Question 1

Three different positions X, Y and Z of a dice are shown in the figures given below. Which number lies at the bottom face in position Y?

Accepted Answer

From positions X and Y we conclude that 1, 5, 6 and 3 lie adjacent to 4. Therefore, 2 must lie opposite 4. From positions Y and Z we conclude that 4, 3, 2 and 5 lie adjacent to 6. Therefore, 1 must lie opposite 6. Thus, 2 lies opposite 4, 1 lies opposite 6 and consequently 5 lies opposite 3. As analysed above, the number on the face opposite 4 is 2. In position Y, since 4 lies on the top, therefore 2 must lie at the bottom face.

Question 2

A dice is thrown four times and its four different positions are shown below. Find the number on the face opposite the face showing 2.

Accepted Answer

From figures (i), (ii) and (iv) We conclude that 6, 4, 3 and 1 lie adjacent to 2. Hence, 5 must lie opposite 2.

Question 3

Below are depicted the three different positions of a dice. Find the number of dots on the face opposite to the face with one dot.

Accepted Answer

From figures (i), (ii) and (iii), we conclude that 1, 3, 5 and 6 dots appear adjacent to the face with 2 dots. Therefore, 4 dots will appear opposite to 2 dots. Now, from figures (i) and (ii), we conclude that 2, 3 and 5 dots appear adjacent to 1 dot Therefore, either 4 or 6 dots will appear opposite to 1 dot. But since, 4 dots appear opposite to 2 dots it follows that 6 dots will appear opposite 1 dots.

Question 4

The six faces of a dice have been marked with alphabets A, B, C, D, E and F respectively. This dice is rolled down three times. The three positions are shown as: Find the alphabet opposite A.

Accepted Answer

From figures (ii) and (iii), we conclude that the alphabets C, D, B and F appear adjacent to the alphabet E. Therefore, the alphabet A appears opposite E. Conversely, E appears opposite A.

Question 5

Two positions of a dice are shown below: When 2 is at the bottom, what number will be at the top?

Accepted Answer

Number 3 is common to both the figures (i) and (ii). The dice in fig. (ii) is assumed to be rotated so that 3 remains on the FR-RH face (i.e. face I as per activity 1) and the numbers 5 and 2 move to the faces hidden behind the numbers 6 and 1 respectively [in fig. (i)]. Thus, the combined figure will have 3 on FR-RH face (i.e. face I), 5 on RR-RH face (i.e. face II), 2 on Bottom face (i.e. face VI), 1 on the Top face (i.e. face V) and 6 on FR-LH face (i.e. face IV). Clearly, 2 lies opposite 1. Hence, when 2 is at the bottom, then 1 will be at the top.

Question 6

Given below are three different positions of a dice. Find the number of dots on the face opposite the face bearing 3 dots.

Accepted Answer

From figures (i), (ii) and (iii), we conclude that 3, 4, 6 and 1 dots appear adjacent to 2 dots. Therefore, 5 dots appear opposite 2 dots. Now, from figures (i) and (iii), we conclude that 2, 4 and 1 dots appear adjacent to 3 dots. Therefore, either 5 or 6 dots appear opposite 3 dots. Since, 5 dots appear opposite 2 dots, it follows that 6 dots appear opposite 3 dots.

Question 7

Three different positions X, Y and Z of a dice are shown in the figures given below. Which numbers are hidden behind the numbers 6 and 5 in the position Z?

Accepted Answer

From positions X and Y we conclude that 1, 5, 6 and 3 lie adjacent to 4. Therefore, 2 must lie opposite 4. From positions Y and Z we conclude that 4, 3, 2 and 5 lie adjacent to 6. Therefore, 1 must lie opposite 6. Thus, 2 lies opposite 4, 1 lies opposite 6 and consequently 5 lies opposite 3. As analysed above, the number opposite 6 is 1 and the number opposite 5 is 3. Therefore, the numbers hidden behind the numbers 6 and 5 in position Z (these are the numbers opposite 5 and 6 respectively) are 1 and 3.

Question 8

Two positions of a dice are shown below. If the face with 1 dot is at the bottom, then the number of dots on the top is

Accepted Answer

From figures (i) and (ii), we conclude that 5, 4, 6 and 2 dots appear adjacent to 3 dots. Therefore, 1 dot must appear opposite 3 dots. Thus, if the face with 1 dot is at the bottom, then the face with 3 dots will appear on the top.

Question 9

Two positions of a block are shown below: When six is at the bottom, what number will be at the top?

Accepted Answer

From figures (i) and (ii) we conclude that the number 1, 2, 3 and 4 appear adjacent to 6. Thus, the number 5 will appear opposite 6. Therefore, when six is at the bottom, then 5 will be at the top.

