Basic Dice

A standard dice has:

6 Faces
12 Edges
8 Vertices (Corners)

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Standard Opposite Faces

For a normal dice:

1 ↔ 6
2 ↔ 5
3 ↔ 4

Sum:

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

Useful shortcut when explicitly stated as a standard die.

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Important Dice Rules

Rule 1

Opposite faces never touch.

Example:

Top = 1
Bottom = 6

Then:

1 and 6 can never be adjacent.

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Rule 2

Adjacent faces share an edge.

Example:

1 and 2

shown together repeatedly.

Likely adjacent.

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Rule 3

If two faces appear together in multiple views,

they are usually adjacent.

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Dice Rotation

If the top remains the same:

Only side faces rotate.

Example:

Top = 1

Possible side rotation:

2 → 3 → 4 → 5

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Dice Shortcut

Questions usually ask:

Which face is opposite?

Which face is adjacent?

Which face appears on top after rotation?

Most questions are solved using:

Opposite Faces

Adjacent Faces

Common Face Method

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Common Face Method

View 1:

1 2 3

View 2:

1 3 5

Common faces:

1 and 3

Remaining faces:

2 and 5

Therefore:

2 and 5 are opposite.

This is one of the most important dice shortcuts.

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Dice Quick Revision

Opposite faces never touch.

Adjacent faces share an edge.

Common-face method is frequently used.

Standard dice opposite sums = 7.

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2. CUBE

Very common in TCS.

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Painted Cube Concept

A large cube is painted from the outside and then cut into smaller cubes.

Questions ask:

How many cubes have 3 faces painted?

How many cubes have 2 faces painted?

How many cubes have 1 face painted?

How many cubes have no face painted?

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Cube Terminology

Suppose the cube is divided into:

n × n × n

Total smaller cubes:

n³

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Corner Cubes

Always:

8

Reason:

A cube has 8 corners.

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Cubes with 3 Faces Painted

Always:

8

These are the corner cubes.

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Edge Cubes

Formula:

12(n − 2)

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Cubes with 2 Faces Painted

Formula:

12(n − 2)

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Face-Center Cubes

Formula:

6(n − 2)²

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Cubes with 1 Face Painted

Formula:

6(n − 2)²

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Internal Cubes

Formula:

(n − 2)³

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Cubes with No Face Painted

Formula:

(n − 2)³

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Most Important Example

Cube divided into:

3 × 3 × 3

Total cubes:

27

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Three faces painted:

8

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Two faces painted:

12

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One face painted:

6

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No face painted:

1

Memorize.

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Cube Formula Box

3 Faces Painted = 8

2 Faces Painted = 12(n − 2)

1 Face Painted = 6(n − 2)²

0 Face Painted = (n − 2)³

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3. CUBE & CUBOID

Basic formulas.

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Volume

Cube:

a³

Cuboid:

lbh

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Surface Area

Cube:

6a²

Cuboid:

2(lb + bh + hl)

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Diagonal of Cuboid

√(l² + b² + h²)

Rare but sometimes asked.

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4. VISUAL REASONING

Pattern-based questions.

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Common Types

Mirror Image

Water Image

Figure Completion

Embedded Figures

Pattern Recognition

Paper Folding

Paper Cutting

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Mirror Image

Mirror placed vertically.

LEFT ↔ RIGHT

changes.

Example:

ABC

Mirror image:

CBA

with mirrored letters.

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Water Image

Mirror placed horizontally.

UP ↔ DOWN

changes.

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Embedded Figure

Find the smaller shape hidden inside the larger figure.

Strategy:

Ignore distractions.

Focus on the outline.

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Pattern Recognition

Look for:

Rotation

Reflection

Increase

Decrease

Movement

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Visual Reasoning Shortcut

Check:

Rotation?

Reflection?

Size Change?

Position Change?

Shape Addition?

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5. CRYPTARITHMETIC

Most students fear it.

Actually, it is rule-based.

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Example:

 SEND
+MORE
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MONEY

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Rules

Rule 1

Same letter:

Same digit

Example:

S = S

always.

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Rule 2

Different letters:

Different digits.

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Rule 3

Leading digit cannot be zero.

Example:

SEND

Therefore:

S ≠ 0

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Solving Method

Start from the:

Rightmost column

Then move left.

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Carry Concept

Example:

8 + 7 = 15

Write:

5

Carry:

1

to the next column.

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Common Questions

Find digit value.

Find missing number.

Find carry.

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6. SELECTION DECISION TABLES

Very common in placement portals.

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Structure

Given:

Conditions

Rules

Decision

Need to:

Determine the output.

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Example

Age	Income	Decision
>18	>30000	Approve
>18	<30000	Reject

Candidate:

Age = 25

Income = 40000

Decision:

Approve

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Solving Method

Step 1:

Read conditions.

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Step 2:

Match candidate data.

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Step 3:

Follow the applicable rule.

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Step 4:

Reach the decision.

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Common Mistake

Students jump to the answer.

Always verify every condition.

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7. ATTENTION TO DETAIL

One of the easiest topics.

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What They Test

Ability to spot small differences.

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Common Types

Missing Number

1 2 3 5 6

Missing:

4

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Missing Letter

A B C E F

Missing:

D

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Wrong Symbol

+ − × ÷

One symbol altered.

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Spelling Difference

SEPARATE

SEPERATE

Choose the correct one.

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Extra Element

One item does not belong.

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Attention to Detail Checklist

Check:

Spelling

Order

Symbols

Case

Alignment

Shape

Position

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MOST IMPORTANT FORMULAS OF ENTIRE LOGICAL REASONING

Cube

Total Cubes:

n³

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Two Faces Painted:

12(n − 2)

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One Face Painted:

6(n − 2)²

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No Face Painted:

(n − 2)³

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Cuboid

Volume:

lbh

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Surface Area:

2(lb + bh + hl)

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Direction Sense

Shortest Distance:

d = √(x² + y²)

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FINAL 5-MINUTE REVISION BOX

Memorize:

Standard Dice Opposites

Common Face Method

Cube Painting Formulas

Mirror vs Water Image

Cryptarithmetic Rules

Decision Table Approach

Attention-to-Detail Checklist