Question 152
A polygon (not necessarily convex) on the coordinate plane is called plump if it satisfies the following three conditions:
* coordinates of all vertices are integers;
* each side forms an angle of $0^\circ, 90^\circ$ or $45^\circ$ with the abscissa axis;
* internal angles belong to the interval $[90^\circ, 270^\circ]$.
Prove that if a square of each side length of a plump polygon is even, then such a polygon can be cut into several convex plump polygons.
(A. Yuran)
* coordinates of all vertices are integers;
* each side forms an angle of $0^\circ, 90^\circ$ or $45^\circ$ with the abscissa axis;
* internal angles belong to the interval $[90^\circ, 270^\circ]$.
Prove that if a square of each side length of a plump polygon is even, then such a polygon can be cut into several convex plump polygons.
(A. Yuran)