CBSE Important Questions Class 6 Maths Chapter 3 – Number Play

Class 6 Maths Chapter 3 Number Play is part of the new NCERT textbook Ganita Prakash. It teaches students to play with numbers and find interesting patterns in them. Students learn about supercells in a number grid, placing numbers on a number line, digit sums, palindromic numbers and palindromic times on a clock, the reverse-and-add game, and the Kaprekar routine that always reaches the magic number 6174.

These CBSE important questions for Class 6 Maths Chapter 3 cover palindromes with odd and even numbers of digits, assertion-reason questions on the Kaprekar constant and supercells, the largest and smallest numbers from given digits, reading a number line, the maximum number of supercells in a row, reverse-and-add steps and palindromic clock times. Every question has a clear step-by-step answer in simple English, so students can practise on their own, parents can check the working, and teachers can use them for class tests. A free printable PDF of these important questions is also available on this page.

CBSE Important Questions Class 6 Maths Chapter 3 – Number Play

Number Play (New NCERT)
Medium
Q.
Digit sum 14
(a) Write other numbers whose digits add up to 14.
(b) What is the smallest number whose digit sum is 14 ?
(c) What is the largest 5 -digit whose digit sum is 14 ?
(d) How big a number can you form having the digit sum 14 ? Can you make an even bigger number?
Number Play (New NCERT)
Medium
Q.
Always, Sometimes, Never?
Below are some statements. Think, explore and find out if each of the statement is 'Always true', 'Only sometimes true' or 'Never true'. Why do you think so? Write your reasoning; discuss this with the class.
(a) 5-digit number +5 -digit number gives a 5-digit number
(b) 4-digit number + 2-digit number gives a 4-digit number
(c) 4-digit number + 2-digit number gives a 6-digit number
(d) 5-digit number - 5-digit number gives a 5-digit number
(e) 5-digit number - 2-digit number gives a 3-digit number
Number Play (New NCERT)
Medium
Q.
Estimate the number of liters a mug, a bucket and an overhead tank can hold.
Number Play (New NCERT)
Medium
Q.
Estimate the number of holidays you get in a year including weekends, festivals and vacation. Then try to get an exact number and see how close your estimate is.
Number Play (New NCERT)
Medium
Q.
We are the group of 5 -digit numbers between 35,000 and 75,000 such that all of our digits are odd. Who is the largest number in our group? Who is the smallest number in our group? Who among us is the closest to 50,000 ?
Number Play (New NCERT)
Medium
Q.
There is only one supercell (number greater than all its neighbours) in this grid. If you exchange two digits of one of the numbers, there will be 4 supercells. Figure out which digits to swap.
16,200
39,344
29,765
23,609
62,871
45,306
19,381
50,319
38,408
Number Play (New NCERT)
Medium
Q.
We shall do some simple estimates. It is a fun exercise, and you may find it amusing to know the various numbers around us. Remember, we are not interested in the exact numbers for the following questions. Share your methods of estimation with the class.
 
1. Steps you would take to walk:
(a) From the place you are sitting to the classroom door
(b) Across the school ground from start to end
(c) From your classroom door to the school gate
(d) From your school to your home
 
2. Number of times you blink your eyes or number of breaths you take:
(a) In a minute
(b) In an hour
(c) In a day
 
3. Name some objects around you that are:
(a) a few thousand in number
(b) more than ten thousand in number
Number Play (New NCERT)
Medium
Q.
Make some more Collatz sequences like those above, starting with your favourite whole numbers. Do you always reach 1 ?
Number Play (New NCERT)
Medium
Q.
Share and discuss in class the different methods each of you used to solve these questions.
 
a. 
b. 
c. 
d. 
e. 
f. 

Number Play (New NCERT)
Medium
Q.
Write an example for each of the below scenarios whenever possible.
Number Play (New NCERT)
Medium
Q.
Find out the digit sums of all the numbers from 40 to 70 . Share your observations with the class.
Number Play (New NCERT)
Medium
Q.
Can we make 1,000 using the numbers in the middle (25,000, 400, 13,000, 1,500, 60,000)? Why not? What about 14,000,15,000 and 16,000 ? Yes, it is possible. Explore how. What thousands cannot be made?
Number Play (New NCERT)
Medium
Q.
How many rounds does the number 5683 take to reach the Kaprekar constant?
Number Play (New NCERT)
Medium
Q.
The time now is 10 :  01. How many minutes until the clock shows the next palindromic time? What about the one after that?
Number Play (New NCERT)
Medium
Q.
What is the sum of the smallest and largest 5-digit palindrome? What is their difference?
Number Play (New NCERT)
Medium
Q.
Pratibha uses the digits '4', '7', '3' and ' 2 ', and makes the smallest and largest 4 -digit numbers with them: 2347 and 7432. The difference between these two numbers is 7432 - 2347 = 5085. The sum of these two numbers is 9779 . Choose 4-digits to make:
 
