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Real numbers on a chessboard

Source: Problem 2, Brazil MO 1993

March 18, 2006
linear algebramatrixabsolute valuealgebra proposedalgebra

Problem Statement

A real number with absolute value less than 11 is written in each cell of an n×nn\times n array, so that the sum of the numbers in each 2×22\times 2 square is zero. Show that for odd nn the sum of all the numbers is less than nn.
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