Fewest Borders, West to East

On January 1, 2009 · 0 Comments - won't you be the first?

Today’s post serves no useful, practical purpose. Check back in a couple of days if you want something more intellectually challenging. Feel free to hang out if you’re still nursing the after-effects of your New Years Eve revelries. Either is fine.

Regular readers know that I sometimes find topics by combing through search terms that visitors use to find this website. Lately I’ve noticed a recurring query that seems to boil down to something like this: "What is the fewest number of states necessary to cross the width of the United States?"

I’m not sure why this matters. Maybe these people have an irrational fear of "Welcome to [insert state name here]" signs. More likely, some middle school teacher put this question on a take-home project over the Holidays and the kids would rather consult the Great Google than pull out a map. Lazy brats. Nonetheless, and in a sense of decency, fairness and generosity, I’ll provide an answer for the masses.[1] It’s SEVEN.

First, some ground rules. The route has to go from ocean to ocean. It cannot leave the Lower 48 and return; no fair cutting up to Vancouver and heading towards Toronto. Colluding with Canada is prohibited. Sneaky Canadians.


West-East Corridors


The only thing that surprised me was the number of different paths that could be taken to produce the minimal number of states. There’s a northern route (WA, ID, WY, NE, MO, KY, VA). There’s a southern route (CA, AZ, NM, TX, AR, TN, GA). There’s a middle route (CA, AZ, CO, KS, MO, TN, NC). There are all sorts of variations, mixes-and-matches, and permutations that accomplish the same thing. The answer is always SEVEN. I think my favorite one involves the Arizona-Colorado route because it squeezes through a single point. This path would have to be done on foot and would require some dexterity to avoid Utah and New Mexico, not to mention some wandering through the desert.



This is NOT the recommended path. I’m clearly slopping into Utah and New Mexico


How many paths provide this solution? A lot. Remember back in school when they gave you that drawing of nested squares and you had to count all the squares and you always forgot to count the one that went all the way around the border? Right. I hated that one too. That’s how I felt when I was trying to figure out the number of paths. Feel free to count them up and post the answer in a comment if "a lot" doesn’t meet your definition of precision. My deductive reasoning skills are a little lacking this morning. I’m sure the Christmas beers last night had nothing to do with it.

The other aspect I found interesting was the way the numbers line up vertically. The individual states are all of various widths and yet they stack so neatly. The natural inclination would be to leverage a really fat state like Texas to get that 850 mile swing from El Paso to Beaumont, and yet it provides no advantage for this exercise. On the other hand it makes a huge difference in the eastern half of the country that is dominated by smaller states. The deep south (except Georgia), New England and much of the Midwest must be avoided. Likewise the Great Basin provides no outlet to the sea, just like the real thing, with Utah and Nevada vanishing from the map.

That’s way more virtual ink than this topic deserved.

[1] Or what passes for masses on the Twelve Mile Circle. Face it, there aren’t too many of us who enjoy these little oddities. We’ve all been there — dragging dubious family members to these geo-quirks and catching all sorts of grief for it. Oh, the indignities we endure.

On January 1, 2009 · 0 Comments - won't you be the first?

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