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I just thought of this one while on a recent Amtrak trip from DC to NYC: You can travel through 6 states on a trip of less than 200 miles (MD, DE, PA, NJ, NY, and CT) between Elkton, MD and Greenwich, CT, following the I-95 corridor. You can travel entirely within a single state on a trip of 1,071 miles (from Prudhoe Bay to Homer, AK -- yes, there is a road connection!)
UPDATE -- I was curious so I tried this on Google Maps: if you travelled from the southernmost point on I-95 in Maine and went the same 1,071 miles of the Prudhoe Bay to Homer, Alaska trip you would end up in Georgia, near Savannah (approximately). That would give a trip encompassing ME, NH, MA, RI, CT, NY, NJ, PA, DE, MD, VA, NC, SC, and GA for a total of 14 states.
<>UPDATE -- I was curious so I tried this on Google Maps: if you travelled from the southernmost point on I-95 in Maine and went the same 1,071 miles of the Prudhoe Bay to Homer, Alaska trip you would end up in Georgia, near Savannah (approximately). That would give a trip encompassing ME, NH, MA, RI, CT, NY, NJ, PA, DE, MD, VA, NC, SC, and GA for a total of 14 states.
IIR, you can travel all 48 States without crossing any border twice if you start in Maine. I'm not sure how to verify that one.
While Niagara Falls is the best-known falls in New York, it is not its highest falls. That honor belongs to Taughannock Falls, in the Finger lakes region of the state.
Pensacola, Florida is closer to Baton Rouge than it is to Jacksonville or Orlando.
Alaska actually stretches pretty far south and many parts of Alaska have winters that are less brutal than the Great Lakes area.
Also most people will think that southeast Alaska is the southernmost point, which goes down to 54.6N which is right around the Danish/German border. However the actual southern most point is way to the west in the Aleutian Islands which goes even further south down to 51.2N which is just a bit south of London or a bit north of Vancouver Island.
IIR, you can travel all 48 States without crossing any border twice if you start in Maine. I'm not sure how to verify that one.
Well, if I were more ambitious, I would translate the bordering relationships of the US states into a mathematical graph and then verify whether that graph had a Hamilton path. If you are unfamiliar, in graph theory, a graph is simply a set of two different types of elements. There are elements called vertices (singular, vertex) that form the basis of the graph. Each vertex may (or may not) be connected to any other given vertex by an edge. The graph is simply the set of all the vertices and edges. A graph is said to have a Hamilton path if it is possible to travel from a given vertex to all of the other vertices without travelling along any edge more than once.
The application to this problem is obvious; each state would be a vertex, and an edge would exist between any two states that share a border. For example the vertex labeled ME would be connected by an edge only to NH. NH would be connected to VT, MA, and ME, and so on. Technically the vertices labeled HI and AK would have no edges connecting them to other vertices. (In graph theory terms, this graph of US states is called "disconnected" and those vertices are referred to as "isolated"). The other 48 vertices would all have connections, and it is certainly possible to pass from any given one of those 48 to any other by travelling along the edges. This part of the graph is called a subgraph, and this particular subgraph is called connected (which means just what you think it does, namely that there are edges that connect any vertex to any other).
UPDATE: All that abstraction may be interesting to some, but is not necessary. I believe I have verified the claim by the simple expedient of finding such a path. ME, NH, VT, MA, RI, CT, NY, NJ, PA, DE, MD, WV, VA, NC, SC, GA, FL, AL, MS, TN, KY, OH, IN, MI, WI, IL, MO, AK, LA, TX, OK, KS, NE, IA, MN, ND, SD, MT, WY, CO, NM, AZ, UT, ID, WA, OR, CA, NV would be one such path. I have not only found one that doesn't cross the same border twice, but in addition one that does not visit the same state twice. I am sure that there are many other paths that meet the original requirement.
Yuma, Arizona is less than 100 miles away from the Gulf of California. The state just barely missed having a coast.
The southernmost area of Arizona is also farther south then the northernmost point of the Gulf of California.
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