In this section we will try to understand the theory of cubes and dices which is part of the syllabus of verbal reasoning. We have tried our best to draw diagram and illustration for your better understanding but you have to use your imagination to fully grasp the concept.

**Concepts of Cubes and Dice**

**What is Dice**

A dice in shape is same as **cube** or **cuboid.**

At a time we can see only three views of dice that is **front view, top view** and **side view**

There are two types of dice-

#### 1. **Standard dice**

If sum of opposite face or surface of a dice is equal to 7 then the dice is called standard dice

#### 2.**General dice**

If the sum of adjacent face or surface of a dice is equal to 7 then the dice is called general dice

**Note**– A dice can never be both **general dice** and **standard dice**

Two** opposite** numbers or surfaces can **never be adjacent** to each other

**There are four cases through which questions can be asked in exam**

**1st case**

**When only one position or view of dice is given**

In this type of question we generally check that the dice is standard dice or general dice**Examples-**

**When it is standard dice**

Here sum of any adjacent side is not equal to 7

So for calculating the opposite side of any digit we simply subtract that digit from**7**

That is opposite digit of 2 is =**7-2=5**

Opposite digit of**6 = 7-6=1**

**When it is general dice**

Here sum of 4 and 3 is 7

So if we want to find a digit opposite to**4**so it can be either**1**or**6**or 5

We don’t exactly determine which digit should be opposite to**4**

**2nd case**

**When only two position or view of dice are given**

In this type of question there are three possibilities

1.**When there is no common digit between two dice**

**Examples-**

Here there is no common digit

So we find that the dice is standard or general dice

Here the dice is standard dice

So if we find the digit opposite to 6 so it will be **7-6 =1**

Opposite to 5 will be **7-5= 2**

Opposite to 4 will be **7-4= 3**

2.**When there is only one common digit between two dice**

**Example 01**

Here 6 is common in both dice

So in this dice if we have to find digit opposite to 3

Then starting from common digit we move clock wise direction and write all digits in sequence

**Example 02**

Here 3 is common in both dice

So in this dice if we have to find digit opposite to 1

Then starting from common digit we move clock wise direction and write all digits in sequence

**Example 03**

So here E is opposite to C

3. **When there are two common digits between two dice**

In this type of questions besides from common digits reaming digits are opposite to each other

**Example** **01**

Here 6 and 2 are common digits in both dice

**Note**– In above question if we have to find the digits opposite to 6 and 2 that it may be either **4** or **5**

**Example 02**

**Note**– In above question if we have to find the digits opposite to 6 and 2 that it may be either **4 **or **5**

**3rd case**

**When more than two position of view of dice are given**

**Example** **01**

In first view of cube 6 is adjacent to 3 and 2

And in second view of cube 6 is adjacent to 3 and 5

So clearly here **5** is opposite to **2**

And in second view 5 is adjacent to 6, and 3 and 4 and 3 in third view

So from here we say that** 4 **is opposite to **6**

**Example 02**

In this type of question we choose two such dice which have two common elements

Here we have to choose an alphabet which is opposite to word

So we choose **second **and **third** dice for our solution

In both dices E and C are common, so the word opposite to D should be A

**4th case**

**This is the case of opening of a dice**

In this case all alternate surface of a dice are opposite to each other

**Example 01**

This is a unfolded dice and we have to find after folding this where should be position of alphabets

So here alternate alphabets should be opposite to each other

F will be opposite of **B**

E will be opposite of **C** and

A will be opposite of **D**

After folding this our dice is formed as

**Example 02**

If figure of dices are given in question and we have to find which dice is formed after folding

So for that question we use **elimination method**

That is

Here C will be opposite of F

B will be opposite of D

A will be opposite of E

Here **C will be opposite of F **that means F can not be adjacent to C

so here we don’t get C adjacent to F in any dice

**B will be opposite of D ** so eliminate option (c)

And the last **A will be opposite of E** so eliminate option (a)

So here we get (b) and (d) as our required dice

**Cubes and Cuboid**

**In this section the questions are asked as follows-**

**1st case**

**In this type, cube is colored with different colors in which same color is in opposite faces****And we have to find the number of cubes with a combination of different colors**

**Example-**

Here total number of cubes = 4^{3}=64

And we have to find those cubes which has only red painted

So here we find middle cubes of level 2 and 3 (in front side and back side) have only red colors shown below as dotted points

So total number of red colored cubes in front side and back side are 4+4=8

So Here there is **8** such cubes

**Example 02**

Here we have to find how many cubes have two colors

So our figure is-

Here cube is made up of 27 cubes and having 3 different colors

So below dotted points show the cubes which have only two colors

Here in each level we get four such cubes which have two colored surfaces

So total colored surfaces are 4×3=12

So here we get **12 **such cubes

**2 ^{nd} case**

** In this case we have to find total number of cubes in given cuboid**

**Example-**

- Here figure is shown below

So here we have to find total cubes in big cuboid

So we multiply the numbers of column from each view that is

Front view = **6 column**

Top view = **2 column**

Side view = **2 column**

So total number of cubes = **6×6×2 =72**

Here we get total **72** cubes