Question 109
Some cells of a checkered plane are marked so that the figure $A$ formed by the marked cells satisfies the following two conditions:
1) any cell of the figure $A$ has exactly two adjacent cells of $A$; and
2) the figure $A$ can be divided into isosceles trapezoids of area $2$ with vertices at the grid nodes (and acute angles of the trapezoids are equal to $45^\circ$).
Prove that the number of marked cells is divisible by $8$.
( A. Yuran )
1) any cell of the figure $A$ has exactly two adjacent cells of $A$; and
2) the figure $A$ can be divided into isosceles trapezoids of area $2$ with vertices at the grid nodes (and acute angles of the trapezoids are equal to $45^\circ$).
Prove that the number of marked cells is divisible by $8$.
( A. Yuran )