ASU 181 All Soviet Union MO 1973 black colour in an infinite board
Source:
July 4, 2019
combinatoricsinfinite board
Problem Statement
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 -th move