Question

create a magic squre 3×3 by keeping following
row sum 15 ,
column sum 15
,diagonal sum 15
​

Answer 1

Step-by-step explanation:

There after draw a neat 3 x 3 grid and rewrite the numbers as completed in STEP 2.

Now see the magic. the sum across the rows, the columns and diagonals are 15.

Rows Columns Diagonals

4 + 9 + 2 = 15 4 + 3 + 8 = 15 4 + 5 + 6 = 15

3 + 5 + 7 = 15 9 + 5 + 1 = 15 2 + 5 + 8 = 15

8 + 1 + 6 = 15 2 + 7 + 6 = 15

Formula

Of course we have formula for finding the numbers (Arithmetic Progression) used for filling the Magic Square for a given sum.

For any Magic Square of the order 3 x 3; the first term of the progression will be

F = S/ 3 - 4D

Here S denotes the Magic Sum, F the first number of the sequence used for filling and D the common difference between the numbers in the sequence.

To understand the concept follow the second example. See how to form a MS 3 X 3 with a magic sum of 132 and a sequence of common difference 5. Divide 132 with 3,we get 44. 44 minus four times 5- (44 - 20) we get 24. There fore the sequence is 24, 29, 34, 39, 44, 49, 54, 59, 64.