Dice: Meaning, Reasoning Questions and Answers, Examples

Dice is a subtopic of Logical Reasoning that appears in various exams. This topic is commonly found in many Government exams such as SSC, Railway, Defence, and other competitive exams. The questions related to this topic can be tricky, but they are generally easy and scoring. A dice is a cube with a different number on each face, usually from 1 to 6.

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This Story also Contains

1. Types of Questions Based on the Dice
2. Recommended Books and Online Resources on dices
3. Question Weightage of Dice in Competitive Exams
4. Practice Questions For Opposite Faces in Dice-Based Questions
5. Practice Questions For Unfolded Dice-Based Questions
6. Tips to Approach Some Tricky Questions Based on Unfolded Dice
7. Dice Questions for VITEEE exam
8. Dice Questions for SSC CGL/ SSC CHSL/ SSC CPO/ SSC Stenographer exams
9. Dice Questions for Defence/ Railway Recruitment Board exams

Types of Questions Based on the Dice

Different types of questions asked from the dice are as follows -

1. Opposite face in Dice-based questions

2. Unfolded dice-based questions

Let’s understand these types with the help of examples -

1. Opposite Face in Dice-Based Questions

In these types of questions, one has to determine the pair of opposite faces of the given die based on its different positions. There are further rules to solve these types of problems. Let’s analyse different types of rules with the help of examples.

Rule 1: When 2 different positions of a die are given with one common number on the same surface. then, the remaining faces containing different numbers on the same surface are the opposite faces. Let’s understand the case with the help of an example -

Example: In the diagram given below, the face containing 2 is common in both the dice and it is on the same surface. Let’s analyse the conclusions based on the above rule.

Now, considering both the positions of a die, we can see that the common face is 2 and is on the same surface. So, the opposite face to the face containing 3 and 6 is 1, and 4 respectively.

Rule 2: When two positions of the same dice are given with two common faces but in different orientations, then out of those two common faces, the faces that are not common are opposite to each other. Let’s understand the case with the help of an example -

Example: Consider the following diagram, two positions of a dice are given with two common faces.

Now, in the above diagram, we can see that the faces containing 6 and 3 are the common faces, and 1 and 5 are the remaining faces. So, the faces containing 1 and 5 are the opposite faces.

Rule 3: When two positions of the same dice are given with one common face but in different orientations, then start moving in the clockwise direction from one face to the other, (starting from the common face), we will get the pair of opposite faces. Let’s understand the case with the help of an example -

Example: The figure given below shows two different positions of a dice with one face common and in different orientations. (Let us assume that the sixth face of the dice is 3.)

Now, to determine the pair of opposite faces, move in the clockwise direction, starting from the common face, 1. As we move in the clockwise direction from 1, in the first dice the next number is 5 and in the second dice, it is 6. So, 5 and 6 are the opposite faces. Similarly, on moving further in the same direction, the next number in the first dice is 2 and in the second dice, it is 4. So, 4 and 6 are the opposite faces.

So, the pair of opposite faces are - (5⇔6); (2⇔4); (1⇔3).

2. Unfolded Dice-based Questions

These types of questions are based on an open dice. In an open dice, all the six faces of the dice are visible. It is a flat-end version of a 3-D dice. The faces of an open die are folded to form a 3-D version of the dice. In an open dice, alternate faces form the pair of opposite faces and no two opposite faces touch each other either by sides or by corners. Let’s understand this with the help of an example.

Example: An unfolded version of a dice is given below. Determine the pairs of opposite faces as well as the 3-D view of dice that can be formed by folding the given sheet from the given options.

A) B) C) D)

As explained above, alternate faces are the opposite faces. So, here, (3, 2); (6, 1); and (5, 4) are the alternate as well as opposite faces as shown below:

Pairs of opposite faces – (2⇔3), (4⇔6), (1⇔5)

So, in the 3-D view of dice, each face out of three faces in the 3-D view should be from each pair. Two opposite faces cannot appear adjacently in the 3-D view of the dice. As per the above diagram and rules, only option (A) is possible. Because in all other options, opposite faces appear adjacently.

