There was a rook at some square of a 10×10 chessboard. At each turn it moved to a square adjacent by side. It visited each square exactly once. Prove that for each main diagonal (the diagonal between the corners of the board) the following statement is true: in the rook’s path there were two consecutive steps at which the rook first stepped away from the diagonal and then returned back to the diagonal.Alexandr Gribalko boardChess rookTournament of TownscombinatoricsKvant