olymmath

RU-ALLRUSSIAN 1973 Problem 8

    At time 1, n unit squares of an infinite sheet of paper ruled in squares are painted black, the rest remain white. At time k+1\mathrm{k + 1} , the color of each square is changed to the color held at time k by a majority of the following three squares: the square itself, its northern neighbour and its eastern neighbour. Prove that all the squares are white at time n+1\mathrm{n + 1} .

    Dataset text NuminaMath olympiads. Quoted with source.

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