MAGIC SQUARES

‘Magic Squares’ is a term given to squares which are fulfilled with consecutive integers and the total of whose rows, columns or diagonals are added up they reveal the same total. Many people have found these squares fascinating and so they have been regarded as magic.

Example-

4	3	8
9	5	1
2	7	6

We can verify the various totals:

Row 1: 4+3+8=15

Row 2: 9+5+1=15

Row 3: 2+7+6=15

Column 1: 4+9+2=15

Column 2: 3+5+7=15

Column 3: 8+1+6=15

Diagonal 1: 4+5+6=15

Diagonal 2: 8+5+2=15

RULES:

i) First, we place the first number 1 in the center-most square of the last column .

		1

ii) Next we move to the south-east direction from this square

However, there is nothing in the south-east direction. So we have to write in a square farthest from it as shown below.

         

		1
2

iii) Now from the square where we have written the number 2 we come to the south-east. However, it is not possible. So we have to write the number 3 farthest from it as shown below.

	3
		1
2

iv) Next, from 3 we have to come to the south-east direction to fill the number 4. But we realize that the square is already occupied by the number 1. So we have to write the number 4 in the west of the number 3. Refer to the diagram given below:

4	3
		1
2

v) Next, from 4 we move to the south-east direction and write the number 5. From 5, move to the south-east direction and write 5 and hence 6.

4	3
	5	1
2		6

vi) We have already written the number 6 in the last square. So we have to write the number 7 in the west of the number 6.

4	3
	5	1
2	7	6

vii) From 7 we move to the south-east direction.But it is not possible.S we have to write the number 8 farthest from it as shown below:

4	3	8
	5	1
2	7	6

viii) Now, we will put the number 9 in the remaining square.

4	3	8
9	5	1
2	7	6

You can now check it.

An example is given below which is also a magic square

11	10	4	23	17
18	12	6	5	24
25	19	13	7	1
2	21	20	14	8
9	3	22	16	15