Get free step-by-step NCERT solutions for Class 6 Maths Number Play (Chapter 3). All 71 questions across 3 exercises are solved with clear reasoning, following the CBSE 2026–27 syllabus. Work through each solution to understand the method, not just the final answer.
A
Complete Table 2 with 5-digit numbers whose digits are ‘1’, ‘0’, ‘6’, ‘3’, and ‘9’ in some order. Only a coloured cell should have a number greater than all its neighbours.
The biggest number in the table is _________ . The smallest even number in the table is _________ . The smallest number greater than 50,000 in the table is _________ . Once you have filled the table above, put commas appropriately after the thousands digit.
Will reversing and adding numbers repeatedly, starting with a 2-digit number, always give a palindrome? Explore and find out.*
Explore
Take different 4-digit numbers and try carrying out these steps. Find out what happens. Check with your friends what they got.
Explore
Carry out these same steps with a few 3-digit numbers. What number will start repeating?
Make some more Collatz sequences like those above, starting with your favourite whole numbers. Do you always reach 1?
Do you believe the conjecture of Collatz that all such sequences will eventually reach 1? Why or why not?
The first player says 1, 2 or 3. Then the two players take turns adding 1, 2, or 3 to the previous number said. The first player to reach 21 wins!
Play this game several times with your classmate. Are you starting to see the winning strategy? Which player can always win if they play correctly? What is the pattern of numbers that the winning player should say?
The first player says a number between 1 and 10. Then the two players take turns adding a number between 1 and 10 to the previous number said. The first player to reach 99 wins!
Play this game several times with your classmate. See if you can figure out the corresponding winning strategy in this case! Which player can always win? What is the pattern of numbers that the winning player should say this time?
FIO
Colour or mark the supercells in the table below.
Fill the table below with only 4-digit numbers such that the supercells are exactly the coloured cells.
Fill the table below such that we get as many supercells as possible. Use numbers between 100 and 1000 without repetitions.
Out of the 9 numbers, how many supercells are there in the table above?
Find out how many supercells are possible for different numbers of cells.
Do you notice any pattern? What is the method to fill a given table to get the maximum number of supercells? Explore and share your strategy.
Can you fill a supercell table without repeating numbers such that there are no supercells? Why or why not?
Will the cell having the largest number in a table always be a supercell? Can the cell having the smallest number in a table be a supercell? Why or why not?
Fill a table such that the cell having the second largest number is not a supercell.
Fill a table such that the cell having the second largest number is not a supercell but the second smallest number is a supercell. Is it possible?
Make other variations of this puzzle and challenge your classmates.
Identify the numbers marked on the number lines below, and label the remaining positions.
Put a circle around the smallest number and a box around the largest number in each of the sequences above.
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 of 14? Can you make an even bigger number?
Find out the digit sums of all the numbers from 40 to 70. Share your observations with the class.
Calculate the digit sums of 3-digit numbers whose digits are consecutive (for example, 345). Do you see a pattern? Will this pattern continue?
Pratibha uses the digits '4', '7', '3' and '2', and makes the smallest and largest 4-digit numbers with them: and . The difference between these two numbers is . The sum of these two numbers is . Choose 4-digits to make:
a. the difference between the largest and smallest numbers greater than .
b. the difference between the largest and smallest numbers less than .
c. the sum of the largest and smallest numbers greater than .
d. the sum of the largest and smallest numbers less than .
What is the sum of the smallest and largest 5-digit palindrome? What is their difference?
The time now is 10:01. How many minutes until the clock shows the next palindromic time? What about the one after that?
How many rounds does the number 5683 take to reach the Kaprekar constant?
Write an example for each of the scenarios shown in the diagram whenever possible.
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 and 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
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
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
Name some objects around you that are: a. a few thousand in number b. more than ten thousand in number
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.
How many rounds does your year of birth take to reach the Kaprekar constant?
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?
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.
Estimate the number of liters a mug, a bucket and an overhead tank can hold.
Write one 5-digit number and two 3-digit numbers such that their sum is 18,670.
Choose a number between 210 and 390. Create a number pattern similar to those shown in Section 3.9 that will sum up to this number.
Recall the sequence of Powers of 2 from Chapter 1, Table 1. Why is the Collatz conjecture correct for all the starting numbers in this sequence?
Check if the Collatz Conjecture holds for the starting number 100.
Starting with 0, players alternate adding numbers between 1 and 3. The first person to reach 22 wins. What is the winning strategy now?
IT
Think about various situations where we use numbers. List five different situations in which numbers are used. See what your classmates have listed, share, and discuss.
Some children in a park are standing in a line. Each one says a number.
Q. What do you think these numbers mean?
group of children stand in a line. Each child says a number ('0', '1', or '2') representing the number of taller neighbors standing next to them.
Q. Can the children rearrange themselves so that the children standing at the ends say '2'?
A group of children stand in a line. Each child says a number ('0', '1', or '2') representing the number of taller neighbors standing next to them.
