Question 5 - Figure it out - Page 136 - Chapter 6 Class 7 - Number Play - Ganita Prakash

Transcript

Question 5 Discuss ways of creating a magic square using any set of 9 consecutive numbers (like 2 – 10, 3 – 11, 9 – 17, etc.). The easiest way is to use the transformation method. Start with the standard 1-9 magic square. Identify the first number of your new sequence (let's call it x). Calculate the difference: d = x - 1. Add this difference d to every number in the 1-9 magic square. Example: Create a magic square for the numbers 9-17. The first number is x = 9. The difference is d = 9 - 1 = 8. Add 8 to every number in the 1-9 square: Since the magic sum for 1-9 square is 15 And, now each row has three numbers that are each bigger by 8 Thus, New Magic sum = 15 + 8 × 3 = 15 + 24 = 39 Our new magic square is 1-9 Square 9-17 Square