AARoads Forum

National Boards => General Highway Talk => Topic started by: Alps on June 12, 2013, 05:57:18 PM

Title: Largest differences between intersecting numbers
Post by: Alps on June 12, 2013, 05:57:18 PM
A selection to start:
* Greatest difference, all routes (USA): 1, 90005 (GW Pkwy., VA)
* Greatest difference, signed routes (USA): 1, 9336 (FL)
* Greatest difference, Interstates: 85 and 985, 5 and 905 (future)
     ~ Multiplicative: H1, H201
* Greatest difference, Interstates excluding parent routes: 43, 894
     ~ Multiplicative: 5, 710
* Greatest difference, US Highways: 12, 730
     ~ Multiplicative: 1, 601
     ~ Multiplicative, excluding parent routes: 1, 521

BY STATE:
* NJ, all routes: 40, 700 (NJ Tpk.)
* NJ, signed routes only: 30, 676
~ Multiplicative: 1, 495

* DE: 2, 896

* NY, excluding reference routes: 5, 890
     ~ Multiplicative: 3, 812

* MA: 1, 495

* RI: 2, 295
     ~ Multiplicative: 1, 216
Title: Re: Largest differences between intersecting numbers
Post by: agentsteel53 on June 12, 2013, 06:12:28 PM
largest product of US routes:

US-501, US-701.  Conway, SC.

smallest product of US routes:
US-1, US-2.  Houlton, ME. 

honorable mention, smallest product of three US routes, depending on the value of A: US-2A ending at US-1/US-2. 
Title: Re: Largest differences between intersecting numbers
Post by: kkt on June 12, 2013, 06:32:08 PM
California current largest difference between touching route numbers:  980 turning into 24.

In the past, 880 was highway 17, and the junction of 980 and 17 was the largest difference.
Title: Re: Largest differences between intersecting numbers
Post by: agentsteel53 on June 12, 2013, 06:41:45 PM
largest product of interstates: 880 x 980.  a shame that 890 and 990 do not intersect.

three: 97 x 695 x 895 spur is probably it.  80 x 580 x 880 if we don't want to get into spurs.
Title: Re: Largest differences between intersecting numbers
Post by: kkt on June 12, 2013, 06:44:56 PM
In Washington, I think the largest difference is the junction of routes 970 and 10.
Title: Re: Largest differences between intersecting numbers
Post by: dfilpus on June 12, 2013, 06:53:11 PM
Michigan: M-35, M-553 Multiplicative: M-94, M-553
North Carolina: NC 4, NC 903 Multiplicative: NC 904, NC 905
Ohio: OH 872, OH 7 Multiplicative: OH 800, OH 799
Virginia: VA 5, VA 895 Multiplicative I 295, VA 895
Washington: WA 10, WA 970 Multiplicative WA 903, WA 970
Title: Re: Largest differences between intersecting numbers
Post by: NE2 on June 12, 2013, 06:57:00 PM
Guys, by multiplicative he means the largest quotient of two routes. Perhaps geometric would have been clearer.
Title: Re: Largest differences between intersecting numbers
Post by: NE2 on June 12, 2013, 06:58:13 PM
E429 intersects R0 at Brussels.
Title: Re: Largest differences between intersecting numbers
Post by: agentsteel53 on June 12, 2013, 07:01:52 PM
Quote from: NE2 on June 12, 2013, 06:57:00 PM
Guys, by multiplicative he means the largest quotient of two routes. Perhaps geometric would have been clearer.

still fun to come up with large products. 
Title: Re: Largest differences between intersecting numbers
Post by: Alps on June 12, 2013, 07:03:18 PM
Quote from: NE2 on June 12, 2013, 06:58:13 PM
E429 intersects R0 at Brussels.
So that'd be the worldwide winner, tied with any other road intersecting a 0 route.*

* Feel free to dispute aleph-nulls with me, I'm not biting.
Title: Re: Largest differences between intersecting numbers
Post by: agentsteel53 on June 12, 2013, 07:05:52 PM
Quote from: NE2 on June 12, 2013, 06:58:13 PM
E429 intersects R0 at Brussels.

offhand, I see N533 at N6, for arithmetic difference.  for a possible sum and/or product, N532 at N533.

Hungary has an M0, which intersects various routes.  in fact, there is an M0-M1-1 interchange.
Title: Re: Largest differences between intersecting numbers
Post by: Pete from Boston on June 12, 2013, 09:38:30 PM
Quote from: NE2 on June 12, 2013, 06:57:00 PM
Guys, by multiplicative he means the largest quotient of two routes. Perhaps geometric would have been clearer.

I thought he meant which route is the greatest multiple of the other (I may be putting this wrong -- I tested out of math in college and thus have avoided it since high school 875 years ago).

In other words, H201 is 201 times its lowest intersector, H1, greater a difference than 5 and 905 (5 x 181 = 905, 181 < 201).
Title: Re: Largest differences between intersecting numbers
Post by: NE2 on June 12, 2013, 10:04:57 PM
Quote from: Pete from Boston on June 12, 2013, 09:38:30 PM
Quote from: NE2 on June 12, 2013, 06:57:00 PM
Guys, by multiplicative he means the largest quotient of two routes. Perhaps geometric would have been clearer.

I thought he meant which route is the greatest multiple of the other (I may be putting this wrong -- I tested out of math in college and thus have avoided it since high school 875 years ago).

In other words, H201 is 201 times its lowest intersector, H1, greater a difference than 5 and 905 (5 x 181 = 905, 181 < 201).

