Dice – CSAT Notes

Die/Dice is a three-dimensional figure having various numbers, letters, colors, and other symbols on each of its six sides/faces. It has 12 edges and 8 corners. The length, breadth, and height of dice are all the same. Several types of problems based on dice are asked in UPSC-CSAT, which are explained here in detail.

Classification of Dice

1. Standard Dice
2. Ordinary Dice

Classification of Dice

Standard Dice

• The sum of any opposite sides on a Standard Dice is 7.
• The sum of no two adjacent sides is 7.

Ordinary Dice

• Any two opposite sides on an Ordinary or Non-Standard Dice cannot give the sum of 7.
• However, adjacent sides may produce a total of 7.

Types of Questions asked in CSAT

Let's take a look at the various types of questions that may be asked, one by one, from the list below.

Problem-based on Single Dice

In this type, problems relating to single dice will be given.

Problem-based on two or more Dice

In this type, problems related to two or more two dice will be given.

Problem Based on Open Dice

The six faces of the dice are visible in open dice. It shows the opposite position of columns and rows

Example

• 2 is opposite to 4
• 3 is opposite to 6
• 1 is opposite to 5

Rules to Solve Questions

There are a few rules that will help you in solving dice questions in the simplest way possible. The following are the rules:

RULE 1

Adjacent faces of dice cannot be opposite to each other.

Example:

• Two-position of the same dice is shown in the above figure according to Rule-1.
• Adjacent faces of dice cannot be opposite to each other means face with 2 dots is adjacent to 5, 1 & 4 dots, therefore, face with 2 dots will never be opposite to 5,1 & 4 dots.

RULE 2

If two different faces of a dice are shown and one of the two common faces is in the same position then the remaining faces will be opposite to each other.

Example:

• Two-position of the same dice is shown in the above figure according to Rule-2.
• 4 & 6 are common faces with 4 in the same position, therefore 1 and 5 will be opposite to each other.

RULE 3

If two different faces of a dice are shown and the common face is in the same position then the opposite faces of the remaining faces will also be in the same position.

Example:

• Two-position of the same dice is shown in the above figure according to Rule-3.
• 3 is common and in the same position, therefore 2 will be opposite to 6, and 1 will be opposite to 5.

RULE 4

If two different faces of a dice are shown and the common face is not in the same position then the face opposite to the common face will be that which is not shown in any two positions and the opposite faces of the remaining faces will also not be in the same position.

Example:

• Two-position of the same dice is shown in the above figure according to Rule-4.
• 2 is common in both the figure and in different positions therefore number opposite to 2 will be that, which is not shown on any of the faces above. And 5 will be opposite to 3 and 1 opposite to 3.

Previous Year Questions asked in CSAT

Question: A cube has six numbers marked 1,2,3,4,5, and 6 on its faces. Three views of the cube are shown below: (UPSC 2013)

(a) 2 and 3

(b) 6 and 1

(c) 1 and 4

(d) 3 and 1

Question: Consider the following pictures of dice: (UPSC 2000)

What is the number opposite to 3 ?

(a) 1

(b) 4

(c) 5

(d) Data insufficient