Checkered figure must have a hole
Source: Kvant Magazine No. 10 2020 M2625
March 9, 2023
combinatorial geometrycombinatoricsKvant
Problem Statement
A connected checkered figure is drawn on a checkered paper. It is known that the figure can be cut both into 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