Chapter 6: Number Play
Numbers can tell us things without giving everything away, and simple ideas like even and odd can solve puzzles in a flash. In this chapter we play the line game, use parity to prove things impossible, build magic squares, meet the Virahāṅka numbers from Indian poetry, and crack codes where digits hide behind letters.
In this chapter you will
- read information from the line-and-height rule
- use parity to decide sums and prove puzzles impossible
- build and complete magic squares
- count rhythms with Virahāṅka numbers and solve cryptarithms
Topics
- Numbers Tell us Things NCERT 6.1
The rule turns heights into numbers that show the order without the actual heights.
- Picking Parity NCERT 6.2
Even numbers pair up fully; odd numbers have one left over.
- Some Explorations in Grids NCERT 6.3
In a 3 × 3 grid of 1–9, the row sums (and the column sums) add up to 45.
- Nature's Favourite Sequence NCERT 6.4
The number of rhythms of n beats (sums of 1s and 2s) is the nth Virahāṅka number.
- Digits in Disguise NCERT 6.5
In a cryptarithm, start from the units column and keep track of carries.
Key words
- Parity
- whether a number is even or odd
- Consecutive numbers
- numbers that follow one another, like 51 and 52
- Magic square
- a grid where every row, column and diagonal has the same sum
- Magic sum
- the common sum of a magic square
- Virahāṅka numbers
- 1, 2, 3, 5, 8, 13 …, each the sum of the two before
- Cryptarithm
- a sum where letters stand for digits
Summary
- A rule like "how many in front are taller" encodes the order of heights.
- Parity: odd + odd = even; the nth even is 2n and the nth odd is 2n − 1.
- A 1–9 magic square has sum 15 and centre 5; every line is 3 × the centre.
- Virahāṅka numbers count rhythms of short and long syllables: 1, 2, 3, 5, 8, 13 …