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Class 7 Maths Chapter 6 Number Play NCERT Solutions (Complete Explanation, Step-by-Step Answers & Examples | Ganita Prakash)

Class 7 Maths Chapter 6 Number Play NCERT Solutions (Complete Explanation, Step-by-Step Answers & Examples | Ganita Prakash)

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 Introduction

Chapter 6 Number Play from NCERT Class 7 Mathematics is a fascinating journey into the world of patterns, parity, and puzzles. Students learn how numbers tell stories, how grids and magic squares work, and how the famous Virahanka-Fibonacci sequence connects math to nature. This blog provides step‑by‑step solutions, definitions, and extra practice questions to help students master the chapter.

Key Definitions

  • Parity: Property of being even or odd.
  • Magic Square: A square grid where each row, column, and diagonal adds to the same number.
  • Virahanka-Fibonacci Numbers: Sequence formed by adding the two previous terms (1, 2, 3, 5, 8, 13, …).
  • Odd Numbers: Numbers not divisible by 2 (1, 3, 5, …).
  • Even Numbers: Numbers divisible by 2 (2, 4, 6, …).

Section‑wise Solutions & Extra Questions

6.1 Numbers Tell Us Things

Q1. Arrange stick figures so sequence reads (0, 1, 1, 2, 4, 1, 5).


Solution: Each number shows how many taller children stand ahead.

6.2 Picking Parity

Puzzle: 5 odd cards must sum to 30.
 Impossible, since odd + odd + odd + odd + odd = odd, but 30 is even.

Extra Figure it Out:

  • 2 even + 2 odd = Even
  • 2 odd + 3 even = Even
  • 5 even numbers = Even
  • 8 odd numbers = Even

6.3 Magic Squares

Observation:

  • Magic sum for 3×3 using 1–9 = 15.
  • Centre must be 5.
  • 1 and 9 cannot be corners.

✅ Example Magic Square:

2 7 6 9 5 1 4 3 8

Extra Figure it Out:

  • Create magic square using 2–10 → Magic sum = 18.
  • Increase each number by 1 → Magic sum increases by 3.
  • Double each number → Magic sum doubles.

6.4 Virahanka-Fibonacci Numbers


Sequence: 1, 2, 3, 5, 8, 13, 21, 34…

Extra Figure it Out:

  • 100th even number = 200
  • 100th odd number = 199
  • Next 3 numbers after 55, 89 → 144, 233, 377
  • Parity pattern → Odd, Even, Odd, Odd, Even, Odd, Odd, Even…

6.5 Digits in Disguise

Puzzle:

T + T + T = UT

👉 Solution: T = 5, UT = 15.

Extra Figure it Out:

AB + AB = CDE

👉 Solution: AB = 56, CDE = 112.

Conclusion

Chapter 6 Number Play teaches students how numbers reveal hidden patterns in everyday life. From parity puzzles to magic squares and the Fibonacci sequence, this chapter connects math with nature, culture, and problem‑solving.

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15 FAQs – Ganita Prakash (Class 7, Chapter 6 Number Play)

Q1. What rule did the children use to call out numbers?
Each child calls out the number of children in front of them who are taller than them.
Q2. If a person says '0', what does it mean?
It means no one in front is taller. Often, this indicates the person is the tallest in the group.
Q3. Why can’t Kishor arrange 5 odd cards to sum to 30?
The sum of 5 odd numbers is always odd, but 30 is even. Hence, impossible.
Q4. What is parity in mathematics?
Parity refers to whether a number is even or odd.
Q5. What is the sum of two odd numbers?
Odd + Odd = Even. Example: 3 + 5 = 8.
Q6. What is the sum of an even and an odd number?
Even + Odd = Odd. Example: 4 + 3 = 7.
Q7. Why can’t Martin and Maria’s ages sum to 112?
Their ages are consecutive numbers (one even, one odd). Sum of consecutive numbers is always odd, but 112 is even.
Q8. What is the nth even number formula?
nth even number = 2n. Example: 100th even number = 200.
Q9. What is the nth odd number formula?
nth odd number = 2n – 1. Example: 100th odd number = 199.
Q10. What is a magic square?
A square grid where each row, column, and diagonal adds to the same number (magic sum).
Q11. What is the magic sum of a 3×3 square using 1–9?
The magic sum must be 15, since total sum = 45 and each row sum = 15.
Q12. Which number must be at the centre of a 3×3 magic square?
The centre must be 5, as reasoning shows other numbers cannot balance the sums.
Q13. What is the Virahanka-Fibonacci sequence?
A sequence where each term is the sum of the two previous terms: 1, 2, 3, 5, 8, 13, 21, 34, ...
Q14. Who first described the Virahanka numbers?
The Indian scholar Virahanka around 700 CE, in the context of poetry rhythms.
Q15. How many rhythms exist with 8 beats of short and long syllables?
There are 34 rhythms, corresponding to the 8th Virahanka-Fibonacci number.
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