Since nobody was fascinated by this puzzle like I was, I'll just hand out the inner workings. Has anyone ever showed you a few shapes on a piece of paper and said "Try to draw this without lifting your pencil"? (And without drawing a line you already drew) This is exactly the same thing!

The explanation is a bit dry, but here it is, for those who are mathy. The map is based on something called graph theory, which is based on networks of nodes (dots) connected by lines. In my map, the intersections are nodes and the gold chambers are the lines. Nodes have either an odd or an even degree, meaning that either an odd or an even number of paths connect to it. One little facet of graph theory says that if you want to traverse every line in the network only once with one continuous path, then that network must have either 0 or 2 odd-degree nodes, and if it has 2, then you must begin the path on one of the odd-degree nodes (and it will end at the other one). The middle section of the map is just a way to force the player to start in any one of four places. Note that one of those four places is an intersection from which you can only get to three gold chambers - an odd-degree node. Anyway, I like this stuff. Go play other maps now.

So how about that alternative route?