This playful chapter explores numbers through puzzles, parity, grids and famous sequences. Parity is the property of being even or odd: even numbers can be paired with no leftover, odd numbers cannot. You learn rules such as even + even = even, odd + odd = even, even + odd = odd, and use them to decide quickly whether a situation is possible (five odd cards can never sum to the even number 30). Expressions can be designed to be always even \((2n)\), always odd \((2n-1)\), or either. You then build magic squares — grids where every row, column and diagonal share the same magic sum (for the numbers 1–9 the magic sum is 15 and the centre must be 5) — and generalise their structure with a centre letter \(m\). The chapter celebrates the Virahanka–Fibonacci sequence \(1, 2, 3, 5, 8, 13, 21, 34, \dots\), where each term is the sum of the previous two, discovered in Indian poetry centuries before Fibonacci. It ends with cryptarithms, puzzles where letters replace digits.
Parity of numbers and sumsDesigning even/odd expressionsMagic squares and the magic sumGeneralising a magic square with algebraVirahanka–Fibonacci sequence and cryptarithms
Key terms
Parity
The property of a number being even or odd.
Even number
A number that can be arranged in pairs with no leftover; of the form \(2n\).
Odd number
A number that cannot be arranged in pairs; of the form \(2n - 1\).
Magic square
A square grid where each row, column and diagonal add to the same magic sum.
Magic sum
The common total of every row, column and diagonal of a magic square.
Virahanka–Fibonacci sequence
The sequence \(1,2,3,5,8,13,21,\dots\) where each term is the sum of the two before it.
Cryptarithm
A puzzle in which digits are replaced by letters that must be decoded.
Extra questions & answers
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The parity of a number refers to whether it is:
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