pageok
pageok
pageok
[Puzzleblogger Kevan Choset, July 26, 2005 at 2:48pm] Trackbacks
Lines Intersecting States:

Reader Corey Lanum poses the following question: There are many places in the US where the shortest line between two points in the same state passes through another state. E.g., a straight line from Duluth to Rochester, MN, passes through Wisconsin. There is one place in the country where you can draw a straight line between two points in the same state and pass through four other states. There is one place where you can pass through three states, and there is another place where you can pass through more than three states. Where are these places?

(There's no funny business like going from Kansas City, Kansas to Topeka, Kansas, by going east and passing through Missouri, Illinois, Indiana, etc., the Atlantic Ocean, Europe, and Asia, before coming back through the Western US. I'm talking about the shortest path between two places.)

Josh Shamburger (mail):
Can we count DC? If so, I think a line from, say, Cumberland to Ocean City in Maryland would probably qualify.
7.26.2005 3:54pm
A. Nonymous (mail):
New York (Plattbsurg area) to New York (Long Island Montauk Point) through Vermont, Massachusettes and Connecticut?
7.26.2005 3:56pm
Guest:
I think travelling from the Northwestern corner to the Southwestern corner of Missouri could drag you through Nebraska, Kansas, and Oklahoma.
7.26.2005 3:59pm
Puzzler:
Fisher's Island, New York? From there to the northeastern part of the state by Lake Champlaign (Plattsburgh area), you go through Connecticut, Massachusetts, possibly clip New Hampshire, and Vermont. Incidentally, from Fisher's Island to the southwestern part of the state by Lake Erie you pass through Connecticut, New Jersey, and Pennsylvania.
7.26.2005 3:59pm
A. Nonymous (mail):
Ok, I am sure NY to NY is the three stater per the above (VT, CT &MA), but I think that you could with a straight line in a sharp angle just clip, JUST clip, Rhode Island for four states by getting some of the islands that jut out from Long Island.
7.26.2005 4:01pm
Nick (www):
Here is one of the three staters:

Block Island, NY to Champlain, NY
Passes through Rhode Island, Connecticut, Mass, and Vermont.
7.26.2005 4:02pm
Angus Dwyer (mail):
To get from Block Island, New York to Petersburg Junction, NY, directly, you have to go through Rhode Island, Connecticut, Massachusetts, and Vermont.
7.26.2005 4:04pm
Kevan Choset (mail):
"Puzzler" has the four-state example. From NY to NY, you can indeed hit Connecticut, Massachusetts, clip New Hampshire, and Vermont. That's the four-state example.

"Guest" has the three-stater: from Missouri to Missouri, passing through Nebraska, Kansas, and Oklahoma.

And Josh Shamburger has the "more than three states" example. Going from Maryland to Maryland, you can pass through West Virginia, Virginia, Delaware (the three states), and DC. Hence, "more than three states." (Though not "four states".)
7.26.2005 4:05pm
Angus Dwyer (mail):
Am moron; Block Island part of Rhode Island. Was thinking of Fishers, which gets you three.
7.26.2005 4:07pm
Nick (www):
Whoops... that was the 4 stater... and I got beat by a few minutes... damn.
7.26.2005 4:09pm
Jacob Lister (mail):
Harper's Ferry, WV to Powhatan Point, WV.
This takes you through VA, WV, MD, and PA.
7.26.2005 4:11pm
Splunge (mail):
A variation on this theme is that there are certain pairs of points in northern Colorado such that the shortest trip between them requires you to pass through Wyoming and Nebraska. Many people would find that surprising.
7.26.2005 4:17pm
uh clem (mail):
Harper's Ferry, WV to Powhatan Point, WV.
This takes you through VA, WV, MD, and PA.


I don't think you can count WV since you start and end there, so that's only a three stater. Good observation, though.

Here's another three-stater: the southern border of Tennesee takes a one mile jog due south at Pickwick Lake (where TN,AL &MS meet) , thus a line from there to a point due south of Chattanooga just inside the Tennessee border would pass through Mississippi, Alabama, and Georgia.
7.26.2005 4:20pm
Kevan Choset (mail):
WV to WV via VA, MD, and PA does indeed work. So that's another three-stater. (We're not counting the extra crossing of WV, since the problem specified passing through "other" states.)

