Ramanujan Magic square:
An easy way of creating birthday magic square:
Eg :
16
|
3
|
19
|
90
|
91
|
18
|
0
|
19
|
1
|
18
|
92
|
17
|
20
|
89
|
17
|
2
|
All rows:
16+3+19+90 = 128
91+18+0+19 = 128
1+18+92+17 = 128
20+89+17+2 = 128
All Columns:
16+91+1+20 = 128
3+18+18+89 = 128
19+0+92+17 = 128
90+19+17+2 = 128
Middle Numbers: 18+18+92+0 = 128
All corners: 16+90+20+2 = 128
Each block:
16+3+91+18= 128
19+0+90+19 = 128
1+18+20+89 =
128
92+17+17+2 = 128
Sides :
91+1+19+17 = 128
3+19+89+17 = 128
Middle blocks:
91+18+1+18 = 128
0+19+92+17 = 128
Side diagonals:
91+3+92+19
= 128
19+19+1+89 = 128
Diagonals :
16+18+92+2 = 128
20+18+0+90 = 128
Let us take four columns with variables a1,b1,c1,d1
and follwoing the matrices the next rows are a2,b2,c2,d2.....till d4 as the last element.
First we will fill the first now with the DOB of the person.
Now a1 = 16 , b1 = 3 , c1 = 19 ,d1 = 90
Next rows are calculated as follows:
a2 = d1 +1; b2 = c1 - 1; c2 = b1 - 3; d2 = a1 + 3;
a3 = b1 - 2; b3 = a1 + 2; c3 = d1 + 2; d3 = c1 - 2;
a4 = c1 + 1; b4 = d1 - 1; c4 = a1 + 1; d4 = b1 - 1;
Check : Sum of a2 + a3 + a4 = d1 + 1 + b1 -2 + c1 +1 = d1 + b1 + c1 .
Adding this to a1 gives the sum a1 + b1 + c1 + d1 which is sum of our original numbers taken.
Same is applicable for other variables.
Logic : The value of the element position is sum of any other variable plus a constant of type integer.
At any point the sum of any set of four elements as mentioned in the above cases should give a constant sum of zero and no variable should be repeated.Then our square is a magic square.
a1
|
b1
|
c1
|
d1
|
a2
|
b2
|
c2
|
d2
|
a3
|
b3
|
c3
|
d3
|
a4
|
b4
|
d4
|
d4
|
a1
|
b1
|
c1
|
d1
|
d1 + 1
|
c1 – 1
|
b1 - 3
|
a1 + 3
|
b1 – 2
|
a1 + 2
|
d1 + 2
|
c1 – 2
|
c1 + 1
|
d1 – 1
|
a1 + 1
|
b1 - 1
|
By the above procedure we can generate 4 * 4 magic square.
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