# Cubes and Dice Quiz Set 03

### Question 1

When the digit 5 is on the bottom then which number will be on its upper surface ? A
2
B
4
C
5
D
1
Soln.
Ans: d
Common faces with number 3, are in same positions. Hence when the digits 5 is on the bottom then 1 will on the upper surface. Face 5 is opposite 1, and face 6 is opposite face 2.

### Question 2

A dice has numbers 1, 2, 3, 4, 5 and 6 on its face. Four positions of the dice are given below. The number on the face opposite to the face with number 2 is A
6
B
5
C
4
D
11.
Soln.
Ans: b

From the first, second and last figures, 1, 3, 4 and 6 are ruled out. Sir Arthur Conan Doyle's logic: "When you have eliminated the impossible, whatever remains, however improbable, must be the truth." So the answer should be 5.

### Question 3

Six cubes with their upper faces erased are as shown. The sum of the numbers on the opposite faces is 7.

If the dice (1), (2) and (3) have even numbers on their bottom faces then what would be the sum of the numbers on their top faces?

A
7
B
11
C
12
D
14
Soln.
Ans: b

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. 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.

The sum is: 5 + 1 + 5 = 11.

### Question 4

Two positions of a cuboidal brick are shown below. The brick contains all numbers up to 6. When six is at the bottom, what number will at the top?

A
1
B
4
C
5
D
2
Soln.
Ans: c

6 and 5 are on the upper and lower surfaces of this brick.

### Question 5

Which digit will appear on the face opposite to the face with number 4 ? A
5
B
6
C
1
D
2/3
Soln.
Ans: a
Here the common faces with number 4, are in same positions. Hence 6 is opposite to 2 and 3 is opposite to 1. Therefore 4 is opposite to 5. Otherwise also, the dice clearly show that 4 is adjacent to 1, 2, 3 and 6. So it can be opposite only to 5. 