magic square 3x3 sum 18

 MAGIC SQUARE:

In a magic square 3x3, if we take numbers from 1 to 9 then the magic sum equal to 15. The magic square is as follows:

4	9	2
3	5	7
8	1	6

In the above magic square 3x3 magic sum is 15. In the above magic square 3x3 we are used numbers from1 to 9 arranged in 9 boxes. In any direction the sum equal to 15.

Row wise  4+9+2=15, 3+5+7=15, 8+1+6=15.

Column wise 4+3+8=15, 9+5+1=15, 2+7+6=15.

Diagnol wise: 4+5+6=15, 2+5+8=15.

The above magic square also can be written as follows:

5-1	5+4	5-3
5-2	5	5+2
5+3	5-4	5+1

In the above figure , shows the relation between middle number and other numbers. In the magic square we are taken numbers from 1 to 9 and number 5 is between 1 to 9.

If we write  x in place of 5 in above magic square.                                        

X-1	X+4	X-3
X-2	X	X+2
X+3	X-4	X+1

Now we will write different magic square’s with different magic sum’s

2.MAGIC SUM=18. NUMBERS: 2,3,4,5,6,7,8,9,10 10. MIDDLE NUMBER: 6

       

6-1	6+4	6-3
6-2	6	6+2
6+3	6-4	6+1

Result of above magic square:

5	10	3
4	6	8
9	2	7

see also: LOGIC BEHIND MAGIC SQUARE