Bill,

The shortest route in the coin problem is what's called a traveling salesman problem. There are a bunch of fancy formulas, but it's most easily done by what's called "rubberbanding."

Put pins in the map and stretch a long rubberband around the pins. Then grab the inner ones. Whichever route gives the least tension is the shortest.

If I were to teach navigation, I'd start with dead reckoning in an area where bushwacking is easy. I'd lay out a series of points and ask the person to navigate from one to the next using just a compass and pacing. They wouldn't have a map, so topographical features would be useless.

The next step would be to start from a known point and map a trail using dead reckoning.

By this time they will be ready for a Topo map.