MathDB

A polygon (not necessarily convex) on the coordinate plane is called plump if it satisfies the following conditions:

\bullet

coordinates of vertices are integers;

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each side forms an angle of

0^\circ

90^\circ

, or

45^\circ

with the abscissa axis;

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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)

Problem Statement