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Number Play – Formula & Equation Sheet
Essential formulas and equations from Ganita Prakash, tailored for Class 6 in Mathematics.
This one-pager compiles key formulas and equations from the Number Play chapter of Ganita Prakash. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
n = 10^k
n represents the number of digits in a number, k is the position of the highest digit. This formula helps determine the scale of numbers based on their digits.
d(n) = d(a) + d(b)
d(n) is the digit sum of number n. a and b are components of n. This demonstrates how digit sums can be additive.
A - B = C
A and B are two numbers. C is their difference. This formula is essential for understanding subtraction.
A + B = S
A and B are two numbers. S represents their sum. This is fundamental in addition.
P(n) = n(n + 1)/2
P(n) denotes the sum of the first n natural numbers. Useful for finding sums when counting.
f(n) = (n/2) if n is even, f(n) = (3n + 1) if n is odd
f(n) defines a function based on Collatz conjecture. It demonstrates a process of number transformation.
Kaprekar’s operation: A - B = C, where A > B
A is the largest permutation of a number’s digits, B is the smallest permutation. C is often a fixed point in iterations.
n = r(digits)
n is the formed number from r (a specific arrangement) of its digits. This is used to understand number construction.
Palindrome: X = reverse(X)
X is a palindromic number if it reads the same forwards and backwards. Important in identifying symmetric numbers.
Sum of Palindrome: X + reverse(X) = Y
Y is the result of adding a number to its reverse. A foundational concept in exploring palindromic sequences.
Equations
X = Y + H
X is the total, Y is the sum of all numbers, H is the height or additional variable. Useful in context of height comparisons.
Supercell condition: n > adjacents
n is a supercell if it is greater than all its adjacent cells. This is critical in identifying special numbers in sequences.
Height Comparison: Count = neighbours > current
Count refers to the number of taller neighbours. It indicates relative height in arrangements.
Digit Sum: D(n) = a1 + a2 + ... + ak
D(n) signifies the sum of individual digits a1, a2, ... ak of number n. This reinforces digit addition concepts.
Count of d-digit numbers: 9 * 10^(d-1)
This counts possible d-digit numbers (d > 1) using leading digits. Essential for understanding number ranges.
V = r * t (time elapsed)
V is volume. r is rate, and t is time. Used when calculating distance-related problems.
f(n) = n/2 (for even n)
This denotes the operation performed on even numbers in a sequence. Important in iterative processes.
f(n) = 3n + 1 (for odd n)
Defines the operation applied to odd numbers. Important in exploring the Collatz conjecture.
Estimation: Approx = Round(N)
Approximation is the rounded value of a number N, useful for quick large number calculations.
Game Strategy: N + 1, 2, or 3
In the game 21, players can say 1, 2, or 3 to build up to 21. This describes the rules of a mathematical counting game.
