NCERT Solutions for Class 6th Maths Chapter 3 Number Play
Updated on 2026-09-19
About this chapter
Numbers do more than count. They can carry information — in this chapter each child in a line says the number of taller neighbours they have. A cell is a supercell if the number written in it is greater than the numbers in all its neighbouring cells. In a single row of n cells you can get at most ⌈n ÷ 2⌉ supercells by filling the big numbers in alternate cells. The digit sum of a number is found by adding its digits (6 + 8 = 14 for 68). A palindrome reads the same from both ends — 66, 848, 12421. Kaprekar's routine — largest number minus smallest number made from the same four digits, again and again — always lands on 6174 . With 3-digit numbers it always lands on 495 . The Collatz rule (even → take half; odd → 3 × it + 1) seems to bring every number down to 1, but nobody in the world has
- Numbers can Tell us Things
- Supercells
- Patterns of Numbers on the Number Line
- Playing with Digits
- Digit sums of numbers
- Digit Detectives & Pretty Palindromic Patterns
- The Magic Number of Kaprekar
- Clock and Calendar Numbers
- Mental Math
- Digits and Operations
Quick revision
| Idea | What it means | Example from the chapter | Result |
|---|---|---|---|
| Supercell | A cell whose number is greater than every neighbouring cell | 626 sits between 577 and 345 | 626 is a supercell |
| Most supercells | Put the big numbers in alternate cells, starting from the first | a row of 9 cells | 5 supercells |
| Digit sum | Add up all the digits of the number | 68, 176, 545 | digit sum 14 for each |
| How many n-digit numbers | 9 × 10, 9 × 100, 9 × 1000 … | 3-digit / 5-digit numbers | 900 / 90,000 |
| Digit ‘7’ count | Count a digit position by position | 1 – 100 / 1 – 1000 | 20 times / 300 times |
| Palindrome | Reads the same left to right and right to left | 66, 848, 1111, 12421 | 9 three-digit palindromes from 1, 2, 3 |
| Reverse and add | Add a number to its reverse till a palindrome appears | 48 + 84 = 132, 132 + 231 | 363 |
| Kaprekar constant | Largest − smallest from the same 4 digits, repeated | 6382 → 6264 → 4176 | always 6174 |
| Kaprekar for 3 digits | The same steps with three digits | 321 → 198 → 792 → 693 → 594 | always 495 |
| Collatz rule | Even → half it; odd → 3 × it + 1 | 12, 6, 3, 10, 5, 16, 8, 4, 2, 1 | always reaches 1 (unproved) |
| Game 21 (add 1, 2 or 3) | Say 1, 5, 9, 13, 17, 21 | first player starts with 1 | first player always wins |
| Game 99 (add 1 to 10) | Keep the total at 11, 22, 33, … 99 | second player replies 11 − x | second player always wins |
Exercises
- In-text Questions — Numbers can Tell us Things Page 55 & 56
- In-text Questions — Numbers can Tell us Things Page 56
- Figure it Out — Supercells Page 57 & 58
- In-text Questions — Supercells Page 58 & 59
- In-text Questions — Patterns of Numbers on the Number Line Page 59
- Figure it Out — Patterns of Numbers on the Number Line Page 59
- In-text Questions — Playing with Digits Page 60
- Figure it Out — Digit sums of numbers Page 60
- Digit Detectives & Pretty Palindromic Patterns — In-text Questions Page 61 & 62
- In-text Questions — The Magic Number of Kaprekar Page 63
- In-text Questions — Clock and Calendar Numbers Page 64
- Figure it Out — Clock and Calendar Numbers Page 64 & 65
- In-text Questions — Mental Math Page 65 & 66
- Figure it Out — Digits and Operations Page 66 & 67
- In-text Questions — Playing with Number Patterns Page 67 & 68
- In-text Questions — An Unsolved Mystery Page 68 & 69
- Figure it Out — Simple Estimation Page 69 & 70
- In-text Questions — Estimate the answer Page 70 & 71
- In-text Questions — Games and Winning Strategies Page 71 & 72
- Figure it Out — Games and Winning Strategies Page 72 & 73