Monday, October 9, 2017

Different possibilities for 3x3 Magic Square

The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square.

1) Take any normal magic square from previous blog with number sequence as 1,2,3,4,5,6,7,8,9 
Here the Total of all numbers = (9)(9+1)/2 = 45.  


Magic Constant=15 

2) Now create magic square by adding 1 to each cell
Number sequence: 2,3,4,5,6,7,8,9,10 Total= 54 
Magic Constant=18 

3) Create magic square by adding 4 to each cell
Number sequence: 5,6,7,8,9,10,11,12,13; Total= 81
Magic Constant=27 

4)Create magic square by taking sequence as follows
( Difference of 2 between consecutive numbers)

Number sequence: 1,3,5,7,9,11,13,15,17; Total= 71, 
Magic Constant=27 

5) Create magic square by taking sequence as follows
( Increase followed by decrease in difference between consecutive numbers)
Number sequence: 1,3,4,6,7,9,10,12,13; Total= 65, 
Here the differences are 2,1,2,1,2,1,2,1
Magic Constant=22 

Thus we can generate any number of 3x3 magic squares by changing starting number and using sequence with proper adjustment of differences.

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