From Erich Friedman. Tour the 48 states, without repeating a state.
Well -- Maine has to be either first or last. Assuming it's first, then
ME-NH-VT-MA-RI-CT-NY have to be 1-7, because NY can't be crossed twice and
no other pattern exhausts the six states locked behind it. From there,
there are only two patterns -- PA-WV-KY or PA-OH-KY -- that get to TN in
time. Starting from the end, then -- NJ will have to be the last state,
because there's only one way into it. So, to clear out the states
backwards, NJ-MD-WV-VA-NC-SC-GA-FL-AL-MS-LA-TX gets us down to AR's 35. Now
it's just a matter of getting from WY to AR, and there's only one pattern
which will do that:
SD-IA-IL-IN-MI-WI-MN-ND-MT-ID-WA-OR-CA-NV-UT-AZ-NM-CO-KS-OK. Since I assume
the answer is unique, ME's first.
I should note that, as a former resident of dem parts, I'm very happy that
the puzzle required crossing the Mackinac Bridge.
Take care --
Missouri is no. 12, and Nebraska is no. 13. Also, Maine is either no. 1 or
If Maine were no. 48, then New York must be no. 42. But one cannot travel
from Arkansas to New York in seven states, travelling south around
Tennessee. Therefore, Maine is no. 1, and New York is no. 7.
One cannot travel from New York (no. 7) through New Jersey (no. 8) and get
to Tennessee as no. 11. Therefore, Pennsylvania is no. 8.
Now, New Jersey is either no. 9 or no. 48 (for the same reasons Maine was
either no. 1 or no. 48). New Jersey and Tennessee do not border a common
state, and therefore New Jersey cannot be no. 9.
Therefore, New Jersey is last.
Editorial comments as to the appropriateness of this solution will be
New England must be traversed either first or last.
The constrained route TN-MO-NE-WY precludes reaching
New England from AR in sufficient moves, so New
England must be first. Getting to TN as the 11th
state requires the route NY-PA, which forces NJ to
be the last state.
The last state is New Jersey:
New Jersey must be the last state.
The tour must begin or end in Maine.
It cannot end there, because you cannot get there from Arkansas being
35th without either cutting off states or running through Missouri, which
is needed for the 11-14 link.
So it begins there, and as described previously, New York is the 7th state.
>From NY, you can go to either Pennsylvania or New Jersey as the 8th state,
but if you go to New Jersey as 8th, there is no way to get to Tennessee
as the 11th state. So Pennsylvania is 8th.
There are a couple paths from there to Tennessee, but all of them leave
New Jersey connected to only one untraveled state, Delaware, so New
Jersey must be at the end of the tour.
Specifically, the tour must visit either Ohio or West Virginia 9th, then
Kentucky, Tennessee, across to Wyoming 14th, then you must go back to
Indiana 18th (and Ohio 19th if you didn't go there already) to avoid
cutting these states off. This time you are forced to go across the
Great Lakes while in Michigan, and you end up at Montana 23rd or 24th.
Then you tour the west, and you must catch New Mexico, Colorado, Kansas,
and all states to the west before you reach Arkansas you you will not be
able to complete the tour. This is too many states if Ohio is 19th, so
it is 9th and Montana is 23rd, and there's still only one way to cover
the west (Utah is 29th). Then you can reach Arkansas 35th and Texas
36th, and complete the tour by traveling along the Gulf and Atlantic
coasts with a small detour to hit West Virginia.
The entire path is forced by 3 states. Erich has found a great tour.
As far as making words from the initial letters of state tours, I didn't
see much likelihood of beating nonunion, as none of the common long
suffixes besides -ion (and not -tion) appear in the grid.
I fed the state adjacency data and a reduced word list that only contains
words of 8 letters of longer made of only the letters that begin the
names of states to a slightly modified version of my boggle solver
(modified to allow repeated states).
Using the ENABLE list, I found only
atomisms by two paths (AR-TX-OK-MO-IA-SD-MT/MN-SD),
Using the allwords file from the NPL site, I found one 9 letter word,
totonacan (NI3, usu. cap.) TX-OK-TX-OK-NM-AZ-CA-AZ-NV/NM,
and a few more repetitive-sounding 8-letter words mostly of dubious validity:
simonton (sounds like a place name) SD-IA-MO-OK-NM-TX-OK-NM
kiwikiwi (NI2, the kiwi bird) KY-IL-WI-IL-KY-IL-WI-IA/IL
matamata (NI3, a turtle and a tree) many paths, not all combinations work,
MS/MO - AR/AL - TX/TN - AR/AL - MS/MO - AR/AL - TX/TN - AR/AL
minimism (NI2) MN/MO-IA-NE-IA-MN/MO-IA-SD-MT/MN
monoamin (NI2 = monoamine) MO-OK-NM-OK-AR-MO-IA-NE
montalto (name of a mountain) MO-OK-NM-TX-AR-LA-TX-OK
mocomoco (NI2, a S. Amer. aroid) MO-OK-CO-OK-MO-OK-CO-OK
incanton (NI2, to form a canton) ID-NV-CA-AZ-NM-TX-OK-NM
altamont (town in Tennessee) AR-LA-TX-AR-MO-OK-NM-TX
coconuco (NI3, usu. cap.) CA-OR-CA-OR-NV-UT-CO-OK
coconino (NI2 cap., a sandstone and a plateau in AZ) CA-OR-CA-OR-NV-ID-OR-NV
totonaco (NI3, usu. cap.) TX-OK-TX-OK-NM-AZ-CA-OR (also totonaca)
tokonoma (NI3) TX-OK-KS-OK-NM-OK-MO-AR
fatagaga (?) FL-AL-TN-AL-GA-AL-GA-AL
wikiwiki (NI3) WI-IL-KY-IL-WI-IL-KY-IL/IN
Not one of these manages to avoid reusing a state.