I guess what I am saying is that you don't check the suns position when your watch strikes noon, you check the clocks time (set to GMT) at the sun's apex to fix your longitude, so knowing when noon is where you are doesn't really do much for you. Maybe that's so elementary that it's taken for granted here, but I'm not sure most newbies would understand that right off the bat.

I think it's also important to note that being off by just a handful of seconds in your noting the sun's apex can cause an error of miles in your calculations. As it pertains to backpacking, being off a minute could easily fix your location off your map.

I like your gold coin exercise. Finding the shortest route is a great exercise in logic. Check out Dijkstra's algorithm.