Q. Can we arrange the children in a line so that all would say only 0s?
A group of children stand in a line. Each child says a number ('0', '1', or '2') representing the number of taller neighbors standing next to them.
Q. Can two children standing next to each other say the same number?
A group of children stand in a line. Each child says a number ('0', '1', or '2') representing the number of taller neighbors standing next to them.
Q. There are 5 children in a group, all of different heights. Can they stand such that four of them say '1' and the last one says '0'? Why or why not?
A group of children stand in a line. Each child says a number ('0', '1', or '2') representing the number of taller neighbors standing next to them.
Q. For this group of 5 children, is the sequence 1, 1, 1, 1, 1 possible?
A group of children stand in a line. Each child says a number ('0', '1', or '2') representing the number of taller neighbors standing next to them.
Q. Is the sequence 0, 1, 2, 1, 0 possible? Why or why not?
A group of children stand in a line. Each child says a number ('0', '1', or '2') representing the number of taller neighbors standing next to them.
Q. How would you rearrange the five children so that the maximum number of children say '2'?
Find out how many numbers have two digits, three digits, four digits, and five digits.
Among the numbers 1–100, how many times will the digit ‘7’ occur? Among the numbers 1–1000, how many times will the digit ‘7’ occur?
Consider the digits '1', '2', '3'.
Q. Write all possible 3-digit palindromes using these digits.
Try the same procedure for some other numbers, and perform the same steps. Stop if you get a palindrome. There are numbers for which you have to repeat this a large number of times. Are there numbers for which you do not reach a palindrome at all?
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? _____________
What happens if we continue doing this?
Try and find out all possible times on a 12-hour clock of each of these types.
Manish has his birthday on 20/12/2012 where the digits '2', '0', '1', '2' repeat in that order.
Q. Find some other dates of this form from the past.
His sister, Meghana, has her birthday on 11/02/2011 where the digits read the same from left to right and from right to left.
Q. Find all possible dates of this form from the past.
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?
Observe the figure below. What can you say about the numbers and the lines drawn?
Numbers in the middle column are added in different ways to get the numbers on the sides (1500 + 1500 + 400 = 3400). The numbers in the middle can be used as many times as needed to get the desired sum. Draw arrows from the middle to the numbers on the sides to obtain the desired sums.
Two examples are given. It is simpler to do it mentally!
38,800 = 25,000 + 400 × 2 + 13,000 3400 = 1500 + 1500 + 400
Can we make 1,000 using the numbers in the middle? Why not? What about 14,000, 15,000 and 16,000? Yes, it is possible. Explore how. What thousands cannot be made?
Using the numbers in the boxes, we are allowed to use both addition and subtraction to get the required number. Complete the equations shown in the diagram.
3.9 Playing with Number Patterns
Here are some numbers arranged in some patterns. Find out the sum of the numbers in each of the below figures. Should we add them one by one or can we use a quicker way?
Share and discuss in class the different methods each one of you used to solve these questions.
3.10 An Unsolved Mystery—the Collatz Conjecture!
Look at the sequences below—the same rule is applied in all the sequences:
a. 12, 6, 3, 10, 5, 16, 8, 4, 2, 1
b. 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1
c. 21, 64, 32, 16, 8, 4, 2, 1
d. 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1
Do you see how these sequences were formed?
Estimate the answer
Try to guess within 30 seconds. Check your guess with your friends.
Number of words in your maths textbook: a. More than 5000 b. Less than 5000
Estimate the answer
Try to guess within 30 seconds. Check your guess with your friends.
Number of students in your school who travel to school by bus: a. More than 200 b. Less than 200
Estimate the answer
Try to guess within 30 seconds. Check your guess with your friends.
Roshan wants to buy milk and 3 types of fruit to make fruit custard for 5 people. He estimates the cost to be ₹100. Do you agree with him? Why or why not?
Estimate the answer
Try to guess within 30 seconds. Check your guess with your friends.
Estimate the distance between Gandhinagar (in Gujarat) to Kohima (in Nagaland). Hint: Look at the map of India to locate these cities.
Sheetal is in Grade 6 and says she has spent around 13,000 hours in school till date. Do you agree with her? Why or why not?
Earlier, people used to walk long distances as they had no other means of transport. Suppose you walk at your normal pace. Approximately, how long would it take you to go from:
a. Your current location to one of your favourite places nearby. b. Your current location to any neighbouring state's capital city. c. The southernmost point in India to the northernmost point in India.
Make some estimation questions and challenge your classmates!
Frequently asked questions
Common questions about Class 6 Maths Number Play solutions.
How many questions are there in Class 6 Maths Number Play?
Number Play (Chapter 3) in Class 6 Maths has 71 questions across 3 exercises. Every question is solved step by step on this page.
Are these Number Play solutions based on the latest NCERT syllabus?
Yes. These solutions follow the current CBSE 2026–27 syllabus and the latest NCERT textbook for Class 6 Maths. If the exercises change, the solutions here are updated to match.
How should I use these Number Play solutions?
Try each question yourself first, then read the step-by-step solution to see where your approach diverged. Focus on understanding the method behind each step, not just the final answer.