Any other three-, four-, or more-state examples?
7.26.2005 4:20pm
Angus Dwyer (mail):
from the non-contiguous part of westernmost Kentucky (just south of New Madrid, MO), it appears that you have to go through Missouri, Illinois and Indiana to get to the part of Kentucky just south of Evansville, IN. So that's three, assuming my line is straight.
7.26.2005 4:26pm
Random Guest:
Along the lines of Splunge's variation, you could pick points on the south edge of Michigan and the upper segment that would make you travel through Indiana, Illinois, and Wisconsin.
7.26.2005 4:28pm
Justin (mail):
Another 3 state conclusion, tho I can't give you the name of towns, is that you can travel from VA to VA and hit KY, WV, and MD and get back into VA.
7.26.2005 4:28pm
Jacob Lister (mail):
This may be cheating more than you would like, but from Lake Mead, AZ to a point southwest of Yuma, AZ, you can go through Nevada, California, and Baja California.
7.26.2005 4:29pm
Anthony (www):
Point west of Moundsville, WV, to point south of Charles Town, WV. Pass through Ohio (barely), WV, Pennsylvania, WV, Maryland, WV, and Virginia.
7.26.2005 4:40pm
Bill Twist:
I think a four stater is starting in far Western Maryland to the point just South of where Maryland and Delaware meet the Atlantic Ocean, You get MD, WV, VA, (possibly DC), DE, MD. Starting point is 39 deg 43 min North, 79 deg 26 min West. Then go 251 miles at a heading of 111 deg True. You end up in the vicinity of 38 deg 20 min North, 75 deg 09 min West.


Another 3 state conclusion, tho I can't give you the name of towns, is that you can travel from VA to VA and hit KY, WV, and MD and get back into VA.


Not in a straight line you can't. I just tried it using DXATLAS and there is no straight line that starts and ends in VA that goes through all three. Best you can do is VA, KY, VA, WV, VA, WV, VA, WV, VA. Traveling on the road, probably you could.
7.26.2005 4:54pm
Mark (www):
Traveling in a straight line from El Paso, TX, to Brownsville, TX, takes you through the States of: Chihuahua, Coahuila, Nuevo Leon, and Tampaulipas.

Yes, these are Mexican States, but nonetheless I think it qualifies, since it meets the originally stated problem.
7.26.2005 5:03pm
Mark (www):
Oops. Spelled Tamaulipas wrong. Lo siento.
7.26.2005 5:04pm
Splunge (mail):
Then go 251 miles at a heading of 111 deg True.

Hey, that's a loxodrome, not a geodesic!

Although for 0.063 radians what the heck...
7.26.2005 5:24pm
chris:
From the NW point of Maryland to where Maryland meets Delaware on the Atlantic (already mentioned, I know), the line starts in Maryland, goes into WV, from there to VA, back to WV, back to VA, back into Maryland, into Delaware, and finally back into Maryland. So this is a three states (WV,VA and Delaware)
but seven border crossings. This may be a record.

BTW, the line from the tip of Long Island to the NE corner of NY does go through Conn, Mass, NH, and Vermont.
7.26.2005 5:58pm
Anthony (www):
Chris - I think I have you beat with number of border crossings. However, it's rather too easy to rack up large numbers of border crossings along the Mississippi River. There are plenty of places where one can draw a straight line which gets 10 or more border crossings.
7.26.2005 6:03pm
chris:
Anthony - Point conceded.
7.26.2005 6:30pm
Joshua Hosseinof:
From Clymer, NY to Cutchogue, NY you pass through PA, NJ, NY, CT - so that's another three stater.
7.26.2005 7:18pm
dasch (mail):
Another 4-state great-circle solution:

WV-VA-WV-MD-WV-PA-WV-OH-WV. One passes out of West Virginia 4 times to accomplish it.

Start west of Unger, Morgan Co., WV at the WV-VA state line. Travel slightly north of west 134 miles to the bottoms of the Ohio Valley in WV about 3 miles west of Moundsville, Marshall Co.

Try co-ordinates for beginning and end of 39.4648N 78.3450W and 39.9170N 80.7982W.
7.26.2005 7:37pm
karl:
The answer is any place in north jersey to any non-beach location in south jersey since people from jersey will go through every other state in the country before going to any place in south jersey that doesnt have sand.
7.27.2005 12:16am
dasch (mail):
Anthony already has posted the 4-stater I gave above, but here's another 4-state great-circle route from southeast to northeast Missouri:

MO-TN-KY-MO-IL-MO-IA-MO.

