# Dice

‘Dice’ is a three-dimensional shape in the shape of a cubic or cuboid that has a total of 6 panels (surface). Looking at any side of the dice, only three surfaces are visible, while the three surfaces are hidden, also the two opposite surfaces of the dice do not appear simultaneously.  That is, the opposite surfaces of the Dice given above are the following  Type 1

Generally, the numbers of digits from 1 to 6 are written on the sides of the dice. On this basis of it we can divide the dice into two parts.

### Normal Dice:

The sum of the digits of opposite sides of this type is not 7, but the sum of digits of adjacent surfaces can be 7.  Hence the given dice is a normal dice.
Therefore, if the number opposite to surface of 2 is asked, then it can be 1, 4 or 6.

### Standard Dice:

In this type of dice the sum of any two opposite surfaces is 7. . So if the sum of the adjacent two surfaces is not 7, then it can be the standard dice.  Hence the given dice is a standard dice.

In this way, if the opposite surface’s number is asked in the question, then the number can be found by subtract it from 7.
That is
opposite to 1 → 7 – 1 = 6
opposite to 2 → 7 – 2 = 5

### Types of Questions based on dice –

(i) Two states of dice are displayed  (Note that if the same number is seen on the same surface, then the numbers of the same surfaces are opposite to each other).
opposite to 6, → 3
opposite to 4, → 5
So opposite to 2, → 1

If the same number appears on two different surfaces, then start with the same number and write it in clockwise direction in different categories such as  For X dice → 2, 4, 6
For Y dice → 2, 5, 3

Opposite to 4 → 5
Opposite to 6 → 3
Opposite to 2 → will be 1.  (ii) If none of the two numbers are same in both dice, then check the Standard Dice rule.  So both are standard dice.

(iii) If the given dice has three or four positions, then you can follow the rules outlined below.  (i) question-  What is the number of opposite surface to 3 ?
Answer – Position of 5 is on the same surface for ‘X’ and ‘Z’.
So Opposite to 3 → 1

(ii) Question – What is on the opposite surface of 6 in the face of the displayed dice?
Answer –  From Dice ‘X’ and ‘Y’, After clockwise positioning of Dice ‘X’ → 1, 4, 5
After clockwise positioning of Dice ‘Y’, → 1, 4, 6
Hence Opposite to 6 → 5

(b) In Below Figure one dice is represented by four different variations.  (1) Question – Which digit on the lower surface of the position ‘B’?
(a) 6 (b) 5 (c) 3 (d) 1
Answer – In Dice A and B, Number 4 and 5 is common. Hence, 1 will be on the opposite surface of 2.

(2) Question – Which Number is on the opposite side of 3?
(a) 1 (b) 2 (c) 5 (d) None of these
Answer : From A and B, 1 is opposite to 2
From B and D, 4 is opposite to 6
Therefore, 5 will be on the opposite surface of 3.

(iv) If special symbols or colors are used in place of numbers.

→ Based on the status shown, what will be the opposite of the sign (@) ?  (a) X (b) □ (c) ∆ (d) \$
Answer – In the Given Situation,  Starting clockwise from the symbol , X will be on the opposite of @.

Type 2

In these questions, a spread-ed picture or shape is given which has to be converted into a cube or a dice. There are six squares in the shape and it is marked with numbers / letters / symbols. The number/ letter / symbol is decorated to be answered correctly.  On turning the shape into a cube, only one surface of the two opposite surface pairs will be visible, because no opposite surface or letter or symbol is shown together.
Like 1 is opposite to 5, 3 is opposite to 6, 2 is opposite to 4

Example: Below is a spread-ed picture, which of the following four options can be obtained by folding it ?  Solution: (d) The above-mentioned picture illustrates that E is opposite to A, F is opposite to B and D is opposite to C. The alternatives (a), (b) and (c) in the opposite surfaces are shown around, which is not possible. However, numbers depicted in the dice of option (d) is not contrary to one another. Therefore, they can all be on adjacent surfaces. So it is possible to make this cube by folding the spread-ed cube.  Example: A spread-ed picture of Dice is Given below, which of the following four options can be obtained by folding it ?  Resolve: (c) From the above illustration picture it is clear that ∆ is opposite  to O, X is opposite to @ and the other two are opposite to one another.
Since the opposite surfaces cannot be adjacent, option (a), (b) and (d) are not possible.

In the shape shown in the option (C) and none of the empty surfaces are opposite to one another. Therefore, it can be made by folding the spread-ed diffusion picture.  Example: Below is a spread picture, which one of the four options can be obtained by folding the picture to make a cube?  Solution: (b).

In Options (a) O and X are adjacent, which are opposite to each other according to the spread picture. So it is not possible to make this cube with a spread picture.

None of the symbols shown in the option (b) are opposite to one another. So this option is possible.

Option (C) in ∆ And # are shown together, which are shown opposite to each other in the spread picture. So this cube is not possible.

Option (d) □ and ⋈ Are shown together, which are opposite to each other according to the spread picture. So this cube is not possible.  When the four triangles form a surface together , look at the picture on the four triangles carefully and do not change its arrangement, neither clockwise nor anticlockwise . In the diffusion seen above, the picture located in the four triangle will be decorated clockwise by X, ∆, O and □.  Example: Below is a spread-ed picture, which is used to make a cube shaped box. Which of the four cubes given in the options is possible to make?  Solution: (d)

In option (a) The diffusion of four triangles is on the opposite surface of 5, but in the picture both are shown side by side, which is not possible.

In the option (b) There are no two opposite surfaces shown together  but the arrangement of triangles in the surface made of all four triangles is inaccurate. So this option is also wrong.

In Options (c) 2 and 4 are shown on the adjacent surface, which is contrary to each other according to the spread picture. So this option is also not possible.

In the option (d) There are no two opposite surfaces which are shown adjacent and the arrangement of four triangles is also correct. So this option is possible.

(v) Four smaller squares will form a surface together .  Just be careful that the sequence of letters in the cube do not change.

Example: Below is a spread-ed picture, if a cube is formed by folding the given picture, then which of the given cubes in the options is possible?  Solution: (a) The rule is not followed in any option other than option (a). So all other options are wrong.  