Equals sums in rows and columns

[Susam Pal]

Each square of a chessboard contains a number. The sum of the
two largest numbers in each row is the same. The sum of the two
largest numbers in each column is also the same. What is the
maximum possible difference between the two sums?

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Originally posted at: http://cotpi.com/p/39/
Solutions to 'Factors of factorials': http://cotpi.com/p/38/#responses