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Putting numbers on a chessboard

Source: India Postal Set 5 P 5 2016

January 18, 2017
combinatoricsnumber theory

Problem Statement

For even positive integer nn we put all numbers 1,2,⋯ ,n21, 2, \cdots , n^2 into the squares of an n \times n chessboard (each number appears once and only once). Let S1S_1 be the sum of the numbers put in the black squares and S2S_2 be the sum of the numbers put in the white squares. Find all nn such that it is possible to have S1S2=3964\frac{S_1}{S_2}=\frac{39}{64}.
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