Imagine a grid of size n x n of squares, where each square is colored either white or black. Black spreads as follows: At each step, all the white squares which have at least two black neighbors (where neighbors must share a side – they can not be diagonal neighbors) become black. What is the minimum number of black squares needed at the beginning for the grid to be completely black at some point? (This is from a puzzles Collection by Sophia Yakoubov, January 28, 2019, found in web.mit.edu website).
For $n = 3$, I found 3 and for $n = 4$, I found 7. I am trying to find a recursive relation but am not getting anywhere.
(This is not homework or anything; just challenging myself with nice puzzles!).