A rectangle
is partitioned in several (
) rectangles with sides parallel to those of
. Given that any line parallel to one of the sides of
, and having common points with the interior of
, also has common interior points with the interior of at least one rectangle of the partition; prove that there is at least one rectangle of the partition having no common points with
's boundary.
Author: unknown author, Japan
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
![\ge2](/media/m/c/e/2/ce2927c87c4cbd454aaf32fbc920b51a.png)
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
Author: unknown author, Japan