposite faces,
then it must be a side face (not front/back)
The opposite of a side face is the opposite side face

Step 6: Verify with cube properties
Property: Each face touches 4 other faces, opposite to 1 face
Face adjacent to both A and B must be perpendicular to line joining A and B
Its opposite will also be perpendicular to A-B line

Step 7: Check with actual cube
Take a die: 1 opposite 6
Faces adjacent to both 1 and 6: 2,3,4,5
Take 2 (adjacent to 1 and 6)
Opposite of 2 is 5 βœ“
Take 3 (adjacent to 1 and 6)
Opposite of 3 is 4 βœ“
Pattern holds

Step 8: Write final answer
The face opposite to C is the face that is also adjacent to both A and B but opposite to C
In other words, among the four side faces, each has an opposite side face

Final Answer: The face opposite to C is the one that completes the pair of side faces adjacent to both A and B

4. Cube Nets & Folding Problems

Net Problems: Given a 2D net of a cube, determine which faces are opposite/adjacent when folded into a 3D cube.

Cube Net Patterns

Understanding Cube Nets

A cube net is a 2D arrangement of 6 squares that can be folded to form a cube. There are 11 distinct net patterns.

A
B
C
D
E
F

Sample cube net - when folded, which faces become opposite?

Folding Rules

  • Each square becomes a cube face
  • Shared edges become cube edges
  • Opposite faces in net are separated
  • Faces sharing edge in net become adjacent
  • Some faces become top/bottom
  • Some become front/back
Key Rule:
In net, if two faces share full edge, they become adjacent in cube

Finding Opposites

  • Look for faces separated by one face
  • Opposite faces never share edge in net
  • They're usually at ends of "T" or "L"
  • Count squares between faces
  • Use elimination method
  • Test mental folding
Method:
Pick a face, find which face ends up opposite when folded

Common Net Patterns

  • Cross shape (most common)
  • T shape variations
  • L shape patterns
  • Zigzag patterns
  • SSC uses limited patterns
  • Practice with 2-3 patterns
Tip:
Most SSC nets are cross or T shapes. Learn these well.

Verification Methods

  • Mentally fold step by step
  • Draw folding sequence
  • Use elimination of options
  • Check adjacency conditions
  • Verify opposite face pairs
  • Test with simple examples
Check:
After folding, each face should have 4 adjacent faces and 1 opposite

1 Net Folding Technique

Step 1: Identify which square will be base/bottom

Step 2: Fold adjacent squares up to form sides

Step 3: Fold top squares to complete cube

Step 4: Track face positions during folding

Step 5: Identify opposite faces (those that end up facing each other)

Example Net:
[B]
[A][C][D]
  [E]
  [F]

If we make C the front face:
A = left, D = right, B = top, E = back? Need to visualize folding

2 Quick Opposite Face Method

Method: For cross-shaped nets (most common in SSC)

Rule: Faces at opposite ends of the cross are opposite

Example Cross Net:
   [B]
[A][C][D][E]
   [F]

Opposite pairs:
β€’ A ↔ E (horizontal ends)
β€’ B ↔ F (vertical ends)
β€’ C ↔ ? (center with D? Actually C and D are adjacent)
Wait, in cross net, center squares are adjacent

Actually in standard cross: middle square of cross is adjacent to all four arms
Arms at opposite ends are opposite

Solved Example: Cube Net Problem

Q: Given the cube net below, which face is opposite to face X?

