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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.

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  • 1
    $\begingroup$ Very interesting question! I added a few tags for you. $\endgroup$ – Rewan Demontay Nov 26 '19 at 5:19
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    $\begingroup$ Aside: Wow is there really a Douglas and a Fairbanks in Alaska out of only about 42 towns? $\endgroup$ – Weather Vane Nov 26 '19 at 10:18
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Here's a list that satisfies the rule that upon entering a state, you are forced to choose a town with a strictly different name

Ocean View, Hawaii
Ocean View, Delaware
Lincoln, Delaware
Lincoln, Rhode Island
Hope, Rhode Island
Hope, Alaska
Douglas, Alaska
Douglas, Wyoming
Dayton, Wyoming
Dayton, Nevada
Paradise Valley, Nevada
Paradise Valley, Arizona
Picacho, Arizona
Picacho, New Mexico
Clayton, New Mexico
Clayton, Idaho
Lewiston, Idaho
Lewiston, Utah
Richmond, Utah
Richmond, Vermont
Woodstock, Vermont
Woodstock, New Hampshire
Danbury, New Hampshire
Danbury, Connecticut
Chester, Connecticut
Chester, Montana
Jackson, Montana
Jackson, South Carolina
Jefferson, South Carolina
Jefferson, Oregon
Portland, Oregon
Portland, North Dakota
Colfax, North Dakota
Colfax, Washington
Manchester, Washington
Manchester, Maryland
Aberdeen, Maryland
Aberdeen, South Dakota
Bristol, South Dakota
Bristol, Florida
Venice, Florida
Venice, Louisiana
Jamestown, Louisiana
Jamestown, Colorado
Georgetown, Colorado
Georgetown, Mississippi
Liberty, Mississippi
Liberty, Maine
Princeton, Maine
Princeton, New Jersey
Florence, New Jersey
Florence, Massachusetts
Pocasset, Massachusetts
Pocasset, Oklahoma
Cherokee, Oklahoma
Cherokee, Alabama
Lafayette, Alabama
Lafayette, Tennessee
Nashville, Tennessee
Nashville, Arkansas
Salem, Arkansas
Salem, West Virginia
Athens, West Virginia
Athens, Georgia
Omaha, Georgia
Omaha, Nebraska
Aurora, Nebraska
Aurora, North Carolina
Dublin, North Carolina
Dublin, Virginia
Raven, Virginia
Raven, Kentucky
Monticello, Kentucky
Monticello, Wisconsin
Embarrass, Wisconsin
Embarrass, Minnesota
Buffalo, Minnesota
Buffalo, Kansas
Eureka, Kansas
Eureka, California
Harmony, California
Harmony, Indiana
Homer, Indiana
Homer, Michigan
Napoleon, Michigan
Napoleon, Missouri
Stockton, Missouri
Stockton, Iowa
Rome, Iowa
Rome, Ohio
Houston, Ohio
Houston, Texas
White Deer, Texas
White Deer, Pennsylvania
Rochester, Pennsylvania
Rochester, New York
Genoa, New York
Genoa, Illinois

and to get back to the start

Pearl City, Illinois
Pearl City, Hawaii

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  • 2
    $\begingroup$ This is extremely awesome! :) +1 Question: are all the town names different in every transition? $\endgroup$ – João Mendes Nov 26 '19 at 19:26
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It so happens that

There is a town named " Greenville" in every state in the US. So you can go to each Greenville

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    $\begingroup$ There are astounding 88 Washingtons in US! So some states have more than one? Confusing! There are 41 Springfields also $\endgroup$ – DEEM Nov 26 '19 at 13:00
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    $\begingroup$ Is this actually true or an urban legend? $\endgroup$ – Stiv Nov 26 '19 at 13:04
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    $\begingroup$ In many states towns are named but not incorporated like Greenville in Oregon. I think the puzzle would be more defined if it says "City names only" $\endgroup$ – DEEM Nov 26 '19 at 13:10
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    $\begingroup$ en.wikipedia.org/wiki/List_of_the_most_common_U.S._place_names only lists 31 Greenvilles. $\endgroup$ – Herb Wolfe Nov 26 '19 at 16:35
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    $\begingroup$ @DEEM New Jersey has a "Washington Township" and a "Township of Washington". $\endgroup$ – Kevin Thibedeau Nov 26 '19 at 21:01

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