NCERT Solutions For Class 8 Maths Chapter 5 Number Play

Class 8 Maths Chapter 5 – Number Play is an engaging and exploratory chapter that takes students beyond routine calculations into the fascinating world of number patterns, properties, and puzzles. The chapter encourages students to observe, explore, and discover interesting characteristics of numbers through activities, games, and logical reasoning. Topics covered include palindromes, patterns in numbers, Kaprekar numbers, magic squares, clock arithmetic, and the use of number properties to solve puzzles. The chapter develops mathematical thinking and curiosity rather than focusing solely on procedural skills.

This chapter is part of the revised NCERT Class 8 Maths syllabus and is designed to build a deeper appreciation for mathematics. It strengthens students' logical reasoning, pattern recognition, and problem-solving abilities — skills that are essential for higher mathematics and competitive examinations. The exploratory nature of the chapter makes it both enjoyable and intellectually stimulating for students.

NCERT Solutions For Class 8 Maths Chapter 5 Number Play

Number Play (New NCERT)
Medium
Q.
Take any 4 consecutive numbers. For example, 3, 4, 5, and 6. Place ‘+’ and '−-​' signs in between the numbers. How many different possibilities exist? Write all of them.
Evaluate each expression and write the result next to it. Do you notice anything interesting?
Number Play (New NCERT)
Medium
Q.
Find three consecutive numbers such that the first number is a multiple of 2, the second number is a multiple of 3, and the third number is a multiple of 4. Are there more such numbers? How often do they occur?
Number Play (New NCERT)
Medium
Q.
Make conjectures by examining if there are any patterns or relations between
(i) the parity of a number and its digital root.
(ii) the digital root of a number and the remainder obtained when the number is divided by 3 or 9.
Number Play (New NCERT)
Medium
Q.
If 31z5 is a multiple of 9, where z is a digit, what is the value of z? Explain why there are two answers to this problem.
Number Play (New NCERT)
Medium
Q.
“I take a number that leaves a remainder of 8 when divided by 12.1 take another number, which is 4 short of a multiple of 12. Their sum will always be a multiple of 8”, claims Snehal. Examine his claim and justify your conclusion.
Number Play (New NCERT)
Medium
Q.
When is the sum of two multiples of 3, a multiple of 6, and when is it not? Explain the different possible cases, and generalise the pattern.
Number Play (New NCERT)
Medium
Q.
Sreelatha says, “I have a number that is divisible by 9. If I reverse its digits, it will still be divisible by 9”.
(i) Examine if her conjecture is true for any multiple of 9.
(ii) Are any other digit shuffles possible such that the number formed is still a multiple of 9?
Number Play (New NCERT)
Medium
Q.
If 48a23b is a multiple of 18, list all possible pairs of values for a and b.
Number Play (New NCERT)
Medium
Q.
If 3p7q8 is divisible by 44, list all possible pairs of values for p and q.
Number Play (New NCERT)
Medium
Q.
Write five multiples of 36 between 45,000 and 47,000. Share your approach with the class.
Number Play (New NCERT)
Medium
Q.
Write any number. Generate a sequence of numbers by repeatedly adding 11. What would be the digital roots of this sequence of numbers? Share your observations.
Number Play (New NCERT)
Medium
Q.
The middle number in the sequence of 5 consecutive even numbers is 5p. Express the other four numbers in sequence in terms of p.
Number Play (New NCERT)
Medium
Q.
Write a 6-digit number that is divisible by 15, such that when the digits are reversed, it is divisible by 6.
Number Play (New NCERT)
Medium
Q.
Deepak claims, “There are some multiples of 11 which, when doubled, are still multiples of 11. But other multiples of 11 don’t remain multiples of 11 when doubled”. Examine if his conjecture is true; explain your conclusion.
Number Play (New NCERT)
Medium
Q.
Determine whether the statements below are ‘Always True’, ‘Sometimes True’, or ‘Never True’. Explain your reasoning.
(i) The product of a multiple of 6 and a multiple of 3 is a multiple of 9.
(ii) The sum of three consecutive even numbers will be divisible by 6.
(iii) If abcdef is a multiple of 6, then badcef will be a multiple of 6.
(iv) 8(7b – 3) – 4(11b + 1) is a multiple of 12.
Number Play (New NCERT)
Medium
Q.
Choose any 3 numbers. When is their sum divisible by 3? Explore all possible cases and generalise.
