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[Puzzleblogger Kevan Choset, July 22, 2005 at 12:16pm] Trackbacks
Three Countries in a Row:

The Final Jeopardy! clue a few weeks ago was the following:

On the Globe

Moving west from Canada, the next 3 countries through which the Arctic Circle passes

For the answer, click below:

(show)

My challenge for you is this: There is a place in the United States where, if you travel in a straight line in one of the four cardinal directions, the first three foreign countries you hit will all start with the same letter of the alphabet. Where is that place, what direction must you travel, and what are the three foreign countries?

james b (mail) (www):
The location is Detroit, MI.

To the East is Canada.
To the North is Canada.
To the South is Canada.
7.22.2005 1:21pm
William Spieler (mail) (www):
Hawaii; east; Mexico, Mauritania, Mali
7.22.2005 1:22pm
Seamus (mail):
If you go east from around Miami, I believe you will strike, in order: Morocco (people might quibble on the grounds that Morocco's annexation of the former Western Sahara hasn't been recognized internationally), Mauretania, Mali.
7.22.2005 1:24pm
Nick (www):
If you travel south from Florida, you'll hit Cuba, the Caman Islands, then Costa Rica.
7.22.2005 1:24pm
dave finberg (mail):
Assuming a generous definition of the word south, it looks like you can start in alabama at around 83 degrees, and head south to cuba, costa rica, and canada.
7.22.2005 1:25pm
Seamus (mail):
Looking more closely at the map, I think you'd have to be farther south than Miami. Maybe Key West would work. It's latitude is 24° 33′ 33″ N, and the northernmost part of Mali is 25° N.
7.22.2005 1:27pm
Kevan Choset (mail):
On the two suggested answers involving Mauritania and Mali:
From Hawaii, I don't believe you can get to Mauritania without passing through either Cuba or Haiti/Dominican Republic. Could you provide a latitude at which this works?

From Miami, I don't believe you can pass through both Morocco and Mauritania. No part of Morocco seems to be west of any part of Mauritania. Again, could you provide a latitude?
7.22.2005 1:29pm
Kevan Choset (mail):
On the Cuba, Cayman Islands, Costa Rica suggestion:
I believe that all of the Caymans are east of Costa Rica, so you cannot go due south from one to the other. Again, could you provide a longitude?

On the "generous definition of the word south" suggestion:
Even if you were to keep following that line straight down through Antarctica and then come back up the other side, you wouldn't magically appear in Canada. You'd have to first come up through Asia, hitting approximately India or Bangladesh next.
7.22.2005 1:36pm
timekeeper (mail) (www):
For the Mauretania/Morocco suggestions, one must include the Spanish Sahara as part of Morocco. It's been annexed by the Moroccans, but the annexation has not been formally recognized by most of the world. (Spain pulled out in 1976, but there was no plan in place to set up an independent government when they left; the Moroccans and Mauritanians moved in, and the Mauritanians left a few years later. The Moroccans then took over the rest of the territory.)

Without that caveat, it won't work.
7.22.2005 1:39pm
Seamus (mail):
All of Western Sahara (formerly Spanish Sahara), which was annexed by Morocco in 1976 and 1979, is west of Mauritania (which I mispelled last time). As I pointed out, and timekeeper confirms, you have to count it as part of Morocco for the Morocco-Mauritania-Mali answer to work.

For a while, I thought you could avoid the Caymans and Haiti/Dominican Republic by using a lower latitude, but in fact if you go south far enough to avoid those countries, your route ends up passing through Belize (and maybe through one of the Antilles on the other side of the Caribbean).
7.22.2005 1:45pm
senor chumbawumba:
The first poster was right, but for different countries.

Go south from Detroit, and you'll hit Canada, Cuba, and Costa Rica.
7.22.2005 1:47pm
Kevan Choset (mail):
Setting aside the Morocco-Mauritania-Mali answer, which I guess depends on whose view of the world you want to accept, I have another solution in mind that is politically non-controversial.
7.22.2005 1:49pm
Kevan Choset (mail):
Senor Chumbawumba's got it. Can anyone provide an exact longitude that works?

Any other alternative solutions are welcome.
7.22.2005 1:53pm
Paul.H (mail):
W83 works
7.22.2005 2:16pm
Alec (mail):
South from about Talahassee, I think you will hit Cuba, Costa Rica, and Chile (San Fernandez Island).
7.22.2005 2:32pm
Solon Brochado (mail) (www):
I'm not sure how reliable these are, but we have:

Detroit's Wayne County Metropolitan Airport at 083° 20' 55" W. Then, a map of Costa Rica shows us that the southernmost border of the country is to the E of 082°. And this map of Cuba shows Castro's island to span from about 074° to pretty much 085° territory.

