I’m new to puzzle solving in a structured way, so please go easy on me, but I thought the following was interesting (sorry if it’s not or seems like grunt work). I came up with this while staring listlessly at a map of the U.S.:
Let's pretend that you were to start in some town in some U.S. state, say Douglas, Alaska, and then successively move to either a different town in the same state or to a different state with a town that shares that name. For example, let's say that you go from Douglas, Alaska to Douglas, Georgia to Albany, Georgia to Albany, New York. Can you come up with a route that encompasses all 50 states? What if you’re not allowed to re-enter a state once you’ve left it? Additionally. what if upon entering a state, you are forced to choose a town with a strictly different name than you entered with?
Some things I noticed while doing this:
Hawaii seemed to be a choke point until I saw that Volcano, Hawaii can go to Volcano, California.
Alaska and Rhode Island mostly suck.
I originally wanted Alaska and Hawaii to be the endpoints of the journey, but now I don’t know if that’s necessary (I think Hawaii is).
If you are allowed to jump around on one town name, this becomes much easier (I call this type of town with many states containing towns with that name hub towns).
I’m sorry if I’ve done anything wrong (oh, who am I kidding, I’ve done many things wrong), and of course feel free to correct me.