Dice questions test your ability to identify:

• Opposite faces
• Adjacent faces
• Cube rotations
• Cube nets (folding)
• Simple probability

---

1. Standard Dice

A standard die always has the same opposite faces.

1 ↔ 6

2 ↔ 5

3 ↔ 4

Notice:

1 + 6 = 7

2 + 5 = 7

3 + 4 = 7

This is the easiest rule to remember.

---

Visual

      +------+
      |  1   |
+------+------+
|  2   |  3   |
+------+------+
      |  6   |
      +------+

Here,

• Top = 1
• Bottom = 6
• Front = 2
• Back = 5
• Right = 3
• Left = 4

(The exact orientation may rotate, but opposite pairs never change.)

---

Example

A die shows

• Top = 1
• Front = 2

Find

• Bottom
• Opposite of 2
• Opposite of 3

Solution

1 ↔ 6

Bottom = 6

2 ↔ 5

3 ↔ 4

✅ Answer

Bottom = 6

Opposite of 2 = 5

Opposite of 3 = 4

---

2. Finding Opposite Faces Using Two Views

Instead of memorizing the cube, use one important rule.

Rule

Faces visible together are adjacent.

They can never be opposite.

---

Example

View 1

        1
      +---+
     /   /|
    +---+ |
    | 2 |3|
    +---+-+

Visible faces

1

2

3

So

1 touches 2

1 touches 3

2 touches 3

---

View 2

        4
      +---+
     /   /|
    +---+ |
    | 1 |5|
    +---+-+

Now

1 touches 4

1 touches 5

---

Combine everything

Face 1 touches

2

3

4

5

A cube has only 4 adjacent faces.

The only number left is

6

So

1 ↔ 6

✅ Answer

6 is opposite 1.

---

Shortcut

Face 1

Adjacent

2 ✓

3 ✓

4 ✓

5 ✓

Remaining

6

↓

Opposite

---

3. Cube Net (Open Dice)

Sometimes the cube is opened like paper.

Example

        F

        □

        B

        □

D   □   A   □   E

        □

        C

Fold it into a cube.

---

Easy Rule

Center touches every side.

      B

D  A  E

      C

A touches

B

C

D

E

The remaining face

F

becomes opposite A.

---

One Common Cube Net

      2

      □

4  □  1  □ 3

      □

      5

      □

      6

Opposite faces become

1 ↔ 6

2 ↔ 5

3 ↔ 4

---

Quick Folding Trick

Imagine folding all squares upward.

Before

      □

□ □ □ □

      □

      □

↓

Cube

Faces that end up pointing in opposite directions become opposite faces.

---

4. Dice Probability

One Die

Every face has equal chance.

1

2

3

4

5

6

Total outcomes

6

Probability formula

Probability

=

Favourable Outcomes
───────────────────
 Total Outcomes

---

Example

Probability of rolling 5

1 favourable

6 total

= 1/6

---

Two Dice

Total outcomes

6 × 6 = 36

Always remember

Total = 36

---

Sum Table

      1 2 3 4 5 6
    +--------------
1 |  2 3 4 5 6 7
2 |  3 4 5 6 7 8
3 |  4 5 6 7 8 9
4 |  5 6 7 8 9 10
5 |  6 7 8 9 10 11
6 |  7 8 9 10 11 12

---

Example

Find

P(sum ≥ 10)

Possible sums

10

11

12

Outcomes

10

(4,6)

(5,5)

(6,4)

= 3


11

(5,6)

(6,5)

= 2


12

(6,6)

= 1

Total favourable

3 + 2 + 1 = 6

Probability

6/36

=

1/6

✅ Answer

1/6

---

Important Dice Rules

✓ Opposite faces never touch.

✓ Adjacent faces can appear together.

✓ Three visible faces always meet at one corner.

✓ A face has:
   • 4 adjacent faces
   • 1 opposite face

✓ Standard dice:
   1 ↔ 6
   2 ↔ 5
   3 ↔ 4

✓ Two dice:
   Total outcomes = 36

---

Quick Exam Tricks

Question asks...

Opposite face?
→ Find the only face NOT adjacent.

Same die rotated?
→ Adjacent faces remain adjacent.

Cube net?
→ Fold mentally from the centre.

Probability?
→ Count favourable outcomes ÷ 36.

These four ideas solve the vast majority of dice questions asked in aptitude and reasoning exams.