# Coloring A Big Board

**Discrete Mathematics**Level 4

Consider a \(27\times 30\) board in which its squares have been colored red or blue. We know that for each blue square, that is not on the edge, 4 of the 8 squares that are adjacent, are red. Also, we know that for each red square, that is not on the edge, 5 of the 8 squares that are adjacent, are blue. Find the maximum number of red squares on the board.

**Details and Assumptions**:

2 squares are adjacent if they share at least a vertex. Indeed, each square that's not on the edge has exactly 8 adjacent squares.

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