MathDB

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)

Problem Statement