I spent quite a long time searching for a solution to this problem. I drew tons of cross-hatched triangles, counted the triangles in simple cases, and searched for some sort of pattern. Unfortunately, I hit the wall. I'm pretty sure my programming/math skills did not meet the prereq for this problem.

So I found a solution online in order to gain access to the forums. I didn't understand most of the methods at all, and some just seemed too complicated.

Can anyone give me an understanding of this problem? One of the methods, found here: http://www.math.uni-bielefeld.de/~sillke/SEQUENCES/grid-triangles (Problem C) allowed for a single function to be used.

How did they come up with that solution? At this point, I'd really just like to understand some of the concepts behind this interesting problem. I know looking up the solution was not part of the Euler spirit, but I'm fairly sure I would not have solved this problem anyhow.