Question 1

Arrange the stick figure cutouts given at the end, or draw a height arrangement such that the sequence reads:
(a) 0, 1, 1, 2, 4, 1, 5
(b) 0, 0, 0, 0, 0, 0, 0
(c) 0, 1, 2, 3, 4, 5, 6
(d) 0, 1, 0, 1, 0, 1, 0
(e) 0, 1, 1, 1, 1, 1, 1
(f) 0, 0, 0, 3, 3, 3, 3

Accepted Answer

(a) The required arrangement is FCBGADE.
(b) The required arrangement is AECGBDF.
(c) The required arrangement is FDBGCEA.
(d) The required arrangement is EAGCDBF.
(e) The required arrangement is FAECGBD.
(f) The required arrangement is BDFAECG.

Question 2

For each of the statements given below, think and identify if it is Always True, Only Sometimes True, or Never True. Share your reasoning.
(a) If a person says ‘0’, then they are the tallest in the group.
(b) If a person is the tallest, then their number is ‘0’.
(c) The first person’s number is ‘0’.
(d) If a person is not first or last in line (i.e., if they are standing somewhere in between), then they cannot say ‘0’.
(e) The person who calls out the largest number is the shortest.
(f) What is

Accepted Answer

(a) Only Sometimes True: A person says ‘0’ when they see no one taller than themselves. The tallest person will always say ‘0’, but a shorter person can also say ‘0’ if they are at the front or in a position where no one taller is ahead of them. Thus, the given statement is only sometimes true.
(b) Always True: If a person is the tallest, then no one is taller than them, so they will always say ‘0’. So, the given statement is always true.
(c) Always True: Each person is assigned a number that represents how many taller people are ahead of them. Since there is no one ahead of the first person, their number will always be ‘0’. Hence, the given statement is always true.
(d) Only Sometimes True: The statement is only sometimes true. A person standing in between can still be assigned ‘0’ if there are no taller people ahead of them.
(e) Only Sometimes True: The statement is only sometimes true. A person who calls out the largest number has many taller people in front but may not be the shortest overall. For example, if the shortest person is standing at the front, they will call out ‘0’. Meanwhile, the second shortest person could be at the back and might call out the largest number.
(f) If there are 8 people, then the shortest person will see 7 taller people. So the maximum number someone can say is 7.
6.2 Picking Parity
NCERT In-Text Questions (Pages 129-131)
Kishor has some number cards and is working on a puzzle: There are 5 boxes, and each box should contain exactly 1 number card. The numbers in the boxes should sum to 30. Can you help him fid a way to do it?
Can you figure out which 5 cards add to 30? Is it possible?
Solution:
No, it is not possible, as the sum of 5 odd numbers is always odd and 30 is an even number.
Explore what happens to the sum of (a) 4 odd numbers, (b) 5 odd numbers, and (c) 6 odd numbers.
Solution:
Based on the given examples for number cards 1, 3, 5, 7, 9, 11, 13.
(a) Sum of 4 odd numbers = 1 + 3 + 5 + 7 = 16 (even), can be arranged in pairs.
(b) Sum of 5 odd numbers = 1 + 3 + 5 + 7 + 9 = 25 (odd), cannot be arranged in pairs.
(c) Sum of 6 odd numbers = 1 + 3 + 5 + 7 + 9 + 11 = 36 (even), can be arranged in pairs.
Figure it Out (Page 131)

Question 3

We know that:
(a) even + even = even
(b) odd + odd = odd
(c) even + odd = odd
Similarly, find out the parity for the following scenarios:
(d) even – even = ___________________
(e) odd – odd = ___________________
(f) even – odd = ___________________
(g) odd – even = ___________________