Number Play (New NCERT)
Medium
Q.
Is the product of two consecutive integers always a multiple of 2? Why? What about the product of these consecutive integers? Is it always a multiple of 6? Why or why not? What can you say about the product of 4 consecutive integers? What about the product of five consecutive integers?
Number Play (New NCERT)
Medium
Q.
Solve the cryptarithms
(i) EF × E = GGG
(ii) WOW × 5 = MEOW
Number Play (New NCERT)
Medium
Q.
What will be the digital root of the number 9a + 36b + 13?
Number Play (New NCERT)
Medium
Q.
The digital root of an 8-digit number is 5. What will be the digital root of 10 more than that number?
Number Play (New NCERT)
Medium
Q.
​Now, take four other consecutive numbers. Place the ‘+’ and ‘-’ signs as you have done before. Find out the results of each expression. What do you observe?
Number Play (New NCERT)
Medium
Q.
When divided by 7, the number 661 leaves a remainder of 3, and 4779 leaves a remainder of 5. Without calculating, can you say what remainders the following expressions will leave when divided by 77? Show the solution both algebraically and visually.
(i) 4779 + 661
(ii) 4779 – 661
Number Play (New NCERT)
Medium
Q.
​Using our understanding of how parity behaves under different operations, identify which of the following algebraic expressions give an even number for any integer values for the letter-numbers.
Number Play (New NCERT)
Medium
Q.
The sum of four consecutive numbers is 34. What are these numbers?
Number Play (New NCERT)
Medium
Q.
Suppose p is the greatest of five consecutive numbers. Describe the other four numbers in terms of p.
Number Play (New NCERT)
Medium
Q.
For each statement below, determine whether it is always true, sometimes true, or never true. Explain your answer. Mention examples and non-examples as appropriate. Justify your claim using algebra.
(i) The sum of two even numbers is a multiple of 3.
(ii) If a number is not divisible by 18, then it is also not divisible by 9.
(iii) If two numbers are not divisible by 6, then their sum is not divisible by 6.
(iv) The sum of a multiple of 6 and a multiple of 9 is a multiple of 3.
(v) The sum of a multiple of 6 and a multiple of 3 is a multiple of 9.
Number Play (New NCERT)
Medium
Q.
Find a few numbers that leave a remainder of 2 when divided by 3 and a remainder of 2 when divided by 4. Write an algebraic expression to describe all such numbers.
Number Play (New NCERT)
Medium
Q.
“I hold some pebbles, not too many, when I group them in 3’s, one stays with me. Try pairing them up — it simply won’t do. A stubborn odd pebble remains in my view. Group them by 5, yet one’s still around, but grouping by seven, perfection is found. More than one hundred would be far too bold. Can you tell me the number of pebbles I hold?”
Number Play (New NCERT)
Medium
Q.
Tathagat has written several numbers that leave a remainder of 2 when divided by 6. He claims, “If you add any three such numbers, the sum will always be a multiple of 6.” Is Tathagat’s claim true?
Number Play (New NCERT)
Medium
Q.
Find, without dividing, whether the following numbers are divisible by 9.
(i) 123
(ii) 405
(iii) 8888
(iv) 93547
(v) 358095
Number Play (New NCERT)
Medium
Q.
I’m made of digits, each tiniest and odd, No shared ground with root #1 – how odd!
My digits count, their sum, my root – All point to one bold number’s pursuit – The largest odd single-digit I proudly claim. What’s my number? What’s my name?
Number Play (New NCERT)
Medium
Q.
Find the smallest multiple of 9 with no odd digits.
Number Play (New NCERT)
Medium
Q.
Find the multiple of 9 that is closest to the number 6000.
Number Play (New NCERT)
Medium
Q.
How many multiples of 9 are there between the numbers 4300 and 4400?
Number Play (New NCERT)
Medium
Q.
Between the numbers 600 and 700, which numbers have the digital root:
(i) 5
(ii) 7
(iii) 3
Number Play (New NCERT)
Medium
Q.
Write the digital roots of any 12 consecutive numbers. What do you observe?
Number Play (New NCERT)
Medium
Q.
We saw that the digital root of multiples by 9 is always 9. Now, find the digital roots of some consecutive multiples of (i) 3, (ii) 4, and (iii) 6.
Number Play (New NCERT)
Medium
Q.
What are the digital roots of numbers that are 1 more than a multiple of 6? What do you notice? Try to explain the patterns noticed.
Number Play (New NCERT)
Medium
Q.
Which of the following Venn diagrams captures the relationship between the multiples of 4, 8, and 32?