Start in a meander loop of the Mississippi R. south of New Madrid, travel 294 miles north and slightly west to a meander loop of the Des Moines River southeast of Francisville, MO.

Try co-ordinates for beginning and end of 36.4759N 89.4854W and 40.4297N 91.5221W.
7.27.2005 12:21am
karl (mail):
Seriously though, the answer could be Detroit to Isle Royale National Park as one could (and perhaps would) go through, Indiana, Illinois, Wisconsin, Minnesota, and Ottawa to get from point a to point b in michigan.

I suspect, however, you were thinking of the Montauk area to any of the towns near the Vermont/Queebec line in NY as others have noted.
7.27.2005 12:22am
Keith Wright (mail):
If you allow yourself to start in the NY water territory off of the tip of long island, I think you can clip RI and NH on your way up to just below the canadian border, making it a 5 stater (RI, CT, MA, NH, VT). From That jutty out part of Minnisota to Browns Valley you can cross trought North and South Dakota, and Manitoba, and be a short distance from Ontario. Thanks to some river bends, illinois can cross missouri, kentucky, and indiana.

Starting from Island #8 on the west tip of Kentucky, to the northern bend of the river above Burlington, Kentucky; you can cross Missouri, Illinois, Indiana, and clip Ohio.
Texas owns a little piece north of the Red river near the Arkansas Oklahoma border, so it is possible to cross Arkansas, Oklahoma and New Mexico by going from there to El Paso.
7.27.2005 1:10am
dasch (mail):
Starting from the same point in the meander loop south of New Madrid mentioned in my previous comment, there is a second 4-state great-circle route in Missouri, this one in a northwesterly direction.

State lines are MO-TN-KY-MO-KS-MO-KS-MO-KS-MO-KS-MO-KS-NE-MO. The multiple passages from MO to KS are due to traverse of the great circle route through meanders of the Missouri River. The end point to the northwest is west of Big Lake in Holt Co., MO.

Co-ordinates that work for beginning and end are 36.4789N 89.4854W and and 40.0280N 95.3895W.
7.27.2005 2:47am
Brian WWWW (mail) (www):
From a Kentucky oxbow east of New Madrid, MO, continue
NE through KY, MO, KY, IL, KY, IN, KY, IN, KY, OH, and KY. Finish at a curve in the Ohio river across from North Bend, OH.

That's four states (besides KY) and even includes both Red and Blue states. I also liked the WV-VA-MD-WV-PA-WV-OH-WV run proposed above.
7.27.2005 2:58am
Bob Woolley (mail):
I disagree with Bill Twist. VA does work, barely. See below. Also, your 4-state solution is really just a 3-state one (WV, VA, MD), assuming we're not counting DC as a state, and you don't count the one in which you start and end.

Karl's suggested 4-stater for Michigan does not work, because the line would never cross any part of Minnesota.
7.27.2005 7:16am
Bob Woolley (mail):
OK, I've spent the last 10 hours on this--I really need to get a life! Actually, I got a new National Geographic World Atlas for my birthday a couple of months ago, and just this week downloaded the wonderful Google Earth software, so this was an ideal puzzle to use as an excuse to explore both tools.

I can contribute 4 more solutions to those given above. There are (so far) 15 total (8 of which I came up with on my own, though 4 of them have been previously posted here, and 7 of which I missed on my own, but gleaned from previous comments here. The new ones are Nebraska, North Carolina, Indiana, and Arkansas.

Although it wasn't in the puzzle specifications, I added the requirement that the start and end points be on land, not on water (it makes a difference!), and that states traversed must also be crossed over land, not just water.

Three of these are 4-state solutions (KY, NY, WV), the rest 3-state. (One is 3 states plus DC.)

The latitude and longitudes listed below are as given by Google Earth. In many (most) cases, there's only a very narrow range of starting and ending points that will work. Others have a pretty wide range, comparitively speaking, but I just picked one spot for each, and used the same degree of specificity whether it was needed or not.

Sorry for the formatting. I don't know any easy way to do a tabular format here. If anybody wants it in a nice Word table, just email me. That's how I compiled it.