Accepted Answer

(d) even – even
Example:
6 – 2 = 4 → even
8 – 4 = 4 → even
Parity of result = even
∴ even – even = even
(e) odd-odd
Example:
7 – 3 = 4 → even
9 – 5 = 4 → even
Parity of result = even
∴ odd – odd = even
(f) even-odd
Example:
8 – 3 = 5
12 – 5 = 7
Parity of result = odd
∴ even – odd = odd
(g) odd-even
Example:
7 – 2 = 5
9 – 6 = 3
Parity of result = odd
∴ odd – even = odd
Small Squares in Grids
NCERT In-Text Questions (Pages 131-132)
In a 3 × 3 grid, there are 9 small squares, which is an odd number. Meanwhile, in a 3 × 4 grid, there are 12 small squares, which is an even number.
Given the dimensions of a grid, can you tell the parity of the number of small squares without calculating the product?
Solution:
Yes, we can determine the parity of the number of small squares in a grid without directly calculating the full product, simply by observing the parity of the dimensions.
Rule: The product of two numbers is:
Even if at least one of the numbers is even.
Odd if both numbers are odd.
Find the parity of the number of small squares in these grids:
(a) 27 × 13
(b) 42 × 78
(c) 135 × 654
Solution:
(a) Both 27 and 13 are odd numbers, and Odd × Odd = Odd.
So, the parity of the number of small squares is odd.
(b) Both 42 and 78 are even numbers, and Even × Even = Even.
So, the parity of the number of small squares is even.
(c) 135 is odd, 654 is even, and Odd × Even = Even.
So, the parity of the number of small squares is even.
Parity of Expressions
NCERT In-Text Questions (Pages 132-133)
Consider the algebraic expression: 3n + 4.
For different values of n, the expression has different parity:
Come up with an expression that always has even parity.
Some examples are: 100p and 48w – 2. Try to find more.
Solution:
Expressions that have even parity are 2p + 10, 8n, 6m – 2, etc.
Come up with expressions that always have odd parity.
Solution:
Expressions that always have odd parity are 2m + 1, 8a + 3, etc.
Come up with other expressions, like 3n + 4, which could have either odd or even parity.
Solution:
Expressions, like 3n + 4, which could have either odd or even parity are: 5k – 2, n + 5, etc.
Are there expressions that we can use to list all the even numbers?
Hint: All even numbers have a factor of 2.
Solution:
All even numbers are multiples of 2, so to generate every even number, use 2n (where n = 1, 2, 3,…). This can list all the even numbers.
Are there expressions that we can use to list all odd numbers?
We saw earlier how to express the nth term of the sequence of multiples of 4, where n is the letter-number that denotes a position in the sequence (e.g., fist, twenty third, hundred and seventeenth, etc.).
Solution:
To list all odd numbers, we use 2n – 1 (where n = 1, 2, 3, ….).
This generates 1, 3, 5, 7, 9, …, capturing all odd numbers.
What would be the nth term for multiples of 2? Or, what is the nth even number?
Solution:
The nth term for multiples of 2 is 2n. The nth even number is also 2n.
6.3 Some Explorations in Grids
NCERT In-Text Questions (Pages 133-136)
Observe this 3 × 3 grid. It is filed following a simple rule— use numbers from 1 – 9 without repeating
any of them. There are circled numbers outside the grid.
Are you able to see what the circled numbers represent?
The numbers in the yellow circles are the sums of the corresponding rows and columns.
Fill the grids below based on the rule mentioned above:
Solution:
Make a couple of questions like this on your own and challenge your peers.
Solution:
Do it yourself.
Can you find the other possible positions for 1 and 9?
Now, we have one full row or column of the magic square! Try completing it!
[Hint: First fill the row or columns containing 1 and 9]
Solution:
Figure it Out (Page 136)

Question 4

What other operations can be performed on a magic square to yield another magic square?

Accepted Answer

Do it yourself.

Source: This question is from Number Play, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Number Play: Operations, Performed, Magic, Square, Yield, Another. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Number PlayQ1: Arrange the stick figure cutouts given at the end, or draw a height arrangement such that the...
Q10: Identify the true statements. (a) The expression 4m – 1 always gives odd numbers. (b) All even...
Q2: For each of the statements given below, think and identify if it is Always True, Only Sometimes...
Q3: We know that: (a) even + even = even (b) odd + odd = odd (c) even + odd = odd Similarly, find out...
Q5: Discuss ways of creating a magic square using any set of 9 consecutive numbers (like 2-10, 3-11,...
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Question 5

Discuss ways of creating a magic square using any set of 9 consecutive numbers (like 2-10, 3-11, 9-17, etc.).

Accepted Answer

The magic square for numbers 2-10 can be seen in solution 2 above.
For the magic square using numbers 3-11, add 2 to each number in the original, and we get the adjoining magic square.
Here, magic sum = 21
For the magic square using numbers 9-17, add 8 to each number in the original, and we get a square as shown alongside.
Here, magic sum = 39
Generalising a 3 × 3 Magic Square
NCERT In-Text Questions (Pages 136-137)
We can describe how the numbers within the magic square are related to each other, i.e., the structure of the magic square.
Choose any magic square that you have made so far using consecutive numbers. If m is the letter-number of the number in the centre, express how other numbers are related to m, how much more or less than m.
[Hint: Remember how we described a 2 × 2 grid of a calendar month in the Algebraic Expressions chapter].
Solution:
Consider the magic square
We can express it using the letter-number m as:
Once the generalised form is obtained, share your observations with the class.
Solution:
Do it yourself.
Figure it Out (Page 137)

Question 6

What is the parity of the sum of numbers from 1 to 100?

Accepted Answer

The sum of numbers from 1 to 100 is as follows:
Since 5050 is an even number, the parity is even.

