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Class 7 Number Play: cheat sheet
CBSE Mathematics. 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
| Parity | odd + odd = even; odd × odd = odd; even × anything = even |
| Magic square | magic sum = 3 × centre |
| Virahanka numbers | next = sum of the two before |
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
Is the sum of all the numbers from 41 to 120 even or odd? How many of them are odd?
Working: the parity of a sum depends only on how many odd numbers there are
Answer: even; 40 odd numbers
Practise Number Play
Revise with this page, then practise: every Number Play sheet in the app is new, with an answer key and working.
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