Reasoning Section of any competitive exam is easy to score, condition you know how to solve it. In this post, we will learn the simplest way to solve the coloured Cube question of Reasoning Section.

These types of questions are often asked in the SSC and Railway exams of 1-2 marks. There is one more type of question that is called Dice questions in Reasoning.

Questions on Dice will also be shared, but right now we focus on coloured cube questions.

#### Type of questions

Type – 1: A picture is given and one has to figure out the number of cubes visible or placed.

This type of question is easy as you only have to figure out the number of cubes cut from a big cube.

Type – 2: A big cube is painted, either in the same colour or in different colours. The larger cube is cut into smaller ones and the candidate is asked to the number of cubes with different specifications.

For example, a larger cube painted red colour at the corners, two sides or one sides and cut into 1 unit each with 3x3x3 specifications, as shown in the figure below

Now, the candidates are asked to find out the followings:

1. Number of cubes with no colour side

2. Number of cubes with 1 colour side

3. Number of cubes with 2 colour side

4. Number of cubes with 3 colour side

I have shared below the coloured images of cube cut into 1×3 units. With seeing the images, you can visualize the answer.

But visualizing an image does not mean you will the correct answer of it. You may miss out any face which is not visible and jump to the wrong answer.

To save time and avoid complications, I tell you one short formula for all your question as discussed above, by which you can get the correct answer instantly in the exam.

#### Formula to find the answer

Let’s take the above question only. But, I will use a formula to get the answer.

1. Number of cubes with no colour side = (n-2)3 = (3-2)3 = 1

2. Number of cubes with 1 colour side = 6x(n-2)2 = 6x(3-2)2 = 6.

3. Number of cubes with 2 colour side = 12x(n-2) = 12x(3-2) = 12.

4. A number of cubes with 3 colour side = 8 (this will be 8 only in any case) or you can use formula = add answers of sl no. 1,2,3 and minus it from the cube of n units. It means 33 – (1+6+12) = 27 – 19 = 8

Now, you can solve the question related to cubes by using the above formula.

#### Formula test with other cubes

Let’s take a larger cube and cut into 1×4 units as shown below

To find

1. Number of cubes with no colour side

Ans – (n-2)3 = (4-2)3 = 8

2. Number of cubes with 1 colour side

Ans – 6x(n-2)2 = 6x(4-2)2 = 24

3. Number of cubes with 2 colour side

Ans – 12x(n-2) = 12x(4-2) = 24

4. Number of cubes with 3 colour side

Ans – cube if 1×4 units is 64 and the total of sl no 1,2,3 are 56. Then, the number of cubes with 3 colour side = 64-56 = 8.

This is the simplest way to solve the coloured Cube question of Reasoning Section, I have shared with you which is useful for every competitive exam.

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