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Solutions

Overview

Step-by-step NCERT solutions for Number Play (Chapter 3, NCERT Class 6 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Number Play textbook chapter.

Solved

What these solutions cover

All 46 questions in Number Play are solved in the PDF. Here's what's inside, exercise by exercise:

Numbers can Tell us Things

  1. Can the children rearrange themselves so that the children standing at the ends say '2'?
  2. Can we arrange the children in a line so that all would say only 0s?
  3. Can two children standing next to each other say the same number?
  4. 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?
  5. For this group of 5 children, is the sequence 1, 1, 1, 1, 1 possible?
  6. Is the sequence 0, 1, 2, 1, 0 possible? Why or why not?
  7. How would you rearrange the five children so that the maximum number of children say '2'?

Supercells

  1. Colour or mark the supercells in the table below. 6828 | 670 | 9435 | 3780 | 3708 | 7308 | 8000 | 5583 | 52
  2. Fill the table below with only 4-digit numbers such that the supercells are exactly the coloured cells. The coloured (given) cells are at positions 1, 4 and 8: 5346 | ___ | ___ | 1258 | ___ | ___ | ___ | 9635 | ___
  3. Fill the table below such that we get as many supercells as possible. Use numbers between 100 and 1000 without repetitions.
  4. Out of the 9 numbers, how many supercells are there in the table above?
  5. Can you fill a supercell table without repeating numbers such that there are no supercells? Why or why not?
  6. 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?
  7. Fill a table such that the cell having the second largest number is not a supercell.
  8. 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?

Supercells — Table

  1. 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. Fill in the blank: The biggest number in the table is ___.
  2. The smallest even number in the table is ___.
  3. The smallest number greater than 50,000 in the table is ___.

Patterns of Numbers on the Number Line

  1. Identify the numbers marked on the number lines below, and label the remaining positions. Also put a circle around the smallest number and a box around the largest number in each sequence. a. Number line showing 2010 and 2020 b. Number line showing 9996 and 9997 c. Number line showing 15,077, 15,078, and 15,083 d. Number line showing 86,705 and 87,705

Playing with Digits

  1. Find out how many numbers have two digits, three digits, four digits, and five digits. (1-digit numbers: 9, from 1–9)
  2. 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 number 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?
  3. Calculate the digit sums of 3-digit numbers whose digits are consecutive (for example, 345). Do you see a pattern? Will this pattern continue?

Pretty Palindromic Patterns

  1. Write all possible 3-digit palindromes using the digits 1, 2, 3 (digits can repeat).
  2. Puzzle time: I am a 5-digit palindrome. I am an odd number. My 't' (tens) digit is double of my 'u' (units) digit. My 'h' (hundreds) digit is double of my 't' (tens) digit. Who am I?

The Magic Number of Kaprekar

  1. Carry out the Kaprekar steps with a few 3-digit numbers. What number will start repeating?

Clock and Calendar Numbers

  1. 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 is 7432 – 2347 = 5085. The sum 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…
  2. What is the sum of the smallest and largest 5-digit palindrome? What is their difference?
  3. The time now is 10:01. How many minutes until the clock shows the next palindromic time? What about the one after that?
  4. How many rounds does the number 5683 take to reach the Kaprekar constant?

Mental Math

  1. Using the numbers 40000, 7000, 300, 1500, 12000, 800 (each may be used multiple times), find expressions using addition and subtraction for: 45000, 5900, 17500, 21400.
  2. Write an example for each of the scenarios below whenever possible:
    • (i) 5-digit + 5-digit giving a 5-digit sum more than 90,250
    • (ii) 5-digit + 3-digit giving a 6-digit sum
    • (iii) 4-digit + 4-digit giving a 6-digit sum
    • (iv) 5-digit + 5-digit giving a 6-digit sum
    • (v) 5-digit + 5-digit giving 18,500
    • (vi) 5-digit − 5-digit giving a difference less than 56,503
    • (vii) 5-digit − 3-digit giving a 4-digit…
  3. Always, Sometimes, Never? Determine for each statement: 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

Playing with Number Patterns

  1. Find out the sum of the numbers in each of the below figures. a. Grid with 40s and 50s (3 rows of four 40s alternating with 2 rows of five 50s) c. Grid with 32s (4 rows × 8 columns) and 64s (4 rows with 3 on left and 1 on right)

Simple Estimation

  1. 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?
  2. Estimate the distance between Gandhinagar (in Gujarat) to Kohima (in Nagaland).
  3. 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?

Games and Winning Strategies

  1. There is only one supercell (number greater than all its neighbours) in this grid: 16200 | 39344 | 29765 23609 | 62871 | 45306 19381 | 50319 | 38408 If you exchange two digits of one of the numbers, there will be 4 supercells. Figure out which digits to swap.
  2. How many rounds does your year of birth take to reach the Kaprekar constant?
  3. 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? Who among us is the closest to 50,000?
  4. 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.
  5. Estimate the number of liters a mug, a bucket and an overhead tank can hold.
  6. Write one 5-digit number and two 3-digit numbers such that their sum is 18,670.
  7. 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.
  8. 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?
  9. Check if the Collatz Conjecture holds for the starting number 100.
  10. Starting with 0, players alternate adding numbers between 1 and 3. The first person to reach 22 wins. What is the winning strategy now?
Sample

Worked examples

3 questions from Number Play, solved step by step.

Numbers can Tell us Things

Can the children rearrange themselves so that the children standing at the ends say '2'?

A child says '2' if both neighbours are taller than them.

A child at the end of a line has only ONE neighbour (no one on the other side).

With only one neighbour, the maximum number a child at the end can say is 1, never 2.

Answer: No. End children have only one neighbour, so the maximum they can say is 1, never 2.

Playing with Digits

Find out how many numbers have two digits, three digits, four digits, and five digits. (1-digit numbers: 9, from 1–9)

1-digit numbers: 1 to 9 → 9 numbers.

2-digit numbers: 10 to 99 → 99 − 10 + 1 = 90 numbers.

3-digit numbers: 100 to 999 → 999 − 100 + 1 = 900 numbers.

4-digit numbers: 1000 to 9999 → 9999 − 1000 + 1 = 9000 numbers.

5-digit numbers: 10000 to 99999 → 99999 − 10000 + 1 = 90000 numbers.

Answer: 2-digit: 90, 3-digit: 900, 4-digit: 9000, 5-digit: 90,000.

Pretty Palindromic Patterns

Write all possible 3-digit palindromes using the digits 1, 2, 3 (digits can repeat).

A 3-digit palindrome has the form ABA where first and last digits are the same.

A can be 1, 2, or 3; B can be 1, 2, or 3.

Listing all (3 choices for A × 3 choices for B = 9 palindromes):

A=1: 111, 121, 131

A=2: 212, 222, 232

A=3: 313, 323, 333

Answer: 111, 121, 131, 212, 222, 232, 313, 323, 333 — nine 3-digit palindromes in all.

All 46 questions in Number Play are solved step by step in the Solutions PDF above.

Keep solving

More solutions in Ganita Prakash

01Patterns in Mathematics02Lines and Angles04Data Handling and Presentation05Prime Time06Perimeter and Area07Fractions08Playing with Constructions09Symmetry10The Other Side of Zero
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More NCERT Solutions for Class 6

Read the Number Play textbook chapter / PDF, or browse all NCERT Class 6 Mathematics solutions.

← PreviousCh 2: Lines and AnglesNext →Ch 4: Data Handling and Presentation

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