MathDB

C4

Part of 2013 Balkan MO Shortlist

Problems(1)

closed, non-self-intersecting broken line drawn on chseeboard, red squares

Source: Balkan MO Shortlist 2013 C4 BMO

3/8/2020
A closed, non-self-intersecting broken line LL is drawn over a (2n+1)×(2n+1)(2n+1) \times (2n+1) 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 LL is a side of some board square. All board squares lying in the interior of LL are coloured in red. Prove that the number of neighbouring pairs of red squares in every row of the board is even.
ColoringChessboardcombinatorics