Coloring A Big Board
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.