CBSE Class 7 Mathematics Question 5 of 11

Number Play — Question 5

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5
Question
Discuss ways of creating a magic square using any set of 9 consecutive numbers (like 2-10, 3-11, 9-17, etc.).
Answer

The magic square for numbers 2-10 can be seen in solution 2 above. For the magic square using numbers 3-11, add 2 to each number in the original, and we get the adjoining magic square. Here, magic sum = 21 For the magic square using numbers 9-17, add 8 to each number in the original, and we get a square as shown alongside. Here, magic sum = 39 Generalising a 3 × 3 Magic Square NCERT In-Text Questions (Pages 136-137) We can describe how the numbers within the magic square are related to each other, i.e., the structure of the magic square. Choose any magic square that you have made so far using consecutive numbers. If m is the letter-number of the number in the centre, express how other numbers are related to m, how much more or less than m. [Hint: Remember how we described a 2 × 2 grid of a calendar month in the Algebraic Expressions chapter]. Solution: Consider the magic square We can express it using the letter-number m as: Once the generalised form is obtained, share your observations with the class. Solution: Do it yourself. Figure it Out (Page 137)