# Cubes and Dice Quiz Set 05

### Question 1

Observe the numbers on a dice (one to six numbers) in the following figures, which number is contained on the face opposite to the face containing 4 ?

A
2
B
3
C
5
D
6
Soln.
Ans: a
Two common faces appear in this arrangement. One of them, i.e., 5 is in the same position, then the remaining faces with numbers 4 will be opposite to face with number 2.

### Question 2

Study the three different positions of a cube given below and answer the question.

What is printed on the bottom face of figure 1.

A
A
B
D
C
E
D
None of these.
Soln.
Ans: a

By seeing all the three figures we can conclude that D, B, E and F cannot be opposite C. So the alphabet that is left is the answer.

### Question 3

Six cubes with their upper faces erased are as shown.

The sum of the numbers on the opposite faces is 7.

If dice (1), (2) and (3) have even numbers on their bottom faces and the dice (4), (5) and (6) have odd numbers on their top faces, then what would be the difference in the total number of top faces between these two sets ?

A
0
B
2
C
4
D
6
Soln.
Ans: d

Since the sum of digits on opposite faces is 7, faces with odd digits would have even digits opposite them. Hence, the digits at the top of all these dice are odd. Let's deduce them. We have been given that the sum of the digits on each of the opposite faces is 7. To find the odd number at the top, we should prove that two out of the three odd numbers 1, 3 and 5 appear on the sides. Then the third will automatically be on the top.

1. Dice 1: The number opposite 6 is 1, and the number 3 is already visible, so the number at the top is 5.
2. Dice 2: The number opposite 4 is 3, so the number at its top is 1.
3. Dice 3: The number opposite 6 is 1, the number opposite 4 is 3, so the number at the top is 5.
4. Dice 4: By the same logic as above, the number at the top is 1.
5. Dice 5: By the same logic as above, the number at the top is 3.
6. Dice 6: By the same logic as above, the number at the top is 1.

The difference is 5 + 1 + 5 - (1 + 3 + 1) = 6.

### Question 4

The following are three views of the same cube. Instead of having 6 unique digits, it has 5 unique digits only, so one of the digits is repeated. Study these views and determine what digit is opposite the digit 6 on view (3).

A
3
B
2
C
1
D
4
Soln.
Ans: b

We can see that the above cube is like this.

### Question 5

Four positions of a cube are shown below. Which letter will be on the face opposite to the face with 'A' ?

A
D
B
B
C
C
D
F
Soln.
Ans: a
The letters of the adjacent faces to the face with letter A, are B, F, C and E. Hence D is the letter of the face opposite to the face with letter A.