It's Magic

Number Theory Level 4

We all know about magic squares. Aren't they special , huh ?

Draw a square with same numbers of row as column. Do you know if certain values are added in it then the sum of values of each row , each column and each of the two diagnols is the same. Condition , that natural numbers till the total number of cells in the square can be entered . For example , there is a square with rows and columns 5 then positive values upto 25 , the total number of cells , can be entered with , one more condition that any number once entered in the square COULD NOT be entered in the square AGAIN . NO block should be left empty. One more information , the two diagonals are from top leftmost cell to bottom rightmost cell and top rightmost cell to bottom leftmost cell.

An example of magic square,


NOTE : The image of this square might appear irregular but it's a square with 9 cells, and please do try to understand it. Where you shall see sum of every row , column and each of two diagnols is 15.

Now , for the problem , if there exist , as will surely exist , a magic square with number of row and column 11 or with total number of cells 121 , what will be the sum of each row , column or diagnal , if it retains all the qualities of a magic square ?


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