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MathNet 2010 — Part 01 Question 98

Math Olympiad Vault · MathNet 2010 — Part 01

Question 98

Exactly one integer number is written in each cell of an $8 \times 8$ square table. Per move it is allowed to choose any $n \times n$ square, $1 \lt n \lt 8$, and either to increase by 1 or to decrease by 1 all numbers in the cells of the chosen square.
Is it possible to get the table with zeros in all its cells from the arbitrary initial table?
(V. Kaskevich)