Problems on Dice MCQ Quiz - Objective Question with Answer for Problems on Dice - Download Free PDF

A cube is painted on all the faces with the same color and cut into 27 smaller cubes of equal size.

Clearly, the cube has been cut into a 3 × 3 × 3 arrangement.

So, n = 3 (n is the number of divisions on the face of an undivided cube)

By formula:

Number of cubes that are painted on 2 faces = 4n = 4 × 3 = 12

Hence, “12” is the correct answer.

Alternate Method

A cube is painted on all the faces with the same color and cut into 27 smaller cubes of equal size.

Clearly, the cube has been cut into a 3 × 3 × 3 arrangement.

So, n = 3 (n is the number of divisions on the face of an undivided cube)

The number of cubes with 2 sides painted = 12 (n - 2)

= 12 (3 - 2) = 12 × 1 = 12

Hence, “12” is the correct answer.

HintFor 1 side painted, we found that the pattern was 6(n - 2)^2 = the number of cubes with 1 side painted.

For a cube with 2 sides painted, we found that the pattern was 12(n - 2) = the number of cubes with 2 sides painted.

For the cubes with 3 sides painted, it will always be 8.

The faces with numbers 3 and 5 are adjacent to the face with number 1 in the first position. The faces with numbers 2 and 6 are adjacent to the face with number 1 in the second position. The only number left is 4.

The logic followed here is :-

From the given two different cubes the adjacent sides are as shown below :

As T is common on both the dice, it is clear that S, Q, P and U are adjacent to it and remaining number i.e., R will be opposite to it.

Opposite pairs:

Q → P

S → U

T → R

So, the opposite side of "T" will be side "R".

Hence, the correct answer is "R".

For find the opposite surface of 'triangle', we need to compare the common surface in the given dices, 

So, From Dice 1 and Dice 3,

→ Square and Circle is the common surface in the both dice, so the Triangle and 'Hexagon' will be the opposite face.

Hence, the correct answer is "Option 4".

From the given open Dice:

G and R is the opposite sides.

H and C is the opposite sides.

B and F is the opposite sides.

So, the face of 'B' is opposite to the face showing 'F'.

Hence, the correct answer is "Option 1".

For find the adjacent faces of '4', we need to compare the common surface in the given dices,

Now,

From Dice 2 and Dice 3,

Here, 3, 5, and 6 is the adjacent surfaces of 4.

So, according to the options '6 and 5' will be the adjacent surfaces of 4.

Hence, the correct answer is "Option 4".

From the given dice:

L is the common letter in both Dice,

So, 7 is the opposite surface of 8.

and, F and 9 is the opposite surface.

Therefore, among the given options, 8 and L will be the adjacent surface of 'F'.

Hence, the correct answer is "Option 1".

Common number in both the positions = 2

Start with common number 2 moving clockwise.

Opposite letters:

2 ⇒ 6

3 ⇒ 4

1 ⇒ 5

Hence, "1" is the opposite of 5.

The faces with numbers 3 and 5 are adjacent to the face with number 1 in the first position. The faces with numbers 2 and 6 are adjacent to the face with number 1 in the second position. The only number left is 4.

The figure given below is:

From figure 2 and 3, we understand that 5 and 4 is not the opposite face of 1 and 2.

The opposite faces are 1 - 2

Hence, the correct answer is "2".

Given,

A cube is painted Orange on all surfaces and then the cube cuts into 27 small cubes of equal part.

So, it has been cut into: 3 × 3 × 3.

Here, n = 3.

Now, using formula: (n - 2)² × 6

⇒ (n - 2)2 × 6

⇒ (3 - 2)2 × 6

⇒ 12 × 6

⇒ 1 × 6 = 6.

So, total '6' cubes will have only one face painted.

Hence, the correct answer is "6".

Concept:

The 3 adjacent faces of the dice which we see will never be the opposite among them.

In figure 1, Adjacent of B is D, F

In figure 2, Adjacent of B is C, D.

In figure 4, Adjacent of B is A, C.

This will never be the opposite of B.

Only remaining alphabet is E, which becomes the opposite of B.

Hence, E is the correct answer.  

For find the opposite surface of 'U', we need to compare the common surface in the given dices,

Now,

From the given Dice,

→ P and S is the common surface in both Dice, 'U' is the opposite surface of 'R'.

Here, 'U' is opposite to the face containing 'R'.

Hence, the correct answer is "R".

From the given dice:

A is the common letter in both Dice,

Here, H, B, K and T are the adjacent of A.

and, the remaining face will be opposite of A.

Now, checking the options:

Option 1) H and T → False (H is the opposite face of K).

Option 2) H and B → False (H and B is the adjacent of A, not K).

Option 3) B and A → True (B and A will be the adjacent surface of K).

Option 4) A and H → False (A and H is the adjacent of B, not K).

Therefore, 'B and A' the adjacent faces of the face containing 'K'.

Hence, the correct answer is "Option 3".

In the first two given dice numbers, 6 and 3 are common means 2 and 5 are in opposite faces.

Here, Number 5 is the Opposite of 2.

Hence, Option (4) is the answer.