MAGIC SQUARES
MAGIC SQUARES will have numbers giving same total row wise, column wise and diagonal wise.
The resulting square will be a magic square if same number is added to all cells or each cell is multiplied by same number.
Rows and colums can be interchanged.
So you can create many types of magic squares
Demo Magic Square 3 by 3 (for many combinations)
Input a
Input b
Mean x
Row or column or diagonal sum =
x-a
x+a-b
x+b
x+a+b
x
x-a-b
x-b
x+b-a
x+a
Changing a, b to any positive number but a is not equal to b
Another Demo of Magic Square 3 by 3 (for many combinations)
Input a
Input b
Input c
Row or column or diagonal sum =
a
b
c
x+c-a
x=(a+b+c)/3
x+a-c
2x-c
2x-b
2x-a
Changing a, b and c to any positive number. Sum of a+b+c should be multiple of 3. c will be corrected and magic square will be made with new c.
Demo Magic Square 4 by 4 (for many combinations)
Input a
b
c
d
Mean x
Row or column or diagonal sum =
x+a
x-a-d
x+b+d
x-b
x-a+c
x+d
x-c
x+a-d
x-b-c
x+c
x-d
x+b+d
x+b
x+a-c
x-b+c
x-a
Changing a, b,c and d to any positive number but all different
Another Demo Magic Square 4 by 4 (for many combinations)
Input a
b
c
d
Row or column or diagonal sum =
a
b
c
d
d+1
c-1
b-3
a+3
b-2
a+2
d+2
c-2
c+1
d-1
a+1
b-1
Changing a, b,c and d to any positive number but all different and 1) a less than b-3 2) b less than c and 3) c less than d-1
Magic Square 3 by 3: basic one with sum of 15, sum increased by adding multiple of 3
Multily cell by
Add each cell by
Row or column or diagonal sum
Magic Square 4 by 4: basic one with sum of 34, sum increased by adding multiple of 4
Multily cell by
Add each cell by
Row or column or diagonal sum
Magic Square 5 by 5: basic one with sum of 65, sum increased by adding multiple of 5
Multily cell by
Add each cell by
Row or column or diagonal sum
Magic Square 6 by 6: basic one with sum of 111, sum increased by adding multiple of 6
Multily by
Add each cell by
Row or column or diagonal sum
Magic Square 7 by 7: basic one with sum of 175, sum increased by adding multiple of 7
Multily by
Add each cell by
Row or column or diagonal sum
Magic Square 8 by 8: basic one with sum of 260, sum increased by adding multiple of 8
Multily by
Add each cell by
Row or column or diagonal sum
Magic Square 9 by 9: basic one with sum of 369, sum increased by adding multiple of 9
Multily by
Add each cell by
Row or column or diagonal sum
Magic Square 10 by 10: basic one with sum of 505, sum increased by adding multiple of 10
Multily by
Add each cell by
Row or column or diagonal sum
Magic Square 11 by 11: basic one with sum of 671, sum increased by adding multiple of 11
Multily by
Add each cell by
Row or column or diagonal sum
Magic Square 12 by 12: basic one with sum of 870, sum increased by adding multiple of 12
Multily by
Add each cell by
Row or column or diagonal sum
Sample magic Squares
18 magicsquare
27 magicsquare
54 magicsquare
60 magicsquare
108 magicsquare
432 magicsquare