On a standard 8×8 chessboard there are 7 infected cells. Every minute each cell which has at least 2 infected neighbors gets infected as well. Is it possible for the entire chessboard to get infected eventually?
The total perimeter of the infected regions never increases. If there are 7 infected cells initially, their total perimeter is at most 28. The perimeter of an 8×8 square is 36. Therefore it is impossible to infect the entire chessboard.