UPSC CSAT Simplified: How to approach ‘Cubes and Dice’ questions?

About our Expert: Mudit Gupta has been a mentor and faculty for the UPSC Civil Services exam for 8 years with expertise in CSAT, Polity, International Relations, and Current Affairs. He is known to break complex concepts into simpler ones that allow UPSC aspirants to develop a grip over the subject matter.

What questions on ‘Cubes and Dices’ the aspirants must prepare for UPSC CSAT?

Mudit Gupta: ‘Cubes and Dice’ are one of the most frequently tested areas in the UPSC CSAT examination. Within cubes and dice, the question on ‘opposite faces’ is often asked. In these types of questions, we are usually given a set of different views of the same dice and we have to find the face opposite to one specific face.

Depending upon the views of the dice that are given, there are two ways in which we can easily solve such questions. Let us consider both the types one by one: 

TYPE 1 – SINGLE COMMON FACE

The figure given below depicts the same dice from three different angles:

(image courtesy: Mudit Gupta)

Now, let us consider a question: Find the face of the dice opposite to the face with 1 dot. 

Observe that in Figure (1) and Figure (2) the face with 5 dots is the only common face. Now, to solve this question, write 5 in two rows one below the other (because the face with 5 dots is the single common face in Figure (1) and Figure (2) ):

Row 1: 5 __ __

Row 2: 5 __ __

In Figure (1) move clockwise starting from the face with 5 dots and write the numbers in the first row. We observe that as we start moving clockwise starting from the face with 5 dots, we encounter the face with 4 dots followed by the face with 6 dots. So we will write these numbers in Row (1):

Row 1: 5 4 6

Row 2: 5 __ __

In Figure (2), we will again start moving in the clockwise direction starting from the face with 5 dots. As we move, we will encounter the face with 3 dots followed by the face with 1 dot. We will write them sequentially in Row (2)

Row 1: 5 4 6

Row 2: 5 3 1

In Row (1) and Row (2), the numbers in the second and the third column will be opposite to each other i.e. face with 4 dots will be opposite to the face with 3 dots and the face with 6 dots will be opposite to the face with 1 dot.

Using the same technique, you can use Figure (2) and Figure (3) to find the face opposite to the face with 2 dots. Hint: Figure (2) and Figure (3) have a common face with 3 dots.

TYPE 2 – TWO COMMON FACES

Let us consider another cube with two different views:

(image courtesy: Mudit Gupta)

Now, let us consider a question: Find the face opposite to the face with 5 dots.

If we observe Figure (4) and Figure (5), then faces with 1 dot and 3 dots are common in both figures. If we have 2 common faces in 2 views, then the third faces are always opposite. Hence, in Figure (4) and Figure (5), faces with 1 and 3 dots are the common faces and the faces with 4 and 5 dots will be opposite to each other.

Check your progress: 

Using the same technique as given above, find the face opposite to the face with 6 dots in the dice below:

(image courtesy: Mudit Gupta)

(Please post your answers in the comment box.)

Previous Article in the UPSC CSAT Simplified series:

How to approach Reading Comprehensions?

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