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Two black neighbours implies black

Q: Consider a 10 x 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 x n array black.


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