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Encapsulate
math

NuMBER PlAY

Numbers 1, 2, 3, 4, ... and so on are the counting numbers and used for counting things.

Comparing Numbers Formation of Numbers

Supercells and Subcells Without Repetition
• Supercells: A cell becomes Example: A smallest 5 digit number using 6,
a supercell if the number 9 5 16 11 8 2, 7, 3, 0 is 20367.
in it is greater than all the With Repetition
numbers in its Supercells Example: A largest 5 digit number using 5,
neighbouring cells. 6, 8, 9 repeating 9 twice is 99865.
• Subcells: A cell becomes
a subcells if the number 9 5 16 11 8
in it is smaller than
all the numbers in its Subcells
neighbouring cells. Palindromic Pattern
Number that read the some backward and
forward, like 121 or 797 can be identified by
Playing with Number Patterns observing patterns in digits.

Numbers can be arranged in some patterns
which we figured out by using multiplication
instead of repeated addition.
2 2 2 4 2 2 2 Estimation
2 2 4 4 4 2 2 An estimation is an approximate calculation
2 4 2 4 2 4 2 or rounding of the number to the nearest
place value making the calculation easy.
4 4 4 4 4 4 4 Total distance = 785 m + 2 km 225 m + 150 m
2 4 2 4 2 4 2 ≈ 800 m + 2200 m + 200 m
(Rounding off to the nearest hundreds)
2 2 4 4 4 2 2
≈ 3200 m or 3 km
2 2 2 4 2 2 2

Breaking up Numbers
Kaprekar Constant
Algorithm: A number can be expressed as a sum/
1. Take any 3/4 digit number with atleast two digits difference of two or more numbers.
different. Example: 6500 = 7000 – 800 + 300
2. Arrange the digits in ascending and then in or 1200 –700 + 1500
descending order.
3. Subtract the smaller number from the bigger
number.
4. Repeat the process until you reach a constant. Collatz Conjecture
Example: If number be 198, then
Step 1: 981 – 189 = 792 If even ÷ 2
Step 2: 972 – 279 = 693 Choose a
Step 3: 963 – 369 = 594 number Repeat 4 – 2 – 1
Step 4: 954 – 459 = 495 ← constant for 3-digit number.
Similarly, 6174 is constant for 4-digit number. If odd × 3 + 1

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