# Cubes and Dice Quiz Set 10

### Question 1

Six different dice with their top faces erased have been given. The opposite faces of each dice have numbers which add to 13. All dice have the numbers from amongst 4, 5, 6, 7, 8 and 9 printed on them.

If dice, B, E and F have even numbers at their bottom faces, what would be the sum of those even number ?

A
18
B
16
C
20
D
24
Soln.
Ans: a
1. Dice No. B: Face opposite 8 is 5 because 8 + 5 = 13. Similarly, face opposite 9 is 4. So, the numbers that appear on the sides are 4, 5, 8 and 9. Out of the remaining 6 and 7, the bottom face is 6.
2. Dice E: Similarly, 4 is at the bottom.
3. Dice F: 8 is at the bottom.

So sum is 6 + 4+ 8 = 18.

### Question 2

A dice with faces marked is shown below:

The face opposite to 3 is

A
2
B
3
C
4
D
6
Soln.
Ans: c

From the last two figures, 1, 2, 5 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 4.

### Question 3

Two positions of a dice are shown below which number will appear on the face opposite to the face with the number 5 ?

A
2/6
B
2
C
6
D
4
Soln.
Ans: c
Common faces with number 3, are in same positions. Hence the number of the opposite face to face with number 5 will be 6. 1 is opposite 2.

### Question 4

Two positions of a cubical block are shown. When E is at the top which face will be at the bottom ?

A
A
B
B
C
C
D
D
Soln.
Ans: c
Face with C is in same position. Hence A is opposite to F and D is opposite to B. Therefore E is opposite to C.

### Question 5

Six dice with their top faces erased have been given. The opposite faces of each dice have numbers which add to thirteen.

If dice, A, B and C have odd numbers at their upper faces and dice D, E and F have even numbers on their bottom faces, then what would be the difference in the totals of top numbers of these two sets ?

A
0
B
4
C
8
D
1
Soln.
Ans: b

Since the sum of the numbers on the opposite sides is 13, one of those numbers would be odd, and the other even. So we can say the all these dice have odd numbers at the top.

1. Dice No. A: Face opposite 6 is 7 because 6 + 7 = 13. Similarly, face opposite 4 is 9. So, the numbers that appear on the sides are 4, 6, 7 and 9. Out of the remaining 5 and 10, the top face is 5.
2. Dice No. B: Face opposite 8 is 5 because 8 + 5 = 13. Similarly, face opposite 9 is 4. So, the numbers that appear on the sides are 4, 5, 8 and 9. Out of the remaining 6 and 7, the upper face is 7.
3. Dice C: Similarly, 5 is at the top.
4. Dice D: Similarly, 7 is at the top.
5. Dice E: 9 is at the top.
6. Dice F: 5 is at the top.

The difference is (7 + 9 + 5) - (5 + 7 + 5) = 4.