Recommended Books and Online Resources on dices

1. A Modern Approach to Verbal & Non-Verbal Reasoning by R.S. Aggarwal

2. SSC Reasoning by Rakesh Yadav

Question Weightage of Dice in Competitive Exams

The number of questions based on dice varies from exam to exam -
1) Questions asked in SSC exams i.e. SSC MTS, SSC CGL, SSC CHSL, SSC CPO, Steno - 2 to 3 questions.
2) Questions asked in the Railways exam i.e. Group D, NTPC, JE, ALP etc - 2 to 3 questions.

3) Questions asked in Banking exams, Bank PO, Bank Clerk - 1 to 2 questions.

Practice Questions For Opposite Faces in Dice-Based Questions

Q1. Directions: Two different positions of the same dice are shown (figures 1 and 2). Find the number on the face opposite to the face having 3.

A) 3

B) 6 (Correct)

C) 5

D) 4

Solution: According to the dice rule, if two or three positions of the same dice are given with two common faces but in different orientations, then out of those two common faces the faces that are not common are opposite to each other.

While considering the given Figures 1 and 2, it is seen that two faces 4 and 2 are common. So, the remaining numbers are 3 and 6. So, 3 and 6 are the opposite faces of each other in the given dice.

Therefore, the opposite face of 3 is 6. Hence, the second option is correct.

Q2. Directions: Two different positions of the same dice are shown. Select the letter that will be on the face opposite to the one having A.

A) B

B) F

C) N

D) Z (Correct)

Solution: Two different positions of a dice are given with one face common, ‘Z’ and the sixth face is A. So, move in the clockwise direction from the common face Z as shown below to get the opposite pair of faces.

So, the pair of opposite faces - (B⇔F); (C⇔N); (Z⇔A).

Therefore, the opposite face of the A is Z. Hence, the fourth option is correct.

Q3. Directions: Two positions of a dice are given below. What will come on the face opposite to the face containing R on it?

A) Q

B) P (Correct)

C) A

D) H

Solution: Two different positions of a dice are given with one face common, ‘A’ and assume that the sixth face is B. So, move in the clockwise direction from the common face A as shown below to get the opposite pair of faces.

So, the pair of opposite faces - (P⇔R); (Q⇔H); (A⇔B).

Therefore, the opposite face of the R is P. Hence, the second option is correct.

Q4. Directions: Three different positions of the same dice are shown. Find the number on the face opposite to the one having 8.

A) 3

B) 1

C) 6 (Correct)

D) 5

Solution: According to the dice rule, if two or three positions of the same dice are given with two common faces but in different orientations, then out of those two common faces the faces that are not common are opposite to each other.

While considering Figures 1 and 3, it is seen that two faces 7 and 3 are common. So, the remaining numbers are 8 and 6. So, 8 and 6 are the opposite faces of each other in the given dice.

Therefore, the opposite face of 8 is 6. Hence, the third option is correct.

Q5. Directions: Two dimensions of the same dice are given. What letter will be on the face opposite to the face having the letter F?

A) B (Correct)

B) D

C) C

D) A

Solution: Two different positions of a dice are given with one face common, ‘B’ and the sixth face is F. So, move in the clockwise direction from the common face B as shown below to get the opposite pair of faces.

So, the pair of opposite faces - (A⇔E); (C⇔D); (B⇔F).

Therefore, the opposite face to the face containing F is B. Hence, the first option is correct.

Practice Questions For Unfolded Dice-Based Questions

Q1. Directions: An unfolded version of a dice is given below. Determine the pairs of opposite faces of the given dice.

A) (2⇔3), (4⇔6), (1⇔5)

B) (2⇔5), (4⇔6), (3⇔1)

C) (2⇔3), (1⇔6), (4⇔5) (Correct)

D) (5⇔3), (4⇔2), (6⇔5)

Solution: According to the rules, alternate faces are the opposite faces. So, here, (3, 2); (6, 1); and (5, 4) are the alternate as well as opposite faces as shown below:

So, the pairs of opposite faces – (2⇔3), (4⇔6), (1⇔5). Hence, the third option is correct.

Q2. Directions: An unfolded version of a dice is given below. What letter will be on the face opposite to the face having the letter C?

A) F

B) A

C) B

D) E (Correct)

Solution: According to the rules, alternate faces are the opposite faces and no two opposite faces touch each other. So, here, (B, A); (D, F); and (C, E) are the alternate as well as opposite faces as shown below:

So, the pairs of opposite faces – (B⇔A), (D⇔F), (C⇔E).

