May 20, 2020

Birthday Magic Square- T R Jothilingam



                                  Magic squares

                               Picture Credit: -    
Magic squares are a set of numbers, arranged in a set of 3 × 3 or 4 ×4 or      5 × 5 squares, in which all the Vertical, Horizontal and both diagonal totals are equal. 
Normally a 3 × 3 magic square natural numbers 1 to 9 are used, and for 4 × 4 numbers 1 to 16 are to be used.  In general for a “n × n” magic square numbers    “1 to n2” are to be used.  And the total of the magic square must be “(1 + n 2)   divided by two and multiplied by ‘n’ (number of rows.). (First number plus last number to be added,  and divided by two, and multiplied by the number of rows).    These magic squares can be done from 3 ×3, 4×4…..up to any highest number in the world.

Do you know the the first Magic Square with Magical constant 15 is called Lo-shu Magic square?
King Yu found a tortoise in 12th century with magical constant 15 on its top.


Magic squares can also be made with using fractions, zeros, negative numbers, with squares, cubes also.  We can make magic squares for a given date of birth, or for a given number etc. etc.

Example:
For 3 × 3 magic square numbers 1 to 9 are to be used.
The row total will be 1+9=10 /2 =5 × 3=15.


3  × 3 Magic square: Total 15.                     3 × 3 Total 2019
8
1
6
3
5
7
4
9
2

676
669
674
671
673
675
672
677
670
                 

   
× 4 Magic square total 34.    
   {(1+ 16) /2} × 4 = 34                                 × 4   Total  2022
16
2
3
13
5
11
10
8
9
7
6
12
4
14
15
1
513
499
500
510
502
508
507
505
506
504
503
509
501
511
512
498





                                                                                             
  × 5 Magic square  Total 2020                  5 × 5  Magic Square Total =65
408
415
392
399
406
414
396
398
405
407
395
397
404
411
413
401
403
410
412
394
402
409
416
393
400
17
24
1
8
15
23
5
7
14
16
4
6
13
20
22
10
12
19
21
3
11
18
25
2
9
 Total 1+25= 26/2=13                                  






  Srinivasa Ramanujan Birthday Magic Square 

                    (Srinivasa Ramanujan 22-12-1887 to 26-04-1920)

Kindly follow the simple procedure to unlock the mystery to do the same.The following is a table with variables, which we will use in the explanation
22
12
18
87
68
50
17
4
35
21
51
32
14
56
53
16
        Total    139
A
B
C
D
E
F
G
H
P
Q
R
S
W
X
Y
Z











1)      Write the date in the top row first square (22), month in the second square (12) and year in two parts in the third (18)  and fourth square (87)
2)      Add all the four numbers and write on the top of the square (139).
3)      Now we have to make a 4 × 4 magic square for the Total 139
4)      Draw a empty 4 × 4 square and replace 22 by A, 12 by B, 18 by C and 87 by D.
5)      Now we know A, B, C and D. Rest of the values we have to find out.
6)      Count all numbers in the total 1+ 3 + 9 = 13. Then 1+ 3 = 4. (add all numbers and make it a single digit.  Write this in the H square
7)      Now add B + C ( 12 + 18 = 30). Spilt  30 into two parts. i.e 14 and 16. Write 14 in W square and 16 in the Z square
8)      By using the properties of Magic square, i.e all vertical, Horizontal and both Diagonal totals are equal, we are going to solve this Magic Square.
9)      In the Fourth vertical column, we know the values of D, H, Z.   We have to find Out the value of S. Hence S = 139 – ( D + H + Z ) = 139 — ( 87 + 4 + 16 ) = 139 – 107 = 32. This is the value of S. Write 32 in the S square
10)  Now in Diagonals, we know the value of  A and Z . Hence the value of F + R = 139 – (22 + 16) = 139 - 38= 101. Split  101  into two parts 50 and 51 and write it in the F and R squares. F = 50 and R = 51.
11)  In another diagonal, we know the value of D and W . Hence the value of G + Q = 139 – ( 87 + 14 ) = 139 - 101 = 38. Split it into two parts 17 and 21 and write it in the F and R squares. G = 17 and Q = 21.
12)  In the second row, we know the value of F, G, H. Hence value of E = 139 - ( F + G + H ) = 139 – ( 50 + 17 + 4 )= 139 – 71 = 68. Write 68 in E.
13)  In the third row, we know the value of Q , R , S. Hence value of  P = 139 - ( Q + R+S) = 139 – ( 21 + 51 + 32 ) = 139 – 104 = 35. Write 35 in P.
14)  Now in the second vertical column, we know the values of B, F, Q. Hence value of  X = 139 – (12 + 50 + 21 ) = 139 - 83 = 56. Write 56 in X
15)  Now in the third vertical column, we know the values of C, G, R. Hence value of       Y = 139  – ( 18 + 17 + 51 ) = 139 - 86 = 53. Write 53 in Y
16)  Now add the values of W, X, Y and Z.  You will get 139,   the total of the Magic square
VOW !!!   MAGIC SQUARE FOR 22 - 12 - 1887 IS READY.  All the vertical, Horizontal and both diagonal totals are equal to 139.
Enjoy Magic square for your date of Birth too !!!
Author:- T R Jothilingam
Enjoy more Puzzles in my website and blogs :  http://www.jollymaths.com/

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