  [A]
[X][B][C]
  [D]
Step 1: Understand the net layout
Net shown:
Row 1:   A
Row 2: X B C
Row 3:   D
This is a T-shaped net

Step 2: Choose base face for folding
Let's choose B as the base/front face (central position)
When folded, B becomes front face

Step 3: Fold adjacent faces
Faces adjacent to B (sharing edges in net):
β€’ X (left of B) β†’ becomes left face
β€’ C (right of B) β†’ becomes right face
β€’ A (above B) β†’ becomes top face
β€’ D (below B) β†’ becomes bottom face

Step 4: Identify the missing face
We have used: X, B, C, A, D (5 faces)
Cube has 6 faces, so one face is missing/hidden
When we fold, the face opposite to B (back face) is not visible in this net
But we need opposite of X, not B

Step 5: Refold with X as focus
Alternative: Let's make X the base/front face
If X is front:
β€’ B (right of X) β†’ right face
β€’ A (above and right of X?) Actually A is above B, not directly above X
Let's visualize differently

Step 6: Use elimination method
In the net, X shares edges with B only
So when folded, X is adjacent to B
X does NOT share edges with A, C, D in net
But after folding, some will become adjacent

Step 7: Mental folding sequence
Let's fold step by step:
1. Keep B as center, fold X up to become left face
2. Fold C up to become right face
3. Fold A down to become top face (needs rotation)
4. Fold D up to become bottom face
5. The face originally opposite X in 2D becomes back face
Looking at net: Which face is farthest from X?
X is at left end, C is at right end β†’ likely opposite

Step 8: Check with cube properties
In T-shaped net, the single square at one end (X) is usually opposite to the single square at other end if they're aligned
Here: X at left end, C at right end (both in middle row)
They are likely opposite
Test: Are they separated enough? Yes, with B between them
When folded, X and C end up opposite

Step 9: Verify with other faces
If X opposite C, then:
β€’ X adjacent to B, A, D, and back face (missing)
β€’ C adjacent to B, A, D, and back face
This seems consistent

Step 10: Write final answer
Face opposite to X is C

Alternative verification:
In many T-nets, the two ends of the horizontal bar are opposite
Here horizontal bar: X-B-C
Ends: X and C β†’ opposite
Middle: B β†’ adjacent to both X and C

Final Answer: C is opposite to X

5. Dice Basics & Patterns

Dice Problems: Standard dice have specific numbering patterns. Questions involve determining which numbers are on hidden faces or understanding dice rotations.

Standard Dice Properties

Standard Dice Rules

A standard dice has numbers 1-6 with opposite faces summing to 7. The arrangement follows specific patterns.

β†’
β†’

Dice faces showing 3, 6, and 2 dots respectively

Rule 1: Opposite Faces Sum

1 + 6 = 7
2 + 5 = 7
3 + 4 = 7

Rule 2: Adjacent Faces

Faces sharing an edge are adjacent
Never opposite

Rule 3: Standard Arrangement

When 1 is on top, 6 at bottom
2,3,4,5 on sides

Dice Number Patterns

  • Standard dice: 1↔6, 2↔5, 3↔4
  • Sum of opposite faces = 7
  • Adjacent faces never sum to 7
  • Number arrangement is fixed
  • Two standard arrangements exist
  • SSC uses standard dice rules
Key Fact:
If you see 1, 2, and 3 around a vertex, they're arranged clockwise or anticlockwise

Dice Rotation Rules

  • When dice rotates, faces move
  • Opposite faces remain opposite
  • Adjacent faces remain adjacent
  • Relative positions change
  • Can rotate in 4 directions
  • Track one face during rotation
Example:
If 1 on top, 2 in front, rotate right β†’ 1 still top, 3 in front

Hidden Faces

  • In 2D views, some faces hidden
  • Opposite to visible face hidden
  • Use opposite face rule
  • Sum to 7 rule helps
  • Elimination method works
  • Consider all visible faces
Method:
If top=1, bottom=6 (hidden)
If front=2, back=5 (hidden)

Multiple Dice

  • Problems with 2-3 dice
  • Same rules apply to each
  • Compare faces/positions
  • Find relationships
  • Use elimination
  • Draw diagrams if needed
Tip:
Solve each dice separately first, then compare