Now I hope somebody will archive this, so that nobody ever has to make the list from scratch again! (Well, I admit it was kind of fun.)



State
Starting pt. latitude
Starting pt. longitude
Ending pt. latitude
Ending pt. longitude
States crossed

Arkansas
34d 55m 15.54s N
90d 16m 58.74s W
36d 23m 41.77s N
90d 04m 53.35s W
MS, TN, MO

Illinois
37d 00m 44.61s N
89d 16m 37.28s W
37d 49m 50.52s N
88d 02m 23.43s W
MO, KY, IN

Indiana
38d 52m 29.99s N
84d 47m 09.27s W
41d 45m 36.63s N
84d 48m 21.36s W
KY, OH, MI

Kentucky
36d 37m 01.67s N
89d 20m 47.56s W
39d 08m 30.53s N
84d 45m 01.13s W
MO, IL, IN, OH

Maryland
39d 34m 48.19s N
79d 16m 41.77s W
38d 25m 31.63s N
75d 14m 17.93s W
WV, VA, DE (and DC)

Michigan
46d 20m 47.35s N
90d 06m 17.89s W
41d 42m 09.38s N
84d 47m 50.90s W
WI, IL, IN

Missouri
36d 28m 06.50s N
89d 31m 59.23s W
37d 02m 31.42s N
89d 16m 39.78s W
TN, KY, IL

Missouri
40d 32m 45.03s N
95d 45m 08.95s W
36d 30m 15.45s N
94d 36m 02.40s W
NE, KS, OK

Nebraska
40d 00m 32.52s N
95d 20m 21.73s W
42d 38m 60.00s N
96d 42m 34.15s W
MO, IA, SD

New York
44d 56m 41.97s N
73d 21m 06.40s W
41d 04m 15.93s N
71d 51m 24.41s W
VT, NH, MA, CT

New York
42d 00m 03.29s N
79d 45m 33.21s W
40d 56m 51.80s N
73d 01m 37.52s W
PA, NJ, CT

North Carolina
33d 51m 15.09s N
78d 32m 27.63s W
35d 14m 26.87s N
84d 11m 26.46s W
SC, GA, TN

Texas
31d 56m 19.43s N
106d 33m 50.80s W
33d 38m 37.10s N
94d 27m 19.15s W
NM, OK, AR

Virginia
36d 39m 03.11s N
83d 28m 00.08s W
39d 11m 23.33s N
77d 28m 45.35s W
KY, WV, MD

West Virginia
39d 54m 59.73s N
80d 47m 46.37s W
39d 41m 29.76s N
78d 10m 17.65s W
OH, PA, MD, VA

Notes:
1. The shortest line is Missouri's TN-KY-IL line, 41.97 miles.
2. The Indiana line is exceptionally close. The maximum distance I could create east-to-west included Michigan only in a strip perhaps 30 or 40 yards wide!
3. The first New York line misses Rhode Island by about 1 1/2 miles. If one accepts water, rather than land, as one of the points, then a sliver of RI can be included, making this a five-stater.
4. The Virginia line includes a wedge-shaped piece of Maryland that is only about 1 mile long by 0.1 mile wide, probably 90% of which is water. The line just grazes the edge of land.
7.27.2005 7:35am
karl (mail):
Bob:

Amazingly good. I was thinking "straight line" in the sense of the most direct route driving directions, not a physically straight line, thats what I get for doing a long commute which is why I threw in teh crazy Michigan trip.

For purposes of this question there is a "delicious" curve in the Mississippi river just southwest of Memphis that would appear to permit you to go from TN to AR through a small piece of orther Alabama through an incredibly small sliver (feet if not inches) of Georgia to the most southeast corner of TN. I think that is three states (AR, AL, GA) but the maps I am using could be off by a few hundred meters which would be the difference one way or the other.

Same thing with a curve of the Mississippi north of Tiptonville, TN and southwest of Hickman, KY that strands part of Kentucy to the west of small sliver of Missouri. The IA / MO state line north/northeast of Wayland, Mo makes similiar undulations. Although, again we are talking hundreds of meters one way or another, it appears from the maps I am using that one can go from Mo, through a small portion of TN, KY, MO, IL, and IA.

