closed, non-self-intersecting broken line drawn on chseeboard, red squares
Source: Balkan MO Shortlist 2013 C4 BMO
March 8, 2020
ColoringChessboardcombinatorics
Problem Statement
A closed, non-self-intersecting broken line is drawn over a chessboard in such a way that the set of L's vertices coincides with the set of the vertices of the board’s squares and every edge in is a side of some board square. All board squares lying in the interior of are coloured in red. Prove that the number of neighbouring pairs of red squares in every row of the board is even.