So, I'd say that 083° 20' 50" W would work just fine. (I guess no one needs evidence for Canada, right? hehe).
7.22.2005 2:40pm
Anthony (www):
From the right place near 81W longitude, one passes through Cuba, the Cayman Islands, and San Andres y Providencia, a part of Colombia. So do colonies of the UK count as "countries"? San Andres y Providencia is an integral part of Colombia.
7.22.2005 3:07pm
Paul.H (mail):
Unfortunately, 83d 20' 55" catches the corner of both Honduras and Nicaragua. You have to start further east.
7.22.2005 3:09pm
Paul.H (mail):
Plus, 83d 20' 50" is so far west that it misses Canada.
7.22.2005 3:13pm
Joe White (mail) (www):
Big Bend National Park in Texas borders Mexico to the west, south, and east
7.22.2005 3:23pm
Bob Woolley (mail):
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No, it's to the E of 83, not 82.

Nertheless, I think your answer is otherwise correct. Best I can estimate from my Natl. Geo. world atlas, a line straight south from Detroit misses the land mass of Honduras/Nicaraugua by about 10-15 miles, and runs into Costa Rica.
7.22.2005 4:29pm
Saucy:
The only way to get through Morocco, Mauritania and Mali would take you through the bahamas from florida, Getting to Mauritania and Mali from Mexico is blocked in many places (starting at hawaii), and starting at puerto rico you'll miss morocco. I'm stumped
7.22.2005 4:33pm
Bob Woolley (mail):
Google Earth has a spot in what appears to be downtown Detroit as the place it homes in on when you enter "Detroit," and says that it is at 83 02'44.99 W.

OK, I just proved it to myself. I put that marker at the center of the screen, and had Google Earth (a *very* cool tool, BTW) keep flying me south. Went through Canada, Cuba, missed Nicaragua/Guatemala's eastern edge, and landed in Costa Rica, right in the suburbs of Limon.

Case closed.
7.22.2005 4:54pm
Seamus (mail):
¡Caramba! I forgot about the Bahamas.
7.22.2005 4:56pm
Brian WWWW (mail) (www):
The hundreds of islands and state of Hawai'i extend pretty much out to Guam so finding an appropriate latitude to cross Mexico north of Cuba and head out to Morocco and Mauritania is not problematic. Threading your way through the Bahamas might be trouble, though.

I think we may be able to find four inn a row through Canada, Cuba, Costa Rica, and Chile, though. There are a few off-shore islands that look to be right in the way.

Any access to Costa Rica is going to have trouble with the Nicaraguan offshore islands, though.
7.22.2005 5:30pm
Steve:
By the way, it's fun to be a Detroiter, and tell people you live north of Canada.
7.22.2005 5:50pm
Hayek:
Uhm, maybe I'm dense, but if you go South from Detroit, don't you hit: Canada, United States of America, . . . ?
7.22.2005 7:03pm
Bob Woolley (mail):
Yeah, so?

You might want to read the puzzle again....
7.22.2005 7:38pm
Syd Henderson (mail):
He specified foreign countries.
7.22.2005 7:38pm
Greg S (mail):
Cool puzzle. My first thought was Cuba, Canada, China, but it looks like you can't get to Asia without going through Mexico. (Yes, read the question - looking for three different directions.) How about from Houston, go east to Morocco, south and west to Mexico...
7.22.2005 10:23pm
Greg S (mail):
I stand self-corrected and chagrined! it is in three countries in one direction. Ah, but now we have a second cool puzzle!
7.22.2005 10:27pm
Dr. Weevil (mail) (www):
Do territories count? If you start a little west of Juneau, Alaska and head south along the 135 W longitude line, you eventually cross the Marquesas Islands (French territory: Gambier I. is very near the line), then Antarctica (doesn't count), then (coming up the 45 E longitude) Madagascar, aka Malagasy Republic, then Mayotte (another French territory). That's three M's in a row, though only one is an independent country -- at least according to my map, which is recent enough to include Slovakia and Slovenia as independent countries.
7.23.2005 1:42am
Edward Lee (www):
Actually, if you headed east or west from a certain point and walked in a "straight" line, you'd be walking along a great circle, not a line of latitude. (The Final Jeopardy clue specifically says "going along the Arctic Circle", but Kevan's puzzle says "straight" line.)

Given this alternative interpretation, are there any other solutions?
7.23.2005 12:35pm
Bob Woolley (mail):

Actually, if you headed east or west from a certain point and walked in a "straight" line, you'd be walking along a great circle, not a line of latitude. (The Final Jeopardy clue specifically says "going along the Arctic Circle", but Kevan's puzzle says "straight" line.)


