You must have heard about magic squares-viz squares with 3/3 cells or 4/4 cells filled with numbers when the sum of the numbers in each row/column/both diagonals are the same.However let me now present some data.
I will deal with a 3/3 cell first.
The simplest is formed with the numbers from 1 to 9 .It will be like this-
4 9 2
3 5 7
8 1 6
The totals as per each row,column and both diagonals will be 15-viz .
3 times the number 5 in the central cell.
It is formed as follows-First put the number 5 in the central cell.Put the number 1 in the cell below it.Put the number 2 at the top row right hand corner.The numbers 1,5 and 2 will thus appear as in a clock showing the time as 06-07 or 06-08.Th rest of the numbers can be filled up to make the totals 15 everywhere.
You will be surprised to know that the squares of the numbers in each row viz those of 492,357 and 816 will add up to 1035369 while you will get the same total using the squares of the numbers formed in the reverse order viz 294,753 and618.Similarly the squares of the numbers in each column viz 438,951 and 276 will add up to 1172471 while you will get the same total using the numbers read upside down viz 834,159 and 672.
You can make squares with any number like 45 placed in the central cell instead of 5 and using numbers like 37,39,41,43,47,49,51 and 53 instead of the numbers 1,2,3,4,6,7,8 and 9.The totals everywhere will be 135.
You can also have magic squares using prime numbers-sample shown below-
67 1 43
13 37 61
31 73 7- the totals everywhere will be 117 .
I will deal with a 3/3 cell first.
The simplest is formed with the numbers from 1 to 9 .It will be like this-
4 9 2
3 5 7
8 1 6
The totals as per each row,column and both diagonals will be 15-viz .
3 times the number 5 in the central cell.
It is formed as follows-First put the number 5 in the central cell.Put the number 1 in the cell below it.Put the number 2 at the top row right hand corner.The numbers 1,5 and 2 will thus appear as in a clock showing the time as 06-07 or 06-08.Th rest of the numbers can be filled up to make the totals 15 everywhere.
You will be surprised to know that the squares of the numbers in each row viz those of 492,357 and 816 will add up to 1035369 while you will get the same total using the squares of the numbers formed in the reverse order viz 294,753 and618.Similarly the squares of the numbers in each column viz 438,951 and 276 will add up to 1172471 while you will get the same total using the numbers read upside down viz 834,159 and 672.
You can make squares with any number like 45 placed in the central cell instead of 5 and using numbers like 37,39,41,43,47,49,51 and 53 instead of the numbers 1,2,3,4,6,7,8 and 9.The totals everywhere will be 135.
You can also have magic squares using prime numbers-sample shown below-
67 1 43
13 37 61
31 73 7- the totals everywhere will be 117 .
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