IIT JEE , AIEEE Forum - Articles Category , Community shelf - CREATING MAGIC SQUARES -THE EASY WAY-1

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CREATING MAGIC SQUARES IS NOT AS DIFFICULT AS SOLVING THEM!!

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Creating Magic Squares Is Great Fun-i

Creating Magic squares of odd order-3x3, 5x5, 7x7.....etc

BY NDLL method

Let?s first see the 5x5 magic square (as obtained by NDLL method...... different methods give different squares)

17

24

1

8

15

23

5

7

14

16

4

6

13

20

22

10

12

19

21

3

11

18

25

2

9

General Steps (Of NDLL method)

v Place the number 1 in the middle cell of the top most rows.

v Whenever in the top row place the next number in the bottom cell of the next column to the right.

v After this place the numbers proceeding diagonally to the right. Use this step as far as possible.

v When ever in the last column place the next number in the first left cell of the upper row.

v When the above steps are not possible (the cells are not empty) place the next digit in the cell just below.

Formation of 5x5 magic square: using the above steps

·        Place the number 1 in the 3^rd cell of the top most rows.

·        According to the step 2 ,2 should be placed in the bottom row of the adjacent column to the right

1

4

3

2

·        According to step 3, 3 should be placed diagonally to right.

·        Since we have reached the last column we cannot proceed    diagonally and according to step 4 place no. 4 in the 1^st cell of the upper row.

·        After this we move diagonally to the right and place 5 there.

·        Since further step 2, 3 and 4 fail we follow step 5 and place 6 below 5.

·        Now we can move diagonally and place 7,8

·        We have reached the top most column follow step 2 and place 9 in the next column.

1

5

4

6

3

2

1

8

5

7

4

6

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