Question 101
A checkered polygon $A$ is drawn on the checkered plane. We call a cell of $A$ *internal* if all 8 of its adjacent cells belong to $A$. All other (non-internal) cells of $A$ we call *boundary*. It is known that 1) each boundary cell has exactly two common sides with other boundary cells; and 2) the union of all boundary cells 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 area of the polygon $A$ is congruent to $1$ modulo $4$.
( A. Yuran )
Prove that the area of the polygon $A$ is congruent to $1$ modulo $4$.
( A. Yuran )