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Argentina Cono Sur TST 2013. Problem 6

Source:

January 3, 2015

Problem Statement

Let m≥4m\geq 4 and n≥4n\geq 4. An integer is written on each cell of a m×nm \times n board. If each cell has a number equal to the arithmetic mean of some pair of numbers written on its neighbouring cells, determine the maximum amount of distinct numbers that the board may have.
Note: two neighbouring cells share a common side.
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