Class 6 Maths Chapter 3 Number Play Revision Notes

Quick revision notes for Class 6 Maths Chapter 3, “Number Play” — key facts and formulas at a glance for fast last-minute review. These Class 6 Mathematics Chapter 3 notes are ideal for quick revision just before exams.

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.

Written by Satish

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