SSC Shortcut: Dice Problem Solving

Remember 1↔6, 2↔5, 3↔4: Opposite faces sum to 7

If three faces visible around vertex: They're arranged in order

When dice rolled: Opposite faces remain opposite

For hidden faces: Opposite of visible face is hidden

For rotation problems: Track one face's movement

For comparison problems: Align dice to same orientation first

Solved Example: Standard Dice Problem

Q: In a standard dice, if 1 is on the top face, what number is on the bottom face?
Step 1: Recall standard dice rule
In a standard dice, opposite faces sum to 7
Known pairs: 1↔6, 2↔5, 3↔4

Step 2: Apply to given information
Top face = 1
Bottom face is opposite to top face
Opposite of 1 is 6 (since 1+6=7)

Step 3: Verify with dice properties
In any standard dice configuration:
β€’ If 1 is on top, 6 is on bottom
β€’ If 2 is on top, 5 is on bottom
β€’ If 3 is on top, 4 is on bottom
This is always true for standard dice

Step 4: Consider alternative arrangements
There are two standard dice arrangements (clockwise and anticlockwise)
But opposite faces remain same in both arrangements
So 1 always opposite 6 regardless of arrangement

Step 5: Write final answer
Bottom face = 6

Step 6: Extended understanding
Knowing top=1 and bottom=6, we can find side faces:
The four side faces are: 2,3,4,5
Their arrangement depends on which standard dice pattern
But for this question, only bottom face needed

Final Answer: 6

6. Advanced Dice Patterns & Problems

Complex Dice Questions: These involve multiple dice, rotations, or non-standard views requiring careful analysis.

Advanced Dice Scenarios

Complex Dice Problem Types

SSC sometimes presents dice in unusual positions or requires comparing multiple dice in different orientations.

1

Step 1: Identify Visible Faces

List all numbers visible in the given dice view or description

2

Step 2: Apply Opposite Face Rule

For each visible face, determine its opposite face (sum to 7)

3

Step 3: Determine Hidden Faces

Faces opposite to visible faces are hidden (if not shown)

4

Step 4: Check Adjacency

Verify that visible adjacent faces could actually be adjacent in a real dice

5

Step 5: Solve for Required Face

Use all information to find the asked face number or position

Solved Example: Multiple Dice Problem

Q: Two positions of a dice are shown below. What number will be opposite to 3?

Position 1: 1 on top, 2 in front, 3 on right
Position 2: 5 on top, 1 in front, ? on right
Step 1: Analyze Position 1
Position 1: Top=1, Front=2, Right=3
We need to find complete dice orientation
From Position 1: 1(top), 2(front), 3(right)
Bottom = opposite of top = 6 (since 1+6=7)
Back = opposite of front = 5 (since 2+5=7)
Left = opposite of right = 4 (since 3+4=7)
So complete dice: Top=1, Bottom=6, Front=2, Back=5, Right=3, Left=4

Step 2: Analyze Position 2
Position 2: Top=5, Front=1, Right=?
We know from Position 1 that:
5 is back face, 1 is top face, etc.
But in Position 2, orientation is different
Top=5 (which was back in Position 1)
Front=1 (which was top in Position 1)
So dice has been rotated

Step 3: Determine the rotation
From Position 1 to Position 2:
Original: Top=1, Front=2, Right=3, Back=5, Left=4, Bottom=6
New: Top=5 (was back), Front=1 (was top)
This means dice rotated forward (toward front)
Imagine holding dice with 1 on top, 2 in front
Rotate forward: Top becomes front, front becomes bottom, back becomes top
Actually, let's trace:
Original top (1) moves to front
Original front (2) moves to bottom
Original bottom (6) moves to back
Original back (5) moves to top βœ“ (matches Position 2 top=5)
Original right (3) stays right? Let's check
When rotating forward around right-left axis:
Right and left faces don't change position
So right should still be 3
But Position 2 shows right=? (unknown)
Actually question asks what's opposite to 3
We already know from Position 1: opposite of 3 is 4
But let's continue with Position 2

