Just sum

Number Theory Level 3

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.

Now , if there exist , as will surely exist , a magic square with number of row and column \( 101\). What will be the sum of each row , column or diagonal , if it retains all the qualities of a magic square ?

\(Note\): If you will try to search on \(Google \) , you will gain some points but not good math skills.


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