(a) the difference between the largest and smallest numbers greater than 5085.
(b) the difference between the largest and smallest numbers less than 5085.
(c) the sum of the largest and smallest numbers greater than 9779.
(d) the sum of the largest and smallest numbers less than 9779.
Number Play (New NCERT)
Medium
Q.
But, will any year's calendar repeat again after some years? Will all dates and days in a year match exactly with that of another year?
Number Play (New NCERT)
Medium
Q.
Puzzle time
I am a 5-digit palindrome.
I am an odd number.
My 't' digit is double of my 'u' digit.
My 'h' digit is double of my 't' digit.
Who am I? _________
Number Play (New NCERT)
Medium
Q.
Calculate the digit sums of 3-digit numbers whose digits are consecutive (for example, 345). Do you see a pattern? Will this pattern continue?
Number Play (New NCERT)
Medium
Q.
Write one 5 -digit number and two 3 -digit numbers such that their sum is 18,670 .

CBSE Important Questions Class 6 Maths Chapter 3 – Number Play

Q1. A palindrome is a number that remains the same even if its digits are reversed. A student claims that palindrome numbers always have an odd number of digits. Is this claim correct? Justify your answer with examples.

Answer: No, the student's claim is incorrect. Palindrome numbers can have an odd number of digits or an even number of digits.
For example:
1. The number 121 is a palindrome with 3 digits, which is an odd number.
2. The number 2442 is a palindrome with 4 digits, which is an even number.
Since a palindrome can have an even number of digits, the claim that palindromes always have an odd number of digits is false.

Q2. Read the following statements and choose the correct option from the choices given below:
Assertion (A): On applying Kaprekar routine on Kaprekar constant, the result is again Kaprekar constant.
Reason (R): Kaprekar constant for 4-digit numbers is 6417.
(a) Both Assertion and Reason are true and Reason is the correct explanation of assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation of assertion.
(c) Assertion is true but Reason is false.
(d) Assertion is false but Reason is true.

Answer: (c) Assertion is true but Reason is false.
The Kaprekar constant for 4-digit numbers is 6174 (not 6417), so the Reason is false.
Applying the Kaprekar routine on 6174: 7641 − 1467 = 6174. We get the same number again, so the Assertion is true.

Q3. Read the following statements and choose the correct option from the choices given below:
Assertion (A): Palindrome numbers always have odd number of digits.
Reason (R): A palindrome is a number that remains same even if its digits are reversed.
(a) Both Assertion and Reason are true and Reason is the correct explanation of assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation of assertion.
(c) Assertion is true but Reason is false.
(d) Assertion is false but Reason is true.

Answer: (d) Assertion is false but Reason is true.
Palindrome numbers can have any number of digits (for example 121 has 3 digits and 2442 has 4 digits), so the Assertion is false. The Reason gives the correct meaning of a palindrome, so it is true.

Q4. Read the following statements and choose the correct option from the choices given below:
Assertion (A): Number of times digit 1 occurs is same as that of times digit 8 occurs from 1 to 100.
Reason (R): If we fill the cells in ascending order, then the last cell will be a supercell.
(a) Both Assertion and Reason are true and Reason is the correct explanation of assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation of assertion.
(c) Assertion is true but Reason is false.
(d) Assertion is false but Reason is true.

Answer: (d) Assertion is false but Reason is true.
From 1 to 100, the digit 1 occurs 21 times (1, 10, 11, 12, …, 19, 21, 31, …, 91 and 100), while the digit 8 occurs 20 times. So the Assertion is false.
If cells are filled in ascending order, the last cell holds the biggest number, so it is bigger than its neighbour and is a supercell. The Reason is true.

Q5. Which of the following is the largest 3-digit number whose digits add up to 14?
(a) 905
(b) 950
(c) 851
(d) 923

Answer: (b) 950
9 + 5 + 0 = 14. To get the largest number, put the biggest digit (9) in the hundreds place and the next biggest possible digit (5) in the tens place. Among the options, 923 has digit sum 14 too, but 950 is larger.

Q6. Using the digits '4', '7', '3', find the difference between the largest and the smallest number. Also check whether it is palindromic or not.

Answer: Largest number (digits in descending order) = 743
Smallest number (digits in ascending order) = 347
Difference = 743 − 347 = 396
A number is palindromic if it reads the same forwards and backwards. 396 reversed is 693, and 396 ≠ 693.
So, 396 is not a palindrome.

Q7. How many rounds does the number 3524 take to reach the Kaprekar constant?

Answer: Round 1: Largest = 5432, Smallest = 2345
5432 − 2345 = 3087
Round 2: Largest = 8730, Smallest = 0378 (that is, 378)
8730 − 378 = 8352
Round 3: Largest = 8532, Smallest = 2358
8532 − 2358 = 6174
So the number 3524 takes 3 rounds to reach the Kaprekar constant 6174.

Kaprekar routine on 3524 reaching 6174 in three rounds

Q8. Find the sum and the difference between the largest and the smallest 3-digit palindrome.

Answer: The smallest 3-digit palindrome is 101.
The largest 3-digit palindrome is 999.
Sum = 101 + 999 = 1100
Difference = 999 − 101 = 898

Q9. Identify the number line that correctly marks the numbers.