Step 4: Find right face in Position 2
In Position 2: Top=5, Front=1
From our rotation analysis:
When we rotated forward:
Original right (3) should remain right
So in Position 2, right should be 3
But the question shows "?" for right in Position 2
This suggests the dice might have different rotation

Step 5: Alternative approach
Let's use the standard dice property:
In Position 2: Top=5, Front=1
We need to find right face
From standard dice arrangements:
When 5 is top and 1 is front, what is right?
There are two standard dice types
Type 1 (clockwise): When 1 on top, 2 front β†’ 3 right
Type 2 (anticlockwise): When 1 on top, 2 front β†’ 4 right
But here we have 5 top, 1 front - different orientation

Step 6: Use Position 1 to determine dice type
Position 1: 1 top, 2 front, 3 right
This matches Type 1 (clockwise arrangement)
So dice is Type 1
In Type 1, when 1 on top, 2 front β†’ 3 right (given)
And when 2 on top, 3 front β†’ 1 right, etc.
We need to find: when 5 top, 1 front β†’ ? right
Let's find relationship:
From Position 1: Top=1, Front=2, Right=3
In Type 1 dice, numbers around a vertex go 1-2-3 clockwise
So when 5 is top (opposite of 2?), wait 5 is opposite of 2
If 5 is top, then 2 is bottom
And 1 is front
We need right face
From standard Type 1: Vertex with 1,2,3 has them clockwise
When 5 top (2 bottom), 1 front, the right face would be...
Actually easier: We already know from Position 1 complete dice:
Top=1, Bottom=6, Front=2, Back=5, Right=3, Left=4

Step 7: Reorient dice to Position 2
Position 2: Top=5, Front=1
From our complete dice:
5 was back, 1 was top
To get 5 on top and 1 in front, we need to rotate
Start with original: Top=1, Front=2, Right=3, Back=5, Left=4, Bottom=6
We want: Top=5, Front=1
One rotation: Rotate left (around vertical axis)
Original: Top=1, Front=2, Right=3, Back=5, Left=4, Bottom=6
Rotate left: Top=1, Front=3, Right=5, Back=4, Left=2, Bottom=6
Not yet (top still 1, not 5)
Rotate forward: Top=5, Front=1, Right=3, Back=6, Left=4, Bottom=2
Yes! This gives Top=5, Front=1, Right=3
So in Position 2, right face should be 3

Step 8: Answer the question
Question asks: What number will be opposite to 3?
We know from Position 1 or from dice properties:
Opposite of 3 is 4 (since 3+4=7)
This doesn't change with rotation
So opposite to 3 is always 4

Step 9: Write final answer
Number opposite to 3 is 4

Step 10: Verification
From Position 1: Right=3, so Left=4 (opposite)
From complete dice: Right=3, Left=4
When rotated to Position 2: Right=3, Left=4 (still opposite)
So answer is consistent

Final Answer: 4

7. SSC Shortcuts & Time-Saving Techniques

Exam-Focused Strategies: These shortcuts help solve series, cube, and dice questions quickly in SSC exams.

Time-Saving Techniques

Speed vs Accuracy Balance

In SSC exams, you need to solve reasoning questions quickly without sacrificing accuracy. These techniques help achieve that balance.

Series Shortcuts

β€’ Check differences first (90% of series)
β€’ If differences not constant, check second differences
β€’ Look for simple patterns: +2, +3, Γ—2, Γ·2
β€’ Check squares/cubes: 1,4,9,16 or 1,8,27,64
β€’ Check prime numbers: 2,3,5,7,11
β€’ If stuck, test options by applying pattern backward

Time saver: Most SSC series are arithmetic or simple geometric

Cube Shortcuts

  • Remember: Cube has 6 faces, 8 vertices, 12 edges
  • Opposite faces never adjacent
  • In nets, faces sharing edge become adjacent
  • For T-shaped nets, ends of T are often opposite
  • For cross nets, opposite arms are opposite
  • Draw quick sketch if needed