Source: This question is from Number Play, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Number Play: Parity, Sum, Numbers, Number Play, Mathematics. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Number PlayQ1: Arrange the stick figure cutouts given at the end, or draw a height arrangement such that the...
Q10: Identify the true statements. (a) The expression 4m – 1 always gives odd numbers. (b) All even...
Q2: For each of the statements given below, think and identify if it is Always True, Only Sometimes...
Q3: We know that: (a) even + even = even (b) odd + odd = odd (c) even + odd = odd Similarly, find out...
Q4: What other operations can be performed on a magic square to yield another magic square?
Practice more questions from Number Play &mdash; Mathematics, Class 7 CBSE

Question 7

Two consecutive numbers in the Virahanka sequence are 987 and 1597. What are the next 2 numbers in the sequence? What are the previous 2 numbers in the sequence?

Accepted Answer

The given numbers are 987 and 1597.
In the Virahanka sequence, each number is the sum of the two preceding numbers.
The next two numbers are:
987 + 1597 = 2584
1597 + 2584 = 4181
The previous two numbers are:
1597 – 987 = 610
987 – 610 = 377
The sequence is …..,377, 610, 987, 1597, 2584, 4181,…..

Question 8

Angaan wants to climb an 8-step staircase. His playful rule is that he can take either 1 step or 2 steps at a time. For example, one of his paths is 1, 2, 2, 1, 2. In how many different ways can he reach the top?

Accepted Answer

Ways in which Angaan can climb 8 steps with 1 or 2 steps are as follows:
For n = 8
So, the total ways in which Angaan reaches the top = 1 + 7 + 15 + 10 + 1 = 34 ways.

Source: This question is from Number Play, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Number Play: Angaan, Wants, Climb, Step, Staircase, Playful. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Number PlayQ1: Arrange the stick figure cutouts given at the end, or draw a height arrangement such that the...
Q10: Identify the true statements. (a) The expression 4m – 1 always gives odd numbers. (b) All even...
Q2: For each of the statements given below, think and identify if it is Always True, Only Sometimes...
Q3: We know that: (a) even + even = even (b) odd + odd = odd (c) even + odd = odd Similarly, find out...
Q4: What other operations can be performed on a magic square to yield another magic square?
Practice more questions from Number Play &mdash; Mathematics, Class 7 CBSE

Question 9

What is the parity of the 20th term of the Virahanka sequence?

Accepted Answer

Consider the Virahanka sequence given below:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987,…..
Let us observe the pattern of odd/even in Virahanka numbers given above:
Here 1 → odd
2 → even
3 → odd
5 → odd
8 → even
13 → odd
21 → odd
34 → even
So parity cycle is: odd, even, odd, (repeats every 3 terms)
So the 20th term of the Virahanka sequence is even.

Question 10

Identify the true statements.
(a) The expression 4m – 1 always gives odd numbers.
(b) All even numbers can be expressed as 6j – 4.
(c) Both expressions 2p + 1 and 2q – 1 describe all odd numbers.
(d) The expression 2f + 3 gives both even and odd numbers.

Accepted Answer

(a) Substituting m = 1 in 4m – 1 = 4 × 1 – 1 = 3 (odd).
Substituting m = 2 in 4m – 1= 4 × 2 – 1 = 7 (odd).
Thus, the expression 4m – 1 always gives odd numbers.
This statement is true.
(b) Substituting j = 1 in 6j – 4 = 6 × 1 – 4 = 2 (even).
Substituting j = 2 in 6j – 4 = 6 × 2 – 4 = 8 (even).
This expression produces even numbers, but it does not produce all even numbers (for e.g., it skips 4 and 6).
This statement is false.
(c) Substituting p = 1, 2, 3,….. in 2p + 1, we get 3, 5, 7,…..
Substituting q = 1, 2, 3,…. in 2q + 1, we get 1, 3, 5, 7,…….
Here, 2q – 1 describes all the odd numbers but 2p + 1 does not describe 1.
Thus, this statement is false.
(d) Substituting f = 1, 2f + 3 = 2 × 1 + 3 = 5 (odd).
Substituting f = 2, 2f + 3 = 2 × 2 + 3 = 7 (odd).
The expression 2f + 3 always gives odd numbers because 2f is even and adding 3 makes it odd.
This statement is false.

Question 11

Solve this cryptarithm:

Accepted Answer

Here, T is at hundreds place, so T = 1
⇒ A = 0 and U = 9.
So, we have U = 9, T = 1, and A = 0.

Source: This question is from Number Play, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Number Play: Cryptarithm, Number Play, Mathematics. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Number PlayQ1: Arrange the stick figure cutouts given at the end, or draw a height arrangement such that the...
Q10: Identify the true statements. (a) The expression 4m – 1 always gives odd numbers. (b) All even...
Q2: For each of the statements given below, think and identify if it is Always True, Only Sometimes...
Q3: We know that: (a) even + even = even (b) odd + odd = odd (c) even + odd = odd Similarly, find out...
Q4: What other operations can be performed on a magic square to yield another magic square?
Practice more questions from Number Play &mdash; Mathematics, Class 7 CBSE