Question 10

How many dots are there on the dice face opposite the one with three dots?

Accepted Answer

From figures (i), (ii) and (iv), we conclude that 6, 4,1 and 2 dots appear adjacent to 3 dots. Clearly, there will be 5 dots on the face opposite the face with 3 dots.

Question 11

The four different positions of a dice are given below: Find the number on the face opposite the face showing 6?

Accepted Answer

From figures (i), (ii) and (iii), we conclude that 3, 4, 2 and 6 lie adjacent to 5. Therefore, 1 must lie opposite 5. From figures (i), (iii) and (iv), we conclude that 4, 5, 6 and 1 lie adjacent to 3. Therefore, 2 must lie opposite 3. Now, we have 1 opposite 5 and 2 opposite 3. Hence, 4 must lie opposite 6.

Question 12

What number is opposite 3 in the figure shown below? The given two positions are of the same dice whose each surface bears a number among 1, 2, 3, 4, 5 and 6.

Accepted Answer

From figures (i) and (ii), we conclude that 2, 6, 1 and 4 appear adjacent to 5. Therefore, 3 must appear opposite 5, Conversely, the number opposite 3 is 5.

Question 13

What will be the number at the bottom, if 5 is at the top; the two positions of the dice being as given below:

Accepted Answer

From figures (i) and (ii), it is clear that 4, 1, 3 and 6 he adjacent to 2. Therefore, 5 must lie opposite 2. Thus, if 5 is at the top, then 2 must be at the bottom.

Question 14

In a dice a, b, c and d are written on the adjacent faces, in a clockwise order and e and f at the top and bottom. When c is at the top, what will be at the bottom?

Accepted Answer

Clearly, the six faces are labelled as Face I -> a, Face IV -> b, Face III -> c, Face II -> d, Face V -> e, Face VI -> f Therefore 'a' appears opposite 'c'. Hence, when 'c' is at the top, then 'a' will be at the bottom.

Question 15

Four positions of a dice are shown below. What number must be at the bottom face when the dice is in the position as shown in the figure(iii)

Accepted Answer

From figures (i), (ii), (iv) we conclude that 5, 6, 1 and 2 lie adjacent to 4. Hence, 3 must lie opposite 4 and vice-versa. In fig. (iii), 3 is at the top and consequently 4 must lie at the bottom face.

Question 16

A dice is rolled twice and the two positions are shown in the figure below. What is the number of dots at the bottom face when the dice is in position (i)?

Accepted Answer

From figures (i) and (ii) we conclude that 3, 4, 1 and 5 dots appear adjacent to 2 dots. Therefore, 6 dots must appear opposite 2 dots. Since, there are 2 dots on the top face when the dice is in position (i), therefore, the number of dots at the bottom face must be 6.

Question 17

Observe the dots on a dice (one to six dots) in the following figures. How many dots are contained on the face opposite to that containing four dots?

Accepted Answer

We shall assume the dice in fig. (ii) to be rotated so that the 5 dots appear at the same position as in fig. (i) i.e. on RHS face (i.e. on face II as per activity 1) and 1 dot appears at the same position as in fig; (i) i.e. on Front face (i.e. on face I). Then, from the, two figures, 2 dots appear on the top face (i.e. on face V) and 4 dots appear on the Bottom face (i.e. on face VI). Since, these two faces are opposite to each other, therefore, two dots are contained on the face opposite to that containing four dots.

Question 18

Two positions of a cube are shown below. When the number 4 will be at the bottom, then which number will be at the top?

Accepted Answer

Number 1 is common to both the positions of the dice. We assume the dice in fig. (ii) to be rotated so that 1 remains on the RHS face (i.e. face II as per activity 1) and the numbers 5 and 3 move to the faces hidden behind 2 and 4 respectively (in fig. (i). Then, clearly 3 lies opposite 4. Hence, when 4 is at the bottom then 3 mist lie on the top.

Question 19

A dice is numbered from 1 to 6 in different ways. If 1 is opposite to 5 and 2 is opposite to 3, then

Accepted Answer

If 1 is opposite to 5 and 2 is opposite to 3, then 4 definitely lies opposite to 6. Therefore, 2 cannot lie opposite to any of the two numbers - 4 or 6. Hence, 2 necessarily lies adjacent to both 4 and 6.

Question 20

A dice is numbered from 1 to 6 in different ways. If 1 is adjacent to 2, 3 and 5, then which of the following statements is necessarily true?

Accepted Answer

If 1 is adjacent to 2, 3 and 5, then either 4 or 6 lies opposite to 1. So, the numbers 4 and 6 cannot lie opposite to each other. Hence, 4 necessarily lies adjacent to 6.

Cubes and Dice Questions