Wednesday, July 22, 2015

Magic Square Software (5 x 5) part-1

BLOG-99


Prepare your own two magic squares of 5 rows and 5 columns in which first row is of your choice. You can enter any 5 numbers between -9999 to 9999 (actually you can enter any number, but for the betterment of the look of the sheet, this restriction is implemented in the software) of your choice in the first row. Software will give you two different magic squares with your chosen numbers are in 1 st row. These two magic squares have 120 types of same addition.

Rows
5
Columns
5
Diagonals
2
Broken Diagonals
8
Different Patterns
100
Total
120

The software of magic squares of order 5 x 5 will be uploaded shortly.

Now we will see all the properties of 5 x 5 magic squares one by one. Let us see the magic squares in which we choose the first row with the numbers as 9, 21, 34, 45 and 56. Following two magic squares will be obtained by the software. 


Now we will see all types of addition:

1) Addition of all the numbers in the Rows: (1 to 5)

     a) First Row: (1/5)



                             09 + 21 + 34 + 45 + 56 = 165          09 + 21 + 34 + 45 + 56 = 165

     b) Second Row: (2/5)



                             44 + 55 + 13 + 20 + 33 = 165          36 + 47 + 53 + 11 + 18 = 165

     c) Third Row: (3/5)



                              24+ 32 + 43 + 54 + 54 = 165          55 + 47 + 20 + 38 + 44 = 165

     d) Forth Row: (4/5)



                              55+ 11 + 23 + 36 + 42 = 165          22 + 35 + 46 + 52 + 10 = 165

    e) Fifth Row: (5/5)



                              35+ 46 + 52 + 10 + 22 = 165          43 + 54 + 12 + 19 + 37 = 165

2) Addition of all the numbers in the Columns: (6 to 10)

     a) First Column: (6/10)



                              09+ 44 + 24 + 53 + 35 = 165          09 + 36 + 55 + 22 + 43 = 165

     b) Second Column: (7/10)


                           
                              21+ 55 + 32 + 11 + 46 = 165          21 + 47 + 08 + 35 + 54 = 165


     c) Third Column: (8/10)



                             34+ 13 + 43 + 23 + 52 = 165          34 + 53 + 20 + 46 + 12 = 165

     d) Forth Column: (9/10)



                             45 + 20 + 54 + 36 + 10 = 165          45 + 11 + 38 + 52 + 19 = 165

     e) Fifth Column: (10/10)



                              56 + 33 + 12 + 42 + 22 = 165          56 + 18 + 44 + 10 + 37 = 165

3) Addition of all the numbers in the Diagonals: (11 to 12)

     a) First Diagonal: (11/12)



                             09 + 55 + 43 + 36 + 22 = 165          09 + 47 + 20 + 52 + 37 = 165

     b) Second Diagonal: (12/12)



                             56 + 20 + 43 + 11 + 35 = 165          56 + 11 + 20 + 35 + 43 = 165

8 types of broken diagonal addition and 100 types of different patterns of addition will be published in the next blog.