NCERT Solutions For Class 8 Maths Chapter 5 Number Play

Important Questions and Answers – Chapter 5: Number Play

Question 1. What is a palindrome number? Give three examples.

Answer:

A palindrome number is a number that reads the same forwards and backwards.

Examples: 121 — reads the same from left to right and right to left 1331 — reads the same from both sides 12321 — reads the same from both sides

Any number that is symmetric about its centre digit is a palindrome.

Question 2. Take a 2-digit number. Reverse its digits and add. Repeat this process. What do you observe?

Answer:

Let us take the number 47. Step 1: 47 + 74 = 121 — This is a palindrome.

Let us take 86. Step 1: 86 + 68 = 154 Step 2: 154 + 451 = 605 Step 3: 605 + 506 = 1111 — This is a palindrome.

Observation: If we reverse a number and keep adding, we eventually always reach a palindrome. This is called the reverse-and-add process.

Question 3. What are Kaprekar numbers? Give an example.

Answer:

A Kaprekar number is a number whose square can be split into two parts that add up to the original number.

Example: 45 45² = 2025 Split: 20 + 25 = 45 ✓

Example: 9 9² = 81 Split: 8 + 1 = 9 ✓

Example: 297 297² = 88209 Split: 88 + 209 = 297 ✓

So 9, 45, and 297 are all Kaprekar numbers.

Question 4. What is a magic square? Construct a 3×3 magic square using numbers 1 to 9.

Answer:

A magic square is a square arrangement of numbers where the sum of every row, every column, and both diagonals is the same. This sum is called the magic constant.

For numbers 1 to 9 in a 3×3 magic square, the magic constant = 15.

The magic square is:

2 — 7 — 6 9 — 5 — 1 4 — 3 — 8

Verification: Row 1: 2 + 7 + 6 = 15 ✓ Row 2: 9 + 5 + 1 = 15 ✓ Row 3: 4 + 3 + 8 = 15 ✓ Column 1: 2 + 9 + 4 = 15 ✓ Column 2: 7 + 5 + 3 = 15 ✓ Column 3: 6 + 1 + 8 = 15 ✓ Diagonal 1: 2 + 5 + 8 = 15 ✓ Diagonal 2: 6 + 5 + 4 = 15 ✓

Question 5. Explore the pattern: 1 × 1 = 1, 11 × 11 = 121, 111 × 111 = 12321. What is 1111 × 1111?

Answer:

Observing the pattern: 1 × 1 = 1 11 × 11 = 121 111 × 111 = 12321 1111 × 1111 = 1234321 11111 × 11111 = 123454321

The digits in the product increase from 1 up to the number of 1s and then decrease back to 1. The results are all palindromes.

1111 × 1111 = 1234321

Question 6. What is clock arithmetic? If the time is 10 o'clock now, what time will it be after 8 hours?

Answer:

Clock arithmetic, also called modular arithmetic, is a system where numbers wrap around after reaching a fixed value. On a 12-hour clock, after 12 comes 1 again — so the clock "resets" every 12 hours.

If the current time is 10 o'clock: 10 + 8 = 18 18 mod 12 = 6

The time will be 6 o'clock.

In clock arithmetic with modulus 12: if the result exceeds 12, subtract 12 to get the clock time.

Question 7. Find all 2-digit numbers where the sum of the digits equals the product of the digits.

Answer:

Let the 2-digit number be represented by digits a and b. Condition: a + b = a × b

Testing values: If a = 2, b = 2: 2 + 2 = 4 and 2 × 2 = 4 ✓

The number 22 satisfies the condition that the sum of its digits equals the product of its digits.

This is the only 2-digit number with this property (other solutions like a = 0 give single-digit results).

