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Can five odd numbers add up to 30? Can you fill a grid so every row adds to the same number? The Class 7 chapter Number Play shows how a little reasoning answers such questions without endless trial and error. This guide is for students and parents: what the chapter covers, two worked examples, the usual mistakes and a practice plan.
Where is Number Play in the Class 7 maths book?
Number Play is Chapter 6 of Ganita Prakash, Grade 7, Part 1 (reprint 2026-27). The Number Play chapter PDF has five parts: a height-line puzzle, parity, explorations in grids and magic squares, the Virahanka-Fibonacci numbers, and cryptarithms, where letters stand for digits.
What is parity, and why is it so useful?
Parity means whether a number is even or odd. The book uses pictures: an even number can be arranged in pairs with nothing left over, and an odd number always has one left over. From this:
even + even = even
odd + odd = even
even + odd = odd
So any number of even numbers adds to an even number, an even count of odd numbers adds to an even number, and an odd count of odd numbers adds to an odd number. The chapter's first puzzle uses this: five cards with odd numbers can never add up to 30, because five odd numbers always give an odd total. No checking of cases is needed.
The chapter also writes parity with algebra. The nth even number is 2n and the nth odd number is 2n - 1, so the 100th odd number is 199.
Worked example 1: Lakpa's coins
Lakpa has an odd number of ₹1 coins, an odd number of ₹5 coins and an even number of ₹10 coins. He says the total is ₹205. Is he right?
₹1 coins: an odd number of ₹1 coins makes an odd amount.
₹5 coins: 5 × (odd number) is odd, because 5 is odd and odd × odd = odd.
₹10 coins: 10 × (anything) is even.
Total: odd + odd + even = even.
₹205 is odd, so Lakpa has made a mistake. We never needed to know how many coins he has.
Worked example 2: building a 3 × 3 magic square
A magic square has every row, column and diagonal adding to the same number, the magic sum. Use the numbers 1 to 9 once each. The book points out there are 3,62,880 ways to fill the grid, so guessing is hopeless. Reason instead.
The magic sum. 1 + 2 + ... + 9 = 45. The three rows share this total equally, so each row adds to 45 ÷ 3 = 15.
The centre. If 9 were in the centre, the line through 9 and 8 would need 9 + 8 + something = 15, which is impossible. Similar reasoning rules out the other numbers, so the centre must be 5.
1 and 9. Only two lines of three numbers from 1 to 9 that add to 15 contain 1: 1 + 5 + 9 and 1 + 6 + 8. A corner sits on three lines, so 1 cannot go in a corner; nor can 9. They go in the middle of the edges, opposite each other.
Fill the rest. Put 1 and 9 in, then complete each line to 15. One solution:
Top row: 2, 7, 6
Middle row: 9, 5, 1
Bottom row: 4, 3, 8
Check: each row gives 15; the columns give 2 + 9 + 4, 7 + 5 + 3 and 6 + 1 + 8, all 15; the diagonals give 2 + 5 + 8 and 6 + 5 + 4, both 15.
The OEIS entry on magic squares confirms that there is only one 3 × 3 magic square using 1 to 9 if you count rotations and reflections as the same, and 880 of size 4 × 4. The chapter shows a famous 4 × 4 square, the Chautisa Yantra, recorded in a 10th-century inscription at the Parshvanath Jain temple in Khajuraho, where every row, column and diagonal adds to 34. For a mathematician who wrote general methods for magic squares, read our story of Narayana Pandita.
Where do the Virahanka numbers come from?
In Prakrit and Sanskrit poetry, a short syllable takes one beat and a long one takes two. How many rhythms fill 5 beats? Every rhythm starts with either a 1 or a 2. Starting with 1 leaves 4 beats (5 rhythms); starting with 2 leaves 3 beats (3 rhythms). So there are 5 + 3 = 8. Each number is the sum of the two before it: 1, 2, 3, 5, 8, 13, 21, 34. An 8-beat rhythm can be filled in 34 ways.
NCERT says Virahanka gave this rule around 700 CE, about 500 years before Fibonacci wrote about the numbers in 1202. The OEIS entry for the Fibonacci numbers records the same history, quoting Donald Knuth that Indian scholars studied these rhythm counts before Fibonacci.
Parity appears here too. The pattern goes odd, even, odd, then repeats, so every third number is even. The 20th number is even, since 20 is in the list 2, 5, 8, 11, 14, 17, 20.
Which mistakes come up most?
Checking examples instead of proving. Three examples that work do not show a rule always works.
Forgetting the diagonals when checking a magic square.
Starting the Virahanka sequence wrongly. In the book it starts 1, 2, 3, 5, so the 8th term is 34.
A practice plan for the week
Day 1: Do the parity questions in the chapter and say each answer as a sentence: "odd + odd = even, because ...".
Day 2: Rebuild the magic square from 1 to 9 without looking, then make one from 2 to 10. The magic sum goes up by 3.
Day 3: Write all 13 six-beat rhythms using the "start with 1 or 2" method.
Day 4: Try two cryptarithms from the chapter and explain your steps to someone at home.
When a puzzle step does not make sense, Fermi's AI tutor notices where you are stuck and decides whether to explain, ask or show, so you work out the step yourself. For the Class 6 chapter with the same name, see our guide to Number Play in Class 6.
Start now: with a light that is ON, flip its switch 77 times. Use parity to decide whether it ends up on or off.
