Let $P$ be a $2016$ sided polygon with all its adjacent sides perpendicular to each other, i.e., all its internal angles are either $90^o$ or $270^o$. If the lengths of its sides are odd integers, prove that its area is an even integer.
Problem
Source: Singapore Senior Math Olympiad 2016 2nd Round p4 SMO
Tags: Integer, geometry, integer area, integer sidelengths, perpendicular