On the other hand,

Several types of questions based on Cube and Dice reasoning are asked regularly in various competitive examinations. In this article, we are going to cover the key concepts of the Cube and Dice reasoning section along with the solved examples.

- A cube has 6 square faces or sides
- A cube has 8 points (vertices)
- A cube has 12 edges
- Only 3 sides of a cube are visible at a time (known as “Joint Sides”) and these sides can never be on the opposite side of each other
- Things that are shaped like a cube are often referred to as ‘cubic’
- Most dice are cube shaped, with the numbers 1 to 6 on the different faces.

Here, faces with number 4, 3, 6 and 1 are adjacent to the face number 2.

Therefore, the 4, 3, 6, 1 can’t be opposite to the face number 2.

Therefore, face number 5 is opposite to face number 2.

In both the diagrams, two faces numbered 1 & 3 are common.

Also, 5 & 6 are remaining faces. Hence, the face which is number 5 is opposite to the face number 6.

Note, in the above shown dice, the face having value 6 is not in the similar position.

The face numbered 1 is not shown.

So, the face opposite to the face with number 6 is 1. Also, the opposite face of 3 is the face with number 2 and the opposite to face numbered 5 is the face with number 1.

For a cube of side n

- Number of cubes with 0 side painted= (n-2) 3
- Number of cubes with 1 sides painted =6(n - 2) 2
- Number of cubes with 2 sides painted= 12(n-2)
- Number of cubes with 3 sides painted= 8(always)
- For a cuboid of dimension a
*b*c painted on all sides which is cut into smaller cubes of dimension 1*1*1, - Number of cubes with 0 side painted= (a-2) (b-2) (c-2)
- Number of cubes with 1 sides painted =2[(a-2) (b-2) + (b-2)(c-2) + (a-2)(c-2) ]
- Number of cubes with 2 sides painted= 4(a+b+c -6)
- Number of cubes with 3 sides painted= 8

A) 8

B) 16

C) 27

D) 36

A) Number of small cubes that have exactly three faces painted.

B) How many cubes have two faces painted?

C) How many cubes have only one face painted?

D) What is the number of cubes that have no face painted?

A) B

B) V

C) G

D) I

A) Red

B) Black

C) White

D) Blue

A) The face 2 is adjacent to the face 3

B) The face 6 is between the face 2 and the face 4

C) The face 1 is between the face 5 and the face 6

D) None of the above

A) 9

B) 10

C) 11

D) 12

A) 12

B) 8

C) 6

D) 4

A) 54

B) 44

C) 36

D) 27

A) 32

B) 24

C) 16

D) 8

What possible number can exist on the two faces marked A and B respectively on the cube?

A) 2 and 3

B) 6 and 1

C) 1 and 4

D) 3 and 1

A) 27

B) 8

C) 16

D) 24

A) 4

B) 6

C) 8

D) 10

A) 4

B) 8

C) 27

D) 36

1. C), 2.[A. 8, B. 48 C. 92, D. 64], 3. C), 4. C), 5. A), 6. B), 7. A), 8. B), 9. D), 10. A), 11. A), 12. C), 13. B)

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