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LOGIC BEHIND MAGIC SQUARE3X3

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LOGIC BEHIND 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




2). MAGIC SUM=21. NUMBERS: 3,4,5,6,7,8,9,10,11  MIDDLE NUMBER: 7

7-1
7+4
7-3
7-2
7
7+2
7+3
7-4
7+1
Result of above magic square:
6
11
4
 5
7
9
10
3
8

2). MAGIC SUM=24. NUMBERS: 4,5,6,7,8,9,10,11,12  MIDDLE NUMBER: 8
       
8-1
8+4
8-3
8-2
8
8+2
8+3
8-4
8+1
Result of above magic square:
7
12
5
 5
8
10
11
4
9



 SEE ALSO: LOGIC BEHIND MAGIC SQUARE

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