NCPC 2010 Problem E - Doodling

Hi! This is my first ever post so any criticism on the overall structure or layout of this post is greatly appreciated.

As far as the post itself it is concerned, I am having a hard time figuring out the explanation for the problem “Doodling” which featured in the NCPC 2010 Problem set.

The problem set - Redirecting…

Solution sketches - Redirecting…

Could someone please explain, in a more understandable manner, the second paragraph of the solution explanation for “Doodling” that is provided in the solution sketches. I am not able to grasp as to what “sequences” they are referring to when they say “Each sequence from the left to the right edge intersects each sequence from the upper to the lower edge exactly once”.

Any help would be highly appreciated.

Thank you!