Question 160
A square is dissected into $n\gt 1$ rectangles such that the sides of the rectangles are parallel to the sides of the given square. Every line that is parallel to one of the sides of the square and meets the interior of the square is also required to run through the interior of at least one of the rectangles.
Prove that in such a dissection there is always a rectangle that has no point in common with the boundary of the square.
Prove that in such a dissection there is always a rectangle that has no point in common with the boundary of the square.