Question 8. What patterns do you observe in the following? 7 × 9 = 63, 67 × 99 = 6633, 667 × 999 = 666333

Answer:

Observing the pattern: 7 × 9 = 63 67 × 99 = 6633 667 × 999 = 666333 6667 × 9999 = 66663333

Pattern: The number of 6s in the product equals the number of 6s in the first number, and the number of 3s equals the number of 9s in the second number. The result consists of the same number of 6s followed by the same number of 3s.

Following this pattern: 6667 × 9999 = 66663333

Question 9. A number is divisible by 9 if the sum of its digits is divisible by 9. Verify this for 729 and 12348.

Answer:

For 729: Sum of digits = 7 + 2 + 9 = 18 18 ÷ 9 = 2 (exactly divisible) 729 ÷ 9 = 81 ✓ 729 is divisible by 9.

For 12348: Sum of digits = 1 + 2 + 3 + 4 + 8 = 18 18 ÷ 9 = 2 (exactly divisible) 12348 ÷ 9 = 1372 ✓ 12348 is divisible by 9.

Both numbers verify the divisibility rule for 9.

Question 10. What is the smallest number that gives a remainder of 1 when divided by 2, 3, 4, 5, and 6?

Answer:

We need a number N such that: N – 1 is divisible by 2, 3, 4, 5, and 6.

Find LCM of 2, 3, 4, 5, 6: LCM = 60

So N – 1 = 60 N = 60 + 1 = 61

The smallest number that gives remainder 1 when divided by 2, 3, 4, 5, and 6 is 61.

Question 11. Explore what happens when you multiply any 3-digit number by 1001.

Answer:

Let us take the number 235: 235 × 1001 = 235235

Let us take 471: 471 × 1001 = 471471

Observation: When any 3-digit number is multiplied by 1001, the result is the 3-digit number written twice side by side. The 3-digit number repeats itself to form a 6-digit number.

This happens because 1001 = 1000 + 1, so: abc × 1001 = abc × 1000 + abc × 1 = abc000 + abc = abcabc

Question 12. What is a number that is both a perfect square and a palindrome? Find two examples.

Answer:

A number that is both a perfect square and reads the same forwards and backwards.

Example 1: 121 121 = 11² (perfect square) 121 reads the same forwards and backwards (palindrome) ✓

Example 2: 484 484 = 22² (perfect square) 484 reads the same forwards and backwards (palindrome) ✓

FAQs – Chapter 5 Number Play

Q1. What is the main focus of Chapter 5 Number Play in Class 8 Maths?

Chapter 5 Number Play focuses on developing mathematical thinking through exploration of number patterns, properties, and puzzles. Unlike calculation-heavy chapters, this chapter encourages students to observe patterns, make conjectures, and discover interesting properties of numbers through activities involving palindromes, magic squares, Kaprekar numbers, clock arithmetic, and divisibility rules.

Q2. What are palindrome numbers and why are they interesting?

Palindrome numbers are numbers that read the same from left to right and right to left, such as 121, 1331, and 12321. They are interesting because they appear naturally in many number patterns and can be reached from any number using the reverse-and-add process. Palindromes also connect mathematics to language and patterns in a visually appealing way.

Q3. What is clock arithmetic and where is it used in real life?

Clock arithmetic, also called modular arithmetic, is a system where numbers wrap around after reaching a fixed modulus. On a 12-hour clock, after 12 the count resets to 1. It is used in real life in timekeeping, computer science, cryptography, and calendar calculations. It is also the basis for many coding and encryption systems used in digital security.

Q4. Are the topics in Chapter 5 Number Play important for exams?

Chapter 5 develops logical thinking, pattern recognition, and number sense rather than testing standard algorithms. While it may carry fewer direct marks than chapters like Mensuration or Algebra, the skills it builds — pattern recognition, logical reasoning, and mathematical curiosity — are valuable for competitive examinations like Olympiads and for developing a strong mathematical foundation overall.

Q5. How do Kaprekar numbers relate to the broader study of mathematics?

Kaprekar numbers are an example of recreational mathematics — exploring interesting properties of numbers that go beyond the standard curriculum. Studying Kaprekar numbers develops students' ability to observe, hypothesise, and verify mathematical properties. It also shows students that mathematics is a living, explorable subject full of surprising discoveries, which encourages deeper engagement with the subject.