Therefore, the opposite face of C is E. Hence, the fourth option is correct.

Q3. Directions: A cube is made by folding the given sheet. In the cube so formed, which number letter will be on the face opposite to the face showing 7?

A) A

B) 4 (Correct)

C) 6

D) 8

Solution: According to the rules, alternate faces are the opposite faces and no two opposite faces touch each other. So, here, (8, 9); (7, 4); and (6, A) are the alternate as well as opposite faces as shown below:

So, the pairs of opposite faces – (8⇔9), (7⇔4), (6⇔A).

Therefore, the opposite face of 7 is 4. Hence, the second option is correct.

Q4. Directions: By folding the given paper, which of the following boxes can be made?

A) B) C) D) (Correct)

Solution: According to the rules, alternate faces are the opposite faces and no two opposite faces touch each other. So, here, (@, +); (#, 6); and (4, %) are the alternate as well as opposite faces as shown below:

So, the pairs of opposite faces – (@⇔+); (#⇔6); and (4⇔%).

So, in the 3-D view of dice, each face out of three faces in the 3-D view should be from each pair. Two opposite faces cannot appear adjacently in the 3-D view of the dice. As per the above diagram and rules, only option (D) is possible. Because in all other options, opposite faces appear adjacently.

So, as per the above diagram and rules, the below figure can be formed.

Hence, the fourth option is correct.

Q5. Directions: A cube is made by folding the given sheet. In the cube so formed, which number letter will be on the face opposite to the face showing 4?

A) 7

B) 2

C) 6

D) @ (Correct)

Solution: According to the rules, alternate faces are the opposite faces and no two opposite faces touch each other. So, here, (7, 2); (3, 6); and (4, @) are the alternate as well as opposite faces as shown below:

So, the pairs of opposite faces – (7⇔2), (3⇔6), (4⇔@).

Therefore, the opposite face of 4 is @. Hence, the fourth option is correct.

Tips to Approach Some Tricky Questions Based on Unfolded Dice

The questions related to unfolded dice are solved according to the above-mentioned rules. As in the above example, only one 3-D view of dice is possible from the given options. But, in several cases, more than one 3-D view of a dice can be possible. In that case, we need to thoroughly check which of the views is correct. For this, we need to compare all the possible cases.

Q1. Directions: Which of the following cubes in the answer figure cannot be made based on the unfolded cube in the question?

A) B) C) D) (Correct)

Solution: According to the rules and the properties of dice, opposite faces of the dice cannot appear adjacently and the sides of the opposite faces cannot touch each other. In the unfolded dice, alternate faces are the opposite faces. So, according to the above figure, the pairs of opposite faces are as follows:

According to the above figure and rules discussed above, all the given dice in the options can be formed. But if we compare the fourth option with the other options, the fourth option gives the different opposite faces. So, from this, it can be concluded that the position of the dice given in the fourth option is incorrect. Thus, the image in the fourth option cannot be formed by folding the dice.

Hence, the fourth option is correct.

Q2. Directions: Which of the following cubes in the answer figure cannot be made based on the unfolded cube in the question figure?

A) B) C) D) (Correct)

Solution: According to the rules and the properties of dice, opposite faces of the dice cannot appear adjacently and the sides of the opposite faces cannot touch each other. In the unfolded dice, alternate faces are the opposite faces. So, according to the above figure, the pairs of opposite faces are as follows:

According to the above figure and rules discussed above, all the given dice in the options can be formed. But if we compare the fourth option with the other options, the fourth option gives the different opposite faces. So, from this, it can be concluded that the position of the dice given in the fourth option is incorrect. Thus, the image in the fourth option cannot be formed by folding the dice.

Hence, the fourth option is correct.

Q3. Directions: Which of the following cubes in the answer figure cannot be made based on the unfolded cube in the question figure?

A) B) (Correct) C) D)

Solution: According to the rules and the properties of dice, opposite faces of the dice cannot appear adjacently and the sides of the opposite faces cannot touch each other. In the unfolded dice, alternate faces are the opposite faces. So, according to the above figure, the pairs of opposite faces are as follows:

According to the above figure and rules discussed above, all the given dice in the options can be formed. But if we compare the second option with the other options, the second option gives the different opposite faces. So, from this, it can be concluded that the position of the dice given in the second option is incorrect. Thus, the image in the second option cannot be formed by folding the dice.