I don't see how you reach that conclusion. In spherical geometry, lines of latitude, longitude, and great circle paths are all straight lines (or as straight as lines on a curved surface can be).

Why do you think that walking along the Arctic Circle does not trace a straight line, but walking along a great circil does?
7.23.2005 7:36pm
Mike Friedman (mail):
Lines of longitude are great circles.

Lines of latitude are not straight lines. If they were you could have more than one line defined by two points and all versions of non-Euclidean geometry prohibit that.
7.24.2005 12:01am
Bruce Hayden (mail) (www):
I need to review non-Euclidean geometry. It has now been, I think, 35 years since I took the class. One of the best classes I took in college - I spent the entire term doing "let's pretend".

I guess really what is at issue here is the definition of "east". Not quite as bad as defining "is", but still. I see two different definitions. One is that east means progressing along a latitude line. The second one is to proceed in a direction orthogonal to the Great Circle formed by the two (actual) poles and the designated location (and the center of the Earth, hopefully). And proceeding orthoginal to this Great Circle would appear to be another Great Circle, and not the latitude line.

But, of course, this entire discussion of Great Circles ignores one of the simplifications that we invariably apply to this sort of thing. The Earth is, in fact, not a sphere, but rather is slightly flattened on top and bottom, bulging a bit in the center, presumably due to centripital force. So, in fact, the only actual Great Circle we have is the Equator. The rest are Great Elipses.
7.24.2005 11:24pm
Bruce Hayden (mail) (www):
Whoops, seems that I inadvertantly cut out some definitions I had.

Latitude - "an imaginary line around the Earth parallel to the equator"

Longitude - "an imaginary great circle on the surface of the earth passing through the north and south poles at right angles to the equator; 'all points on the same meridian have the same longitude'"

Great Circle - "Circle formed by the intersection of a sphere and a plane that passes through the center of the sphere", but also "A line on the earth's surface, the plane of which passes through the centre of the globe. This shortest distance between two points on the sphere is also known as an orthodrome."

East - "the cardinal compass point that is at 90 degrees", but also "is the direction in which the Earth rotates about its axis"

Note that arguably the two different definitions of East here give two different results. The first would seem to describe a Great Circle, whereas the second, a line of latitude.
7.24.2005 11:30pm
Bruce Hayden (mail) (www):
Flogging this to death, but the problem is that we live in what appears to us a flat world. That is what we call "Euclidian" space. And in Euclidian space, the orthoginal to a line forms equal angles.

But we actually live on a planet that is typically simplified as being a sphere. And the geometry of the surface of a sphere is different - it is a non-Euclidian geometry. And there, the definition of orthoginal results in another Great Circle cutting the center of the sphere. But that means that it does not follow the latitude lines, but rather loops around the Earth dipping below the Equator on the other side the same distance that the subject point is above (or visa versa).

So, I would suggest that if you define East as being orthoginal to a line between the poles running through the subject location, it is a Great Circle. But the sun doesn't rise in that way. Rather, if you define the term based on the direction in which the sun rises, you would use latitude instead.
7.24.2005 11:44pm
Bob Woolley (mail):
Remember the old question, "What happens when an irresistible force meets an immovable object?" Well, the answer is that in a universe in which there is an irresistible force, by definition there cannot exist an immovable object, and vice-versa.

Here, the puzzle gave us certain parameters, specifically: "...travel in a straight line in one of the four cardinal directions...."

The puzzle thus inhabits a universe in which travel in any of the four cardinal directions is, by definition, travel along a straight line. Traveling east or west along a line of latitude, then, is by definition travel in a straight line--great circles be damned.

BTW, I understand that spherical directionality is a matter of hot debate in some Muslim circles (no pun intended). There are proponents of "facing" Mecca as defined by latitude and longitude from where one is (e.g., in Minnesota one would face roughly ESE), and equally insistent opponents who claim that the only true way is to use great circle routes (which in Minnesota would mean facing roughly NE).

Which is, I suppose, no more intrinsically peculiar a debate than Christians killing each other over whether the holy spirit proceeds from just the father, or from the father and the son (filioque), with 1000 years of schism resulting. Both of them strike me rather like flat-earthers arguing whether the flat earth is circular or square....
7.25.2005 3:55am
Bruce Hayden (mail) (www):
Actually, I might disagree with the above, since in non-Euclidian geometry, the straight line would be the Great Circle and not the latitude line, plus, as I pointed out before, East and West are somewhat ambiguous terms here. Or, more precisely, the Four Cardinal Directions are ambiguous because of the ambiguity of East and West.
7.26.2005 9:38pm