Question 58
On a $8 \times 8$ chessboard, a non-self-intersecting closed broken line is drawn; its vertices are the centers of the cells, and each segment connects the centers of two cells sharing a common point (in particular, they may share a common side). This broken line bounds a polygon $P$. Prove that the total area of white parts of $P$ equals the total area of black parts of $P$. (D. Khramtsov)