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MathNet 2014 Question 31

Math Olympiad Vault · MathNet 2014

Question 31

A chessboard is a board with $8$ rows and $8$ columns, whose squares are coloured alternately black and white, so that the square in the first row and first column is coloured black. An integer is inscribed in each square. It is known that the sum of all numbers on white squares equals $26$, and the sum of all numbers in odd rows equals $43$.
If we change the sign of all numbers on white squares, what will be the sum of all numbers in odd rows after the change? (Italy 2012)