A not necessary nonplanar polygon in $\mathbb{R}^3$ is called Grid Polygon if each of it's edges are parallel to one of the axes. (a) There's a right angle between each two neighbour sides of the grid polygon, the plane containing this angle could be parallel to either $xy$ plane, $yz$ plane, or $xz$ plane. Prove that parity of the number of the angles that the plane containing each of them is parallel to $xy$ plane is equal to parity of the number of the angles that the plane containing each of them is parallel to $yz$ plane and parity of the number of the angles that the plane containing each of them is parallel to $zx$ plane. (b) A grid polygon is called Inscribed if there's a point in the space that has an equal distance from all of the vertices of the polygon. Prove that any nonplanar grid hexagon is inscribed. (c) Does there exist a grid 2014-gon without repeated vertices such that there exists a plane that intersects all of it's edges? (d) If $a,b,c \in \mathbb{N}-\{1\}$, prove that $a,b,c$ are sidelengths of a triangle iff there exists a grid polygon in which the number of it's edges that are parallel to $x$ axis is $a$, the number of it's edges that are parallel to $y$ axis is $b$ and the number of it's edges that are parallel to $z$ axis is $c$. Time allowed for this exam was 1 hour.