# Study Notes on Cubes and Dices

By Gaurav Mohanty|Updated : December 2nd, 2021

As we all know Dice is a part of one of our popular indoor games since immemorial times. Presently, it is one of the interesting chapters of Reasoning and is also included in the syllabus of DU JAT and Other BBA Exams. Now, let us discuss Dice in detail.

Dice is a three-dimensional figure in which there are 6 Surfaces, 12 Edges, and 8 Corners. There are 4 adjacent surfaces to each surface.

Legend:

‘=’ represents Edges

‘→’ represents Surfaces

and, ‘●’ represents Corners

In the exam, two or more positions of a dice are given in a question and your task is to find out the opposite surface of a given surface.

Example:

From the above two positions of dice, it is clear that 2,3,4 and 5 are the adjacent surfaces of surface ‘1’. Therefore, we can say that the opposite surface of ‘1’ is surface ‘6’.

### Types of Dice

I. Standard Dice: The dice in which the sum of two opposite surfaces is

equal to seven is considered as Standard Dice.

For Example:

In the above dice, 5,3 and 1 are adjacent surfaces and it is clear that the sum of any two surfaces shown in dice is not equal to seven.

Therefore, Surface opposite to ‘5’ is Surface ‘2’ (i.e 5+2=7)

The surface opposite to ‘3’ is Surface ‘4’ (i.e 3+4=7)

The surface opposite to ‘1’ is Surface ‘6’ (i.e 1+6=7)

II. General Dice: In General Dice, the sum of two opposite surfaces is not equal to seven. To find out the opposite surface we are required at least two positions of dice having:

(a) one surface common

Here, Surface ‘3’ is a common surface in both the positions of dice. After fixing ‘3’ and then moving in a clockwise direction we can easily find the opposite surfaces.

3 – 6 – 4

3 – 5 – 2

It is clear that 6 and 5 are opposite surfaces and, 4 and 2 are opposite surfaces. Therefore, the surface opposite of surface ‘3’ is surface ‘1’.

(b) Two surfaces common

In the above two positions of dice, two surfaces i.e Surface ‘3’ and Surface ‘2’ are common.

3 – 2 – 1

3 – 2 – 6

After fixing surfaces 3 and 2, we find that surface opposite of surface ‘1’ is surface ‘6’.

As we are not aware surface opposite of surface ‘3’ , it may be surface ‘4’ or surface ‘5’. Similarly, surface opposite of surface ‘2’ is not confirm, it may be surface ‘5’ or surface ‘ 4’.

III. Open Dice: In open dice, all the six surfaces are clearly shown. The opposite surfaces are at the alternate positions of rows or columns. For Example:

Here, opposite of surface ‘1’ is surface ‘4’

opposite of surface ‘3’ is surface ‘5

opposite of surface ‘2’ is surface ‘6’

Exploded Dice Problems

Sometimes in exams, we are given an exploded form or expanded form of two or more positions of dice and we have to represent all the six surfaces in open dice.

For Example:

In the above two positions of dice common surface is ‘4’.

Always fix the common surface at the centre position.

From the first position:

i.e

From the second position:

i.e

Clearly, the blank surface will be filled by the remaining number i.e ‘6’

Therefore, opposite surfaces are 1↔ 2, 4 ↔ 6, and 3 ↔ 5.

we hope that this will help you clear the Dice problems with ease.

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