Dice Shortcuts

β€’ Memorize: 1↔6, 2↔5, 3↔4 (sum=7)
β€’ Standard arrangements: two types
β€’ When three faces visible around vertex, they're in sequence
β€’ For rotation problems, track one face
β€’ For hidden faces: opposite of visible is hidden

Quick check: Adjacent faces never sum to 7

Time Management

β€’ Series: 45 seconds max
β€’ Cube nets: 60 seconds max
β€’ Dice: 45 seconds max
β€’ If stuck > 90 sec, guess and move
β€’ Easy questions first (simple series)
β€’ Hard questions last (complex cube/dice)

Priority: Series β†’ Dice β†’ Cube nets (usually difficulty order)

SSC Shortcut: Common Patterns to Memorize

Series patterns: +2, +3, +5, Γ—2, square numbers, prime numbers

Cube rules: 6 faces, opposite faces never adjacent, in nets faces sharing edge become adjacent

Dice rules: 1↔6, 2↔5, 3↔4 (sum=7), standard arrangements exist

Net patterns: Cross nets: opposite arms opposite; T nets: ends of bar often opposite

Rotation rules: Opposite faces remain opposite after any rotation

Verification: Always check if solution violates basic rules

8. Practice MCQs & Exercises

Hands-on Practice: Apply what you've learned with these SSC-level series, cube, and dice questions.

Interactive Practice Questions

Practice Approach

Time yourself: 45 seconds per series, 60 seconds per cube/dice question. Apply the strategies systematically.

Practice Question 1: Number Series

Find the missing number: 2, 6, 12, 20, 30, ?
1. 40
2. 42
3. 42
4. 44

Practice Question 2: Cube Net

In the cube net shown, if X is opposite to Y, and Y is adjacent to Z, which face is opposite to Z?
Net: [X][Y][Z] in a row
1. X
2. The face not shown
3. Y
4. Cannot determine

Practice Question 3: Dice Problem

In a standard dice, if 2 is on the top face and 4 is on the front face, what is on the right face?
1. 1
2. 3
3. 6
4. 5

SSC Shortcut: Practice Strategy

Daily practice: 10 series + 5 cube/dice questions daily

Pattern recognition: Group similar series patterns together

Visualization practice: Mentally fold cube nets daily

Time yourself: Practice with 45-60 second timer

Previous papers: Solve last 5 years' SSC series/cube/dice questions

Error analysis: Review mistakes to avoid repetition

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Frequently Asked Questions

Q1: How many series/cube/dice questions in SSC CGL?

Answer: Typically 5-8 questions in Tier I. These include number series (3-4 questions), cube nets (1-2 questions), and dice problems (1-2 questions).

Q2: What's the most common series pattern in SSC?

Answer: Arithmetic series with constant or increasing differences (appear in 85% of papers), followed by mixed patterns (70%) and geometric series (65%).

Q3: How to solve cube net problems quickly?

Answer: 1) Identify which faces share edges in net, 2) Remember faces sharing edges become adjacent, 3) For T-shaped nets, ends of bar are often opposite, 4) Practice mental folding.

Q4: What are the standard dice rules?

Answer: 1) Opposite faces sum to 7 (1↔6, 2↔5, 3↔4), 2) Two standard arrangements exist (clockwise/anticlockwise), 3) Faces around a vertex are in sequence.

Q5: How much time per series question?

Answer: Target 45 seconds for series, 60 seconds for cube nets, 45 seconds for dice. If stuck for >90 seconds, make educated guess and move on.

Q6: Best way to improve cube/dice visualization?

Answer: Practice daily with physical cube/dice if possible, draw nets and fold mentally, solve previous year questions, use online visualization tools.

Final Exam Strategy for Series, Cube & Dice

Time Allocation: Series: 45 seconds, Cube nets: 60 seconds, Dice: 45 seconds maximum.

Priority Order: 1) Simple series, 2) Dice problems, 3) Cube nets (usually most time-consuming).

Accuracy Check: For series: verify pattern works for all terms. For cube/dice: check no rule violations.

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