Question 1 - Figure it out - Page 127-132 - Chapter 5 Class 8 - Tales by Dots and Lines (Ganita Prakash II)

Transcript

Question 1 Mean Grids: (i) Fill the grid with 9 distinct numbers such that the average along each row, column, and diagonal is 10.Here, the average of 3 numbers is 10, So, their sum must be 30 Here is one way to fill the grid: Row 1: 13, 6, 11 Row 2: 8, 10, 12 Row 3: 9, 14, 7 Check: 13+10+7 = 30. 30/3 = 10. It works for every row, column, and diagonal!) But, how did we fill it? We used a secret In a 3 × 3 grid where every line has the exact same average, the very middle square must be that target average. Since we want an average of 10 in all directions, you write 10 dead in the center. And, we fill the rest by trial and error Question 1 Mean Grids: (ii) Can we fill the grid by changing a few numbers and still get 10 as the average in all directions?Yes, but you would have to change all the numbers to a completely new sequence that is still perfectly balanced around 10. For example: We could use even numbers: 2, 4, 6, 8, 10, 12, 14, 16, 18. As long as the numbers jump by a consistent amount and center on 10, you can build a new magic square. Let’s try filling it again We use only even numbers Our new 9 numbers will be: 2, 4, 6, 8, 10, 12, 14, 16, 18 And, 10 – our target average is at the center So, our grid will be