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Numbers on a board

Source: Argentina MO 2008

November 19, 2008
abstract algebraabsolute valuealgebra unsolvedalgebra

Problem Statement

In every cell of a 60×60 60 \times 60 board is written a real number, whose absolute value is less or equal than 1 1. The sum of all numbers on the board equals 600 600. Prove that there is a 12×12 12 \times 12 square in the board such that the absolute value of the sum of all numbers on it is less or equal than 24 24.
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