Number Play

Patterns and puzzles with numbers: odd and even, magic squares, Virahanka numbers, consecutive numbers and digit puzzles.

Key ideas

• Even ± even and odd ± odd are even; odd ± even is odd.
• A sum is odd only when it has an odd number of odd terms.
• In a 3 × 3 magic square using 1 to 9, every row, column and diagonal adds to 15, and 5 is in the centre.
• In any 3 × 3 magic square, the magic sum is 3 times the centre number.
• Virahanka numbers: 1, 2, 3, 5, 8, 13, 21, … Each is the sum of the two before it.
• The sum of an odd number of consecutive numbers is the count times the middle number.

Remember

Watch out

• Thinking a sum of many odd numbers is always odd.
• Putting a number other than the middle value in the centre of a magic square.
• Starting the Virahanka sequence wrong (1, 2, 3, 5, …).

Worked example