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red and blue squares in 123 x 123 board

Source: 2012 Cuba MO 1.3

September 18, 2024
combinatoricsColoring

Problem Statement

On a 123×123123 \times 123 board, each square is painted red or blue according to the following conditions:
a) Each square painted red that is not on the edge of the board has exactly 55 blue squares among its 88 neighboring squares.
b) Each square painted blue that is not on the edge of the board has exactly 44 red squares among its 88 neighboring squares.
Determine the number of red-painted squares on the board.
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