PW Class 6 Maths Notes Chapter 3: Number Play
Neha Tanna5 Sept, 2026
Numbers do much more than help you count. They can be grouped according to certain properties, arranged so that they follow a common rule, and connected through sequences. Looking closely at these relationships reveals some interesting ways in which numbers behave.
The PW Class 6 Chapter 3 Number Play Notes cover even and odd numbers, the results of adding them, formulas for finding the nth even and odd numbers, magic squares, Virahānka-Fibonacci numbers, and alphametics. The examples and rules on this page make it easier to see how each number idea works.
What Do Numbers Tell Us?
Numbers are not used only for counting. They can also represent relationships and follow specific rules. One of the simplest ways to see these relationships is by looking at even and odd numbers. Numbers can be represented using dots, showing whether all objects can be grouped into pairs or whether one remains unpaired.
What Are Even and Odd Numbers?
Even and odd numbers can be distinguished by what happens when objects are grouped into pairs.
|
Type |
Meaning |
Examples |
|
Even Numbers |
Can be grouped in pairs with no leftovers |
2, 4, 6, 8, 10, ... |
|
Odd Numbers |
Always leave one object unpaired |
1, 3, 5, 7, 9, ... |
Every dot can be paired in the even-number examples, whereas the odd-number arrangements leave one dot without a pair.
What Happens When Even and Odd Numbers Are Added?
There are three useful conclusions about adding even and odd numbers.
|
Numbers Added |
Result |
|
Even + Even |
Even |
|
Odd + Odd |
Even |
|
Even + Odd |
Odd |
These relationships show that whether the result is even or odd depends on the types of numbers being added.
What Are the Formulas for the nth Even and Odd Numbers?
There are separate formulas for finding the nth even number and nth odd number.
|
Number Type |
Formula |
|
nth Even Number |
2n |
|
nth Odd Number |
2n − 1 |
Therefore, 2n gives the nth even number, while 2n − 1 gives the nth odd number.
What Is a Magic Square?
A magic square is a square grid of numbers in which each row, each column, and each diagonal adds up to the same number. This common total is called the magic sum.
The example given here arranges the numbers 1 to 9 as follows:
|
6 |
1 |
8 |
|
7 |
5 |
3 |
|
2 |
9 |
4 |
In this arrangement, the rows, columns, and diagonals each give a magic sum of 15.
For an n × n square, the magic constant formula is:
M = n(n² + 1) / 2
This example shows how the same set of numbers can be placed in a particular arrangement so that several different directions produce an equal sum.
What Are Virahānka-Fibonacci Numbers?
The Virahānka-Fibonacci numbers follow a special number pattern:
1, 1, 2, 3, 5, 8, 13, 21, 34, ...
In this sequence, each number after the first two is the sum of the previous two numbers.
For example:
-
1 + 1 = 2
-
1 + 2 = 3
-
2 + 3 = 5
-
3 + 5 = 8
-
5 + 8 = 13
We also provide a timeline showing the development of the Virahānka-Fibonacci numbers.
|
Person |
Period Given in the Notes |
Contribution |
|
Pingala |
c. 300 BCE |
Earliest reference |
|
Virahānka |
c. 700 CE |
First explicit rule |
|
Gopala |
c. 1135 CE |
Continued work |
|
Hemachandra |
c. 1150 CE |
Further development |
|
Fibonacci |
1202 CE |
Introduced in Europe |
This timeline places the number pattern alongside the names associated with its development.
What Are Alphametics?
Alphametics are presented as letters for digits. Instead of writing every number directly as a digit, letters are used to represent them.
Three rules are given:
-
Each letter represents one unique digit.
-
The same letter represents the same digit throughout the problem.
-
Different letters represent different digits.
The example is:
T + T + T = UT
It is shown alongside:
5 + 5 + 5 = 15
Therefore:
U = 1
T = 5
The example demonstrates how the value represented by each letter can be identified while following the alphametic rules.
PW Class 6 Maths Notes Chapter 3: Number Play
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How Do PW Class 6 Maths Notes Help with Number Play?
Number Play contains several different kinds of number relationships, so the PW Class 6 Number Play Notes can help you revise them according to the rule or pattern involved.
-
Separate even and odd numbers: Use the pairing idea to recall why an even number has no leftover object while an odd number leaves one unpaired.
-
Compare addition results: Keep the three even-and-odd addition rules together instead of recalling them separately.
-
Recall the nth-number formulas: Refer to 2n for the nth even number and 2n − 1 for the nth odd number.
-
Read the magic square by direction: Look across its rows, columns, and diagonals to see how each produces the same magic sum.
- Follow a sequence term by term: In the Virahānka-Fibonacci pattern, check how each number after the first two comes from the previous two.
-
Work with letters and digits: Use the alphametic rules to keep track of which digit each letter represents.
Complete PW Resources for Class 6 Maths Preparation
After revising the PW Class 6 Number Play Notes, you can use the related PW Class 6 Maths resources for chapter study and question practice.
|
PW Class 6 Resource |
How You Can Use It |
|
Refer to chapter-wise concepts and explanations |
|
|
Check solutions to questions from your NCERT textbook |
|
|
Practise important questions after revising the chapter |
|
|
Work on questions covering different Class 6 Maths chapters |
Number Play shows how much information can be found by looking closely at the rules and relationships behind numbers. The PW Class 6 Number Play Notes keep the chapter’s even and odd number rules, formulas, magic square, Virahānka-Fibonacci sequence, and alphametics organised so that you can return to each idea separately during revision.
