Class 7 Maths Chapter 6 Number Play Infographic | NCF 2023 Ganita Prakash

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✦ NCF 2023 GANITA PRAKASH • GRADE 7 SERIES ✦

Chapter 6: Number Play

Unlocking the Secrets of Numbers: Parity, Magic Squares, Sequences, and Cryptarithms

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📖 The Rules of Parity

Even Parity (E)

Numbers that can be arranged in exact pairs without any leftovers.

Odd Parity (O)

Numbers that leave exactly one item leftover when arranged in pairs.

General Formula

The nth Even number = 2n. The nth Odd number = 2n − 1.

✂️ Parity Operations

The Addition Rules:

• Even + Even = Even
• Odd + Odd = Even (The leftovers pair up!)
• Even + Odd = Odd
Rule: Sum of odd number of odd numbers is Odd.

Virah&amacron;nka-Fibonacci Sequence:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89...
• Next term = Sum of previous two terms.
• Parity Pattern repeats: Odd, Even, Odd.

🧩 3×3 Magic Squares

The Magic Sum Rule:

Using digits 1-9, sum of 1 to 9 is 45. There are 3 rows, so the Magic Sum must be exactly 15 (45 ÷ 3).

The Center Piece:

The center number must always be 5. Neither 1 nor 9 can be placed in corner squares.

Altering Magic Squares:

Adding a constant to every cell, or multiplying every cell by a constant, yields a new valid magic square.

📅 Unveiling Magic Squares

The Structural Secret: To construct the unique 3×3 magic square (digits 1-9), the center must be 5, corners must be even (2, 4, 6, 8), and edge middles must be odd (1, 3, 7, 9).

Standard (1-9) Magic Square

8

1

6

3

5

7

4

9

2

Rows = 15 | Cols = 15 | Diagonals = 15

General Algebra Form

m+3

m−4

m+1

m−2

m

m+2

m−1

m+4

m−3

Magic Sum is always = 3 × m

• History Fact: The first recorded 4×4 magic square is the Chautīsa Yantra (Magic Sum = 34) found in Khajuraho, India. Ancient China also has the 3×3 Lo Shu Square linked to a turtle legend!

• Cryptarithms: Math puzzles where letters replace digits (e.g. U T + T A = T A T). Use logic to decode the unique digits.

⚠️ Common Parity Traps

Trap 1: The Odd Addition Fallacy

Adding 5 odd numbers will NEVER result in an even sum (like 30). Because Odd + Odd = Even, but leaving one Odd out keeps the final sum Odd.

Trap 2: Consecutive Number Parity

The sum of any two consecutive numbers can NEVER be an even number (like 112). Because one is always Even and one is Odd, making their sum strictly Odd.

Designed by Akash Srivastva | Mathematics Hub • NCF 2023 Visual Learning Series

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