OK, back to a billable event, Later.
7.27.2005 12:26pm
Bill Twist:
Bob Woolley, you may be right. The software I was using is called DXATLAS, and it is mainly for ham radio contacts. It probably isn't hyper-accurate, and indeed doesn't have to be. Even so, it didn't look close as far as PA goes.
7.27.2005 1:49pm
uh clem (mail):
OK, I've spent the last 10 hours on this--I really need to get a life!

Good job. I was skeptical about several of these, but spot checks of Texas, Virginia, Illinois and Arkansas show that you're right about them.

But, I think you might want to double check Michigan - the line between the two points in Michigan doesn't appear to come anywhere near Illinois. Here's where mapquest puts the endpoints:

http://makeashorterlink.com/?C3671228B
http://makeashorterlink.com/?H5772528B
(Sorry, I don't know how to put both points on one map)

Also, you missed Tennesee:

35d 0m 1s N
88d 12m 30s W http://makeashorterlink.com/?Q1682328B
30d 0m 30s N
84d 30m 0s W http://makeashorterlink.com/?W2881228B
MS,AL,GA

(Note: coordinates are from mapquest, which is kind of buggy sometimes - a better tool will probably provide better accuracy)
7.27.2005 1:56pm
uh clem (mail):
This time with clickable links!

OK, I've spent the last 10 hours on this--I really need to get a life!

Good job. I was skeptical about several of these, but spot checks of Texas, Virginia, Illinois and Arkansas show that you're right about them.

But, I think you might want to double check Michigan - the line between the two points in Michigan doesn't appear to come anywhere near Illinois. Here's where mapquest puts the endpoints:

http://makeashorterlink.com/?C3671228B
http://makeashorterlink.com/?H5772528B
(Sorry, I don't know how to put both points on one map)

Also, you missed Tennesee:

35d 0m 1s N
88d 12m 30s W http://makeashorterlink.com/?Q1682328B
30d 0m 30s N
84d 30m 0s W http://makeashorterlink.com/?W2881228B
MS,AL,GA

(Note: coordinates are from mapquest, which is kind of buggy sometimes - a better tool will probably provide better accuracy)
7.27.2005 2:01pm
arbitraryaardvark (mail) (www):
These are good answers. Cases can turn on mastery of the facts. But as lawyers, one of the things we do is question the assumptions of the question, as Mark did with his Tamaulipas answer. What are states? Are Indian reservations nations, but not states? Do we have to rule out answers such as WV-VA-WV-confusion-MD-WV-despair--PA-WV-OH-WV? Solid liquid gas plasma? I don't think these work, but it's an approach.
Did we disconfirm NY-CT-RI-MA-NH-VT-NY? Embassies don't count?
7.27.2005 3:00pm
Bob Woolley (mail):
Karl:

Good job on Missouri. You found another 4-stater!

Specifically,

36d 28m 29.41s N
89d 28m 59.36s W
40d 23m 55.51s N
91d 29m 31.18s W
TN, KY, IL, IA
7.27.2005 3:29pm
Bob Woolley (mail):
Karl and Clem:

I tried Tennessee through MS, AL, GA last night and couldn't make it work, and I can't now, either. Just can't get it to cross GA.
7.27.2005 3:41pm
Bob Woolley (mail):
Clem:

You're right about Michigan. I think I started trying for one group of 3 states, and it didn't work, so I shifted the line around, and completely overlooked that the new line missed one of the states. It was way too late at night....
7.27.2005 3:54pm
Bob Woolley (mail):
Arbitraryaardvark:

Keith Wright and I both get the same result about NY: you can only make 5 states (to include RI) if one end of the line is in the ocean off of Long Island. Still within the state border, but just seems wrong, somehow, to end up in the ocean. Doesn't really *seem* like it's a point in the state.
7.27.2005 4:03pm
uh clem (mail):
I tried Tennessee through MS, AL, GA last night and couldn't make it work, and I can't now, either.

Well, it's pretty darned obvious from the map links that the Tennesee example I gave doesn't work. D'OH! What was I thinking? I guess this is what peer review is all about.
7.27.2005 4:36pm
dasch (mail):
Here, for Tennessee, is another 4-state passage on a great-circle route. The states intersected are NC, VA, KY, and MO. Start at a point about 3 1/2 miles southwest of the northeast corner of TN (36.5680N, 81.6866) and travel to the northwest corner of TN on the Mississippi River (36.4980N, 89.5309W).