Four number lines from 1000 to 10,000 marking 1180, 4430, 6930 and 8440

Answer: (a)
On a number line from 1000 to 10,000 with marks every 1000: 1180 lies just after 1000, 4430 lies a little before 5000 (between 4000 and 5000), 6930 lies just before 7000, and 8440 lies between 8000 and 9000. Only option (a) places all four numbers correctly.

Number line correctly marking 1180, 4430, 6930 and 8440

Q10. What is the maximum number of super cells in a table row of 13 cells?
(a) 5
(b) 3
(c) 4
(d) 6

Answer: (d) 6
A supercell is a cell whose number is bigger than the numbers in the cells next to it. Two neighbouring cells can never both be supercells, so supercells must be in alternate positions. In a row of 13 cells, the 2nd, 4th, 6th, 8th, 10th and 12th cells can all be supercells, which gives 6 supercells.

Row of 13 cells with 6 shaded supercells in alternate positions

Q11. How many reverse-and-add steps are needed to convert the number 975 into a palindrome?
(a) 2
(b) 3
(c) 4
(d) 5

Answer: (c) 4
Step 1: 975 + 579 = 1554
Step 2: 1554 + 4551 = 6105
Step 3: 6105 + 5016 = 11121
Step 4: 11121 + 12111 = 23232
23232 reads the same backwards, so it is a palindrome. It takes 4 reverse-and-add steps.

Reverse and add chain from 975 to the palindrome 23232 in four steps

Q12. The digit sum of 35569 is
(a) Odd
(b) Even
(c) 0
(d) Prime

Answer: (b) Even
Digit sum = 3 + 5 + 5 + 6 + 9 = 28
28 is an even number.

Q13. If the time on the clock is 5:30, then how many minutes ago did the clock last show a palindromic time?
(a) 5 minutes
(b) 25 minutes
(c) 86 minutes
(d) 91 minutes

Answer: (a) 5 minutes
A palindromic time reads the same forwards and backwards, like 5:25 (525). The last palindromic time before 5:30 was 5:25, which is 5 minutes earlier.

Two clocks showing 5:30 and the palindromic time 5:25

Related Study Material on Extramarks

Q.1 A greatest 3 ?digit number exactly divisible by 8, 10 and 14 is:

Marks:1

Ans

The prime factors of 8 = 2 × 2 × 2

The prime factors of 10 = 2 × 5

The prime factors of 14 = 2 × 7

LCM of 8, 10 and 14 = 2 × 2 × 2 × 5 × 7

= 280

The greatest number of 3 digits is 999.

999/280 gives, quotient = 3, remainder = 159

Therefore, the greatest 3-digit number exactly divisible by 8, 10 and 12 = 999 ? 159 = 840.

Q.2 Rajesh bought two barrels of oil of capacities 75 litres and 69 litres. The maximum capacity of a container, which can measure the oil in exact number of times, is

25 litres

23 litres

3 litres

15 litres

Marks:1

Ans

The prime factors of 75 = 3 × 5 × 5

The prime factors of 69 = 3 × 23

HCF of 75 and 69 is 3.

Therefore, the maximum capacity of a container used to measure the oil in exact number of times is 3 litres.

Q.3 Which of the following are co-prime numbers?

7 and 14

8 and 24

15 and 21

7 and 15

Marks:1

Ans

The common factor of 7 and 14 is 7, so these are not co-primes.

The common factor of 8 and 24 is 8, so these are not co-primes.

The common factor of 15 and 21 is 3, so these are not co-primes.

The common factor of 7 and 15 is 1, so these are co-primes.

Q.4 What is the HCF of two prime numbers?

Marks:1

Ans

The HCF of two prime numbers is 1.

Q.5 Find the prime factorisation of 96.

Marks:1

Ans

29624822421226231

Prime factorisation of 96 is 2 — 2 — 2 — 2 — 2 — 3

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CBSE Important Questions for Class 6 Maths

Chapter 1 - Knowing Our Numbers

Chapter 2 - Whole Numbers

Chapter 4 - Basic Geometrical Ideas

Chapter 5 - Understanding Elementary Shapes

Chapter 6 - Integers

Chapter 7 - Fractions

Chapter 8 - Decimals

Chapter 9 - Data Handling

Chapter 10 - Mensuration

Chapter 11 - Algebra

Chapter 12 - Ratio and Proportion

Chapter 13 - Symmetry

Chapter 14 - Practical Geometry

FAQs (Frequently Asked Questions)

Number Play is a Class 6 Maths chapter about patterns, digit sums, number lines, palindromes, estimation and number games. It builds logical thinking through puzzles and strategies.

A supercell is a cell whose number is greater than all its neighbouring cells. In a row, the neighbours are the cells immediately left and right.

The Kaprekar constant for 4-digit numbers is 6174. The process uses descending and ascending digit arrangements followed by subtraction.

A palindromic number reads the same forwards and backwards. For example, 121, 575 and 10001 are palindromic numbers.

The Collatz conjecture says every whole number may reach 1 by one rule. Halve even numbers, and for odd numbers multiply by 3 and add 1.