You choose n squares to be black on a 8x8 chessboard. The rest will be white. Every turn, all squares that have 2 or more black neighbors will turn black. All squares that were blackk the previous turn will stay black. all other squares stay white.

a) Prove that the whole board cannot be made all black in finitely many turns if n < 8.
b) Find all choices of 8 squares such that the chessboard can be made all black in finitely many turns.
c) Find the smallest possible n such that it is not possible for the chessboard to be made all black.

GEneralize!