Two black neighbours implies black
Q: Consider a 10 × 10 array of white squares. Colour some initial
set black. Now, if a square has two black orthogonal neighbours, colour
it black. Repeat as much as possible. Show that if the initial set has 9
squares we cannot end with the whole array black.
Dima Fon-Der-Flaass, 24 Feb 1997
Q: More generally, find the minimum initial # blacks required to turn an m × n array black.