Hence, the second option is correct.

Dice Questions for VITEEE exam

1) Directions: From the given options, which answer figure can be formed by folding the figure given in the question?

1)

2)

3)

4)

Hint: Find the opposite pair of faces and choose the correct figure by comparing those opposite faces.

Solution

In a 3D view of dice,

1. Each face out of the three faces in the 3D view should be from all the pairs.

2. Two opposite faces cannot appear adjacently in the 3D view of a folded cube figure. So, the opposite pairs of faces are as follows –

Based on the above diagram and rules, the following image can be formed –

Hence, the first option is correct.

2) Directions: Which of the following cubes in the answer figure cannot be made based on the unfolded cube in the question figure?

1)

2)

3)

4)

Solution

Properties of a dice –

1. Opposite faces of a dice cannot appear or hide together.

2. Sides of the opposite faces of a dice cannot touch each other.

Rules to find out the opposite faces of a dice when two or more positions of the same dice are given –

1. When one face is common: Rotate the faces of one of the given positions of a dice clock/anti-clockwise starting from the common face. Countering faces in this process will be opposite faces.

2. When two faces are common: The remaining faces are opposite faces after the two common faces of a dice.

Opposite faces of the given unfolded dice after folding it –

Now, as per the properties of dice, all the given dice in the options can be formed but by the first rule of the dice (given above), the dice given in the first option give different opposite faces of the same dice after comparing it with another position of the same dice given in the other three options. So, the dice in the first option cannot be formed after folding the given dice.

Hence, the first option is correct.

Dice Questions for SSC CGL/ SSC CHSL/ SSC CPO/ SSC Stenographer exams

1) Directions: Three positions of a cube are shown below. What will come opposite to face containing 1?

1) 2

2) 3

3) 4

4) 6

Solution

Taking dice positions 2 and 3 with 1 as common face,

Moving clockwise from the common face with 1,

Pairs of opposite faces –

The opposite face to the one with 1 is 4. Hence, the third option is correct.

2) Directions: From the given options, which option figure can be formed by folding the figure given in the question figure?

1)

2)

3)

4)

Solution

In a 3D view of dice,

1. Each face out of the three faces in the 3D view should be from all the pairs.

2. Two opposite faces cannot appear adjacently in the 3D view of a folded cube figure. So, the opposite pairs of faces are as follows –

(2 ⇔ 4), (6 ⇔ 3), (1 ⇔ 5) are the opposite pairs of faces.
Thus,

is possible and will be formed by folding the dice. Hence, the third option is correct.

Dice Questions for Defence/ Railway Recruitment Board exams

1) Directions: Three positions of a cube are shown below:

What will come on the two faces marked 1 and 2?

1) θ and δ

2) α and β

3) θ and β

4) θ and γ

Solution

Taking dice positions 1 and 3 with α as the common face. So, on moving in the clockwise direction from α, the following opposite pairs of faces will be formed –

As per the properties of the dice, the opposite faces of a dice cannot appear together and the sides of opposite faces cannot touch each other.

So, the opposite face of Ψ is θ, i.e., θ will not be the adjacent face of the one containing Ψ.

In the first, third, and fourth options θ is present, so those cannot be considered as the adjacent faces of Ψ. Therefore, based on the above diagram and rules, the following image can be formed –

On comparing the diagrams, we get 1 = α and 2 = β. Hence, the second option is correct.

2) Directions: Two different positions of the same dice are shown. Identify the letter on the face opposite the face showing X.

1) W

2) S

3) V

4) T

Solution

According to the dice rule, if two or three positions of the same dice are given with two common faces but in different orientations, then out of those two common faces the faces that are not common are opposite to each other.

In the given dice, two faces S and U are common. So, the remaining letters on the dice are X and T. So, X and T are the opposite faces of each other in the given dice.

So, the opposite face to the face containing X is T. Hence, the fourth option is correct.

About the Faculty
Tanu Gupta, with over a decade of experience as a reasoning faculty, specializes in preparing students for various entrance examinations and career development. Her extensive work with multiple educational platforms and institutions has honed her expertise in logical and analytical thinking. Her dedication to innovative teaching methods ensures these articles provide practical insights and expert guidance.