Cube & Dice

Reasoning is a critical element of a competitive exam. A good performance on the Reasoning examination might result in very high marks on competitive tests. Reasoning can be easily solved if you have exceptional mental abilities. It is fundamentally separated into a few sections based on logic and kind. One of them is cube dice reasoning.

What Does The Term “Cube” Mean?

A cube is a 3-dimensional shape with equal length, breadth, and height, with any two adjoining faces angled at 90° to one another. It is composed of six faces, eight corners, and twelve edges. Because only three sides of a cube can be seen at a time, they’re called “Joint Sides,” and these sides can’t be on the opposite side of each other. Things structured like cubes are frequently referred to as ‘cubic’.

Fundamental Rules: 

There are many dice principles in reasoning that can be used to answer dice-based problems:

1: Two dice with opposing faces cannot be adjacent to one another.

2: If two dice are arranged as illustrated below, one of 2 common faces (Face 4) is in the same position; the remaining faces will oppose one another.

3: If the dice placements are different, but the common face is the same, then the opposing faces of the remaining faces will be the same.

4: If two die positions are given, and it is also mentioned that the common face in each place is different, then the face opposing the specified common side would be the face that is not visible on any specified face in any of the two die positions. Additionally, the opposing face of the remaining faces cannot be the same.

Cube Dice Formula

The figure above can be deconstructed into three horizontal layers:

Layer I, or the top layer

Layer II, or the middle layer

Layer III, or the bottom layer

Also, if n = the number of cube face divisions

Then,

(i) The number of smaller cubes without a painted face equals (n-2)3.

(ii) The number of smaller cubes with a painted face equals (n-2)2 x 6

(iii) The Numbers of smaller cubes painted on two faces = (n-2) x 12

(iv) The number of smaller cubes with three painted faces equals eight.

Here is an example: 

A cube with blue paint on its face is divided into 125 equal-sized cubes. Now answer these questions:

How many cubes do you have where no face has been painted on them?

            (a) 8 (b) 16

            (c) 18 (d) 27

How many cubes can you see to be painted on a single side?

            (a) 8 (b) 16

            (c) 36 (d) 54

Because there are 125 equal-sized smaller cubes, n = number of segments on the face of the undivided cube =5.

(d) The number of cubes that do not have a painted face = (n -2)3 = (5 – 2)3 = 27

(d) Number of only single face painted cubes = (n -2)2 × 6 = (5 -2)2 × 6 = 54

What is Dice?

The dice shape is identical to that of a cube or cuboid. At the same time, we can only see three dice views: the front view, the top view, and the side view. Dice is a variation of Cubes, but with a little higher logic and conceptual applicability than Cubes. Dice is a part of aptitude’s logical reasoning section.

Dice Types:

1. Base Dice

2. Open Dice

Base Dice are classified into two types:

1. Standard Dice

2. Ordinary Dice

Definition of Standard Dice:

If the numbers on two dice do not match, they are considered standard dice.

The numbers on both dice are not the same. So, we can refer to it as standard dice.

Definition of Ordinary Dice:

When the numbers on two dice match, it is an ordinary dice.

Here are two dice, the first with the numbers 2, 3, 4 and the second with the numbers 3, 5, 6. Here, we say that the number 3 is matched. Thus, it is an ordinary dice.

How to Solve Cube and Dice Questions?

Students can use the tips and tactics provided below to assist them in resolving questions relating to the Cube Dice reasoning section.

1: In a cube, the length, breadth, and height are equal. There are six surfaces, twelve edges, and eight corners in all.

2: Cuboid = the length and breadth of a cuboid are not equal to its height.

3: There are two types of dice: Ordinary and Standard Dice.

4: It is a standard cube dice with six numbered sides ranging from 1 to 6, having opposite sides adding to 7.

5: In standard dice, the “6” is the opposite of 1, the “5” is always the opposite of 2, and the “4” is always the opposite of 3.

6: With ordinary dice, the sum of any two adjacent surface values equals 7.

Deconstructing a Dice:

To better understand the theory outlined above, the following diagrams are provided.

1st rule: E & F are always in opposition to one another, as are all other open dice, whether they are B & F, B & F, or c & D. Both of these surfaces are constantly in the opposite direction of each other.

2nd rule: Because these two A and C surfaces do not touch each other, they are on opposite sides.

3rd rule: Here, we notice that B and D are not in contact with one another’s surfaces. Thus, B and D are on opposite sides of one another.

E is the opposite of F.

A is the opposite of C

B is the opposite of D.

Conclusion:

Cubes Dice is a critical chapter of the reasoning aptitude test. Unfortunately, it is hard to visualise dice in three dimensions when dealing with dice. Therefore we flattened the cube. Dice are formed by placing the farthest end of a flattened cube on top of a central square, which serves as both a cube’s top and its bottom. The remainder of the square represents the dice’s adjacent sides.