Construct a magic square by using numbers from 1to9.
Answers
Answer:
Step: 1
Picture
Write nine consecutive numbers in three rows and columns as shown along side.nine consecutive numbers in three rows and columns as shown along side. Say for example, we are using natural numbers from 1 to 9.(Normally we use natural numbers only) Here numbers from 1 to 3 is written in the first row followed by 4 to 6 in the second and 7 to 9 in the third rows..
Step: 2
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Now draw lines diagonally under the numbers from both sides as shown in the figure. Once it's done you shall get a 3 x 3 square grid as high lighted by the red line in the figure. But here 4 cells are empty and 4 numbers are lying outside the square grid. All you will have to do is to use these numbers to fill the empty cells in the opposite side.
Picture
Final answer
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.
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