# Cubes and Dice Quiz Set 02

### Question 1

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 2

Following two different orientations of a dice, find out the color which is opposite to pink.

A
Blue
B
Green
C
Pink
D
Red
Soln.
Ans: b

The other two faces are green. So, in any case, the color opposite pink will be green. The color opposite blue will be green as well.

### Question 3

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 4

Give below are four views of a cube. Each face is marked with certain symbols. The different views of the cubes have been numbered 1 to 4. Carefully examine each view and answer the question below.

In figure 3, which symbol will appear on the face opposite to the face containing "*" ?

A
@
B
#
C
&
D
\$
Soln.
Ans: d

The spread out of the cube shown below explains it all.

### Question 5

Six cubes with their upper faces erased are as shown.

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

If odd numbered dice have even numbers on their top faces, then what would be the sum total of the numbers on the faces of these three dice ?

A
8
B
10
C
12
D
14
Soln.
Ans: a

The odd numbered dice are 1, 3 and 5. Consider this deduction.

1. Dice No.1: Face opposite 3 is 4 because 3 + 4 = 7. So 6 and 4 appear on the sides which means 2 is at the top.
2. Dice No. 3: 6 and 4 are on the sides, so 2 must be at its top.
3. Dice No. 5: The digit 2 should be opposite 5, and 6 should be opposite 1. This reveals 2 and 6, so 4 must be at the top of this dice.

The sum of numbers is 2 + 2 + 4 = 8.