Seven cases of a chessboard $(8 \times 8)$ are on fire. At each step, a case catches fire if at least two of its neighbors (by a side, not a corner) are on fire. Is it possible for the fire to spread everywhere? If not, how many cases initially on fire are needed at a minimum for the fire to be able to spread everywhere?
We can show that the perimeter of the burning area decreases at each step. Therefore, the fire cannot spread to the entire chessboard (perimeter of 32 if the squares have a side of 1) from seven burning squares (maximum perimeter of 28). At least eight squares are needed: if all the squares of a major diagonal are initially burning, the fire will be able to spread everywhere.