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
Some times 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, blank surface will be filled by remaining number i.e ‘6’
Therefore, opposite surfaces are: 1↔ 2, 4 ↔ 6 and 3 ↔ 5.
we hope that this will help you clearing the Dice problems with ease.
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