Class 6 Maths Chapter 3 Number Play Revision Notes

Chapter 3 turns numbers into a game, from spotting supercells in a grid to chasing palindromes and Kaprekar’s constant — here’s the shorthand version of it all.

Last Updated: September 23, 2026

Supercells

• A supercell is greater than all its orthogonal neighbours.
• Largest number in a table is always a supercell; smallest is never a supercell.
• No filled table can have zero supercells.
• A 3×3 grid of distinct numbers can have at most 5 supercells (checkerboard pattern: 4 corners + centre).

Digit Play

• Smallest 2-digit number with digit sum 14 = 59; largest 5-digit number with digit sum 14 = 95,000.
• Digit ‘7’ appears 20 times from 1-100, and 300 times from 1-1000.

Palindromes

• A number reading the same forwards and backwards.
• Smallest/largest 5-digit palindromes: 10,001 / 99,999 (sum 110,000, difference 89,998).

Kaprekar’s Constant

• 4-digit numbers: routine (descending − ascending, repeat) always reaches 6174 within 7 steps.
• 3-digit numbers: routine always reaches 495.

Clock Palindromes

• Consecutive palindromic times (10:01, 11:11, 12:21, …) are always 70 minutes apart.

Mental Math (Always/Sometimes/Never)

• 5-digit + 5-digit = 5-digit: Sometimes.
• 4-digit + 2-digit = 4-digit: Sometimes.
• 4-digit + 2-digit = 6-digit: Never (max sum is only 5 digits).
• 5-digit − 2-digit = 3-digit: Never (min result is still 4 digits).

Collatz Conjecture

• Even → divide by 2; Odd → multiply by 3 and add 1.
• Conjectured (unproven) to always eventually reach 1.
• 100 reaches 1 in 26 steps.

Quick revision: Solutions | Extra Questions for this chapter.

Frequently Asked Questions

What is the difference between odd and even numbers, and how can they be identified quickly?
An even number can be divided exactly by 2 with no remainder, while an odd number leaves a remainder of 1, and this can be identified quickly just by checking whether the last digit is even or odd.

What is meant by the place value of a digit in a number?
The place value of a digit is the value it represents based on its position within the number, so the same digit can represent a different quantity depending on whether it appears in the ones, tens, or hundreds place.

Written by Satish

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