A connected checkered figure is drawn on a checkered paper. It is known that the figure can be cut both into 2×2 squares and into (possibly rotated) [url=https://upload.wikimedia.org/wikipedia/commons/thumb/3/30/Tetromino-skew2.svg/1200px-Tetromino-skew2.svg.png]skew-tetrominoes. Prove that there is a hole in the figure.Proposed by Y. Markelov and A. Sairanov combinatorial geometrycombinatoricsKvant