A square is divided into rectangles.
A "chain" is a subset K of the set of these rectangles such that there exists a side of the square which is covered by projections of rectangles of K and such that no point of this side is a projection of two inner points of two inner points of two different rectangles of K.
(a) Prove that every two rectangles in such a division are members of a certain "chain".
(b) Solve the similar problem for a cube, divided into rectangular parallelopipeds (in the definition of chain , replace "side" by"edge") . (A.I . Golberg, V.A. Gurevich) geometryrectanglecombinatoricscombinatorial geometryprojectionparallelepiped3D geometry