The trip west crosses the following borders:
TN-NC-TN-VA-TN-KY-TN-KY-MO-KY-TN
7.27.2005 7:30pm
karl (mail):
One last one, go to the most extreme corner of southwestern Massachusetts, draw straight line to the Vineyard. You go through three states, NY, CT &RI. I think this is the only one in New England unless there is a weird island out there off the coast or something.
7.28.2005 1:02am
Adam (mail) (www):
Karl, thanks on that last one. I had never realized that the eastern border of NY was not a straight line there and that MA extended out just a little bit to make that possible.
7.28.2005 11:09am
Bob Woolley (mail):
Good catch, karl. The most of NY you can catch in a MA line looks to be a triangle about .3 by .1 mile. Tiny, but it works!

OK, lacking any other candidates suggested so far, here's my final list:

State
Starting pt. latitude
Starting pt. longitude
Ending pt. latitude
Ending pt. longitude
States crossed

Arkansas
34d 55m 15.54s N
90d 16m 58.74s W
36d 23m 41.77s N
90d 04m 53.35s W
MS, TN, MO

Illinois
37d 00m 44.61s N
89d 16m 37.28s W
37d 49m 50.52s N
88d 02m 23.43s W
MO, KY, IN

Indiana
38d 52m 29.99s N
84d 47m 09.27s W
41d 45m 36.63s N
84d 48m 21.36s W
KY, OH, MI

Kentucky
36d 37m 01.67s N
89d 20m 47.56s W
39d 08m 30.53s N
84d 45m 01.13s W
MO, IL, IN, OH

Maryland
39d 34m 48.19s N
79d 16m 41.77s W
38d 25m 31.63s N
75d 14m 17.93s W
WV, VA, DE (and DC)

Massachusetts
42d 03m 00.32s N
73d 29m 46.52s W
41d 29m 57.04s N
71d 07m 04.31s W
NY, CT, RI

Missouri
36d 28m 29.41s N
89d 28m 59.36s W
40d 23m 55.51s N
91d 29m 31.18s W
TN, KY, IL, IA

Missouri
40d 32m 45.03s N
95d 45m 08.95s W
36d 30m 15.45s N
94d 36m 02.40s W
NE, KS, OK

Nebraska
40d 00m 32.52s N
95d 20m 21.73s W
42d 38m 60.00s N
96d 42m 34.15s W
MO, IA, SD

New York
44d 56m 41.97s N
73d 21m 06.40s W
41d 04m 15.93s N
71d 51m 24.41s W
VT, NH, MA, CT

New York
42d 00m 03.29s N
79d 45m 33.21s W
40d 56m 51.80s N
73d 01m 37.52s W
PA, NJ, CT

North Carolina
33d 51m 15.09s N
78d 32m 27.63s W
35d 14m 26.87s N
84d 11m 26.46s W
SC, GA, TN

Texas
31d 56m 19.43s N
106d 33m 50.80s W
33d 38m 37.10s N
94d 27m 19.15s W
NM, OK, AR

Virginia
36d 39m 03.11s N
83d 28m 00.08s W
39d 11m 23.33s N
77d 28m 45.35s W
KY, WV, MD

West Virginia
39d 54m 59.73s N
80d 47m 46.37s W
39d 41m 29.76s N
78d 10m 17.65s W
OH, PA, MD, VA

Notes:
1. The Indiana line is exceptionally close. The maximum distance I could create east-to-west included Michigan only in a strip perhaps 30 or 40 yards wide!
2. The first New York line misses Rhode Island by about 1 1/2 miles. If one accepts water, rather than land, as one of the points, then a sliver of RI can be included, making this a five-stater.
3. The Virginia line includes a wedge-shaped piece of Maryland that is only about 1 mile long by 0.1 mile wide, probably 90% of which is water. The line just grazes the edge of land.
7.28.2005 9:51pm
Bob Woolley (mail):
I'd like to point out that the puzzle stated that there was only one 4-state solution, and only two 3-state solutions. Between us, we came up with *four* 4-state solutions and *eleven* 3-state solutions, just using plane coordinates. (I didn't keep track of the great-circle solutions.) And, of course, there may be another one or two lurking that we all overlooked.

Love the puzzles, Puzzleblogger, but next time don't be so confident about the limit on the range of possible correct answers!
7.28.2005 9:55pm