n squares of the infinite cross-lined sheet of paper are painted with black colour (others are white). Every move all the squares of the sheet change their colour simultaneously. The square gets the colour, that had the majority of three ones: the square itself, its neighbour from the right side and its neighbour from the upper side. a) Prove that after the finite number of the moves all the black squares will disappear. b) Prove that it will happen not later than on the n-th move combinatoricsinfinite board