Moving shapes to form polygon
Source: 43rd International Tournament of Towns, Junior A-Level P2, Fall 2021
February 18, 2023
combinatoricsTournament of Towns
Problem Statement
On a table there are all 8 possible horizontal bars such that each square is either white or gray (see the figure). It is allowed to move them in any direction by any (not necessarily integer) distance. We may not rotate them or turn them over. Is it possible to move the bars so that they do not overlap, all the white points form a polygon bounded by a closed non-self-intersecting broken line and the same is true for all the gray points?Mikhail Ilyinsky