Question 2 - Figure it out - Page 136 - Chapter 6 Class 7 - Number Play - Ganita Prakash

Transcript

Question 2 Create a magic square using the numbers 2 – 10. What strategy would you use for this? Compare it with the magic squares made using 1 – 9. We can use the same logic as the 1-9 square, or we can use a clever shortcut Strategy 1: Building from Scratch Find the new magic sum: The sum of the numbers from 2 to 10 is 54. Since there are 3 rows, the magic sum must be 54 ÷ 3 = 18 Find the new center number: For any set of 9 consecutive numbers, the center of the magic square is the median (the 5th number). In the sequence {2, 3, 4, 5, 6, 7, 8, 9, 10}, the center number is 6. Place the numbers: Using the same pattern as before (even-offset numbers in corners, odd-offset on edges), we can construct the square. Strategy 2: Transformation (The Easy Way) The simplest strategy is to take a completed 1-9 magic square and add 1 to every single number. Since you add 1 to each of the three numbers in a row, The new magic sum will be 15 + 3 × 1 = 15 + 3 = 18