The Chessboard From Greece!
For an even positive integer \(n<10000\), we write down all the numbers \(1, 2, 3, \ \ldots\ , n^2\) on the squares of an \(n\times n\) chessboard.
Let \(S_1\) be the sum of all the numbers written on black squares and \(S_2\) be the sum of all the numbers written on white squares.
How many possible values of \(n\) are there such that it is possible to achieve
Details and assumptions:
Each number appears exactly once on the board.