Class 6 ยท Maths ยท Ganita Prakash
Chapter 3 ๐ข
Chapter 3 ๐ข
Number Play
Quick, colourful revision notes โ easy to read before your test!
Chapter Contents
3.1 โ 3.2 Supercells
Numbers all around us carry meaning โ and hide fun patterns. Let's start with supercells.
A cell in a table is a supercell if the number in it is greater than all its neighbouring cells (the cells immediately above, below, left and right of it).
@edugrown ๐ @edugrown ๐ @edugrown ๐
@edugrown ๐ @edugrown ๐ @edugrown ๐
Fig 1: Supercells (๐) are bigger than every neighbour touching them
The largest number in a table is always a supercell. The smallest number can never be a supercell (it can't be bigger than any neighbour).
3.3 โ 3.4 Number Lines & Digit Sums
Digit sum โ add up all the digits of a number. Example: digit sum of 545 = 5+4+5 = 14.
68, 176 and 545 all look different, but they share the same digit sum: 6+8 = 1+7+6 = 5+4+5 = 14!
On a number line, numbers further right are always bigger. Placing numbers like 2180, 2754, 9950 correctly helps you compare sizes at a glance.
3.5 Palindromic Numbers
A palindrome is a number that reads the same forwards and backwards.
66, 848, 575, 797, 1111 are all palindromes.
Reverse-and-add trick: take any 2-digit number, add it to its reverse; if it's not a palindrome yet, repeat! You will (almost) always reach a palindrome eventually.
3.6 Kaprekar's Constant โ The Magic 6174!
Discovered by Indian mathematician D.R. Kaprekar in 1949. Try this with any 4-digit number (not all digits the same):
Step 1: Arrange digits to make the biggest number (A).
Step 2: Arrange digits to make the smallest number (B).
Step 3: Subtract: C = A โ B.
Step 4: Repeat with C. You will always land on 6174 within 7 steps!
Step 2: Arrange digits to make the smallest number (B).
Step 3: Subtract: C = A โ B.
Step 4: Repeat with C. You will always land on 6174 within 7 steps!
@edugrown ๐ @edugrown ๐ @edugrown ๐
@edugrown ๐ @edugrown ๐ @edugrown ๐
Fig 2: Starting from 6382, we always reach the Kaprekar constant 6174
3.7 โ 3.8 Clock, Calendar & Mental Math
Clock patterns: 4:44, 10:10, 12:21. Date patterns: 20/12/2012 (repeating digits), 11/02/2011 (a palindromic date)!
In mental math with big numbers, break numbers into friendly parts (thousands, hundreds) and add/subtract in convenient chunks โ no need to always do it the "long" way on paper.
3.9 โ 3.10 Number Patterns & the Collatz Conjecture
Collatz Rule: Start with any whole number.
โข If it's even โ divide by 2.
โข If it's odd โ multiply by 3 and add 1.
Repeat forever.
โข If it's even โ divide by 2.
โข If it's odd โ multiply by 3 and add 1.
Repeat forever.
@edugrown ๐ @edugrown ๐ @edugrown ๐
@edugrown ๐ @edugrown ๐ @edugrown ๐
Fig 3: The "hailstone" journey of 17 โ up and down, but always ending at 1
Every whole number ever tried reaches 1 eventually โ but no one has ever proven this is true for all numbers! It's called the Collatz Conjecture (1937), and it's still unsolved today.
3.11 โ 3.12 Estimation & Games
Estimation โ a smart, quick guess when an exact count isn't needed (e.g. "about 500 students in school").
Game "21": players take turns adding 1, 2 or 3 to a running total. First to reach 21 wins. Winning trick: try to land on 20, 16, 12, 8, 4 (multiples of 4, minus 1 pattern)!
๐ฏ Quick Summary
- Supercell = a number bigger than all its grid neighbours.
- Digit sum = sum of all digits; different numbers can share the same digit sum.
- Palindrome = reads the same forwards and backwards (e.g. 1111).
- Kaprekar's constant = 6174 โ reached from almost any 4-digit number via biggest โ smallest, repeated.
- Collatz Conjecture: even โ รท2, odd โ ร3+1 โ always seems to reach 1, but it's still unproven!
- Estimation helps when exact counts aren't needed; numbers also power strategy games.
โ๏ธ Notes by @edugrown โ happy revising! ๐