Solutions of simple motion planning problems inoling collections of orthogonal rectangles in the plane, and orthogonal boxes in 3-dimensional space are described. Proofs of seeral theorems regarding collision-free translation properties of these objects are deried. A new elementary simple proof is gien that for each quadrant in the plane, eery collection of orthogonal rectangles admits precisely one ordering that is alid for collision-free translation of the rectangles in eery fixed direction contained in that quadrant. In addition, it is proed that for eery configuration of n greater than 3 orthogonal rectangles in the plane, at least four of them hae the property that each can be translated independently to infinity in some direction, without disturbing the other n-1 rectangles. The proofs are elementary, and therefore suitable for motiating undergraduate computer science students in courses on discrete mathematics. A list of more challenging adanced problems is also proided.