Yes, H201/H1 is a larger quotient than 905/5.
Title: Re: Largest differences between intersecting numbers
Post by: hbelkins on June 12, 2013, 11:29:27 PM
(will be looking at Kentucky maps tomorrow to see which four-digit 3xxx-series routes intersect KY 1)
Title: Re: Largest differences between intersecting numbers
Post by: bassoon1986 on June 12, 2013, 11:45:05 PM
Quote from: hbelkins on June 12, 2013, 11:29:27 PM
(will be looking at Kentucky maps tomorrow to see which four-digit 3xxx-series routes intersect KY 1)

As will I with Louisiana. I don't think we've made it to 33xx yet
Title: Re: Largest differences between intersecting numbers
Post by: bassoon1986 on June 12, 2013, 11:54:18 PM
Louisiana: LA 1 & LA 3279, and it is signed
Title: Re: Largest differences between intersecting numbers
Post by: sp_redelectric on June 13, 2013, 12:07:34 AM
Oregon:  Interstate 5 and Oregon 569 (Pape Beltline Highway) in Eugene, or U.S. 30 (a.k.a. I-84) and U.S. 730 in Irrigon, or U.S. 730 and Oregon 37 east of Umatilla.
Title: Re: Largest differences between intersecting numbers
Post by: NE2 on June 13, 2013, 12:27:09 AM
Florida state roads: 5 (unsigned) and 9336.

The only other state road to touch 9336 is 997, the second-highest signed number and the highest three-digit number. 5054 only touches 518 (and former 5098 touched nothing below 15), making 5/9336 best arithmetically and geometrically.
Title: Re: Largest differences between intersecting numbers
Post by: Laura on June 13, 2013, 12:48:13 AM
Maryland: US-1 and MD-924 in Bel Air
Title: Re: Largest differences between intersecting numbers
Post by: Scott5114 on June 13, 2013, 04:45:49 AM
Oklahoma: US 412 and OK 3 are concurrent (difference of 409). Restricting it to OK routes only, 325 and 3 (difference of 322). Both of these pairs are present in Boise City.
Title: Re: Largest differences between intersecting numbers
Post by: CNGL-Leudimin on June 13, 2013, 05:29:17 AM
I think this is currently the biggest one in Spain:

A-2 exit 463 is for LP-9221. This is near Lleida.

Edit:
Quote from: Steve on June 12, 2013, 05:57:18 PM
A selection to start:
* Greatest difference, signed routes (USA): 1, 9336 (FL)

At least you remarked it's only USA, since if we go worldwide it gets beaten by the concurrency of G4 and G9411 in southern China. Going multiplicative, that intersection holds the world record, I believe.
Title: Re: Largest differences between intersecting numbers
Post by: amh424 on June 13, 2013, 07:32:26 AM
Illinois:  As far as state routes go, the greatest difference is between IL 1 and IL 394.  The highest and the lowest state roads.
Title: Re: Largest differences between intersecting numbers
Post by: spooky on June 13, 2013, 07:43:40 AM
Quote from: Steve on June 12, 2013, 05:57:18 PM

* RI: 2, 295
     ~ Multiplicative: 1, 216

If I understand your premise correctly, wouldn't this be 1 and 403? RI 403 intersects US 1 in North Kingstown.
Title: Re: Largest differences between intersecting numbers
Post by: Roadsguy on June 13, 2013, 10:02:45 AM
For PA, it might be the intersection of PA 3 and 926 in Willistown, east of West Chester.
Title: Re: Largest differences between intersecting numbers
Post by: NWI_Irish96 on June 13, 2013, 10:15:18 AM
Indiana doesn't use 4-digit routes so none of these are going to rank nationally:

Largest difference: IN 933 and IN 23
- US highways: US 421 and US 6
- Interstates: I-865 and I-65

Multiplicitive: IN 1 and I-469

Largest product: I-865 and I-465
Title: Re: Largest differences between intersecting numbers
Post by: jp the roadgeek on June 13, 2013, 10:42:12 AM
CT.  Largest: US 5 and I-691
       Smallest: US 1 and US 1A, or US 1 and CT 2
       Largest not including interstates or US Routes: CT 3 and CT 372
       Smallest not including interstates or state routes: CT 2 and CT 3

If you include secret state routes: US 1 and SR 916 in New Haven, which just beats US 5 and SR 919 in Wethersfield
Title: Re: Largest differences between intersecting numbers
Post by: NE2 on June 13, 2013, 11:28:07 AM
Quote from: CNGL-Leudimin on June 13, 2013, 05:29:17 AM
At least you remarked it's only USA, since if we go worldwide it gets beaten by the concurrency of G4 and G9411 in southern China. Going multiplicative, that intersection holds the world record, I believe.
God damn it. Multiplicative DOES NOT MEAN you multiply the numbers.

(And in any case sqrt(4*9411) is only 194. That gets totally crushed by so many other intersections.)
Title: Re: Largest differences between intersecting numbers
Post by: PHLBOS on June 13, 2013, 12:28:43 PM
Quote from: Roadsguy on June 13, 2013, 10:02:45 AM
For PA, it might be the intersection of PA 3 and 926 in Willistown, east of West Chester.
For PennDOT's 'secret' route numbers (SR XXXX, first X>0) one would think that it likely be along the SR 0001 (US 1) corridor in southeastern PA.
Title: Re: Largest differences between intersecting numbers
Post by: formulanone on June 13, 2013, 01:06:34 PM
Quote from: NE2 on June 13, 2013, 12:27:09 AM
Florida state roads: 5 (unsigned) and 9336.

The only other state road to touch 9336 is 997, the second-highest signed number and the highest three-digit number. 5054 only touches 518 (and former 5098 touched nothing below 15), making 5/9336 best arithmetically and geometrically.

I guess Jacksonville will probably have the lowest combined numbers in Florida (SR 9A and SR 10 ?), unless we count the various A1A and US 1 intersections.

QuoteMultiplicative

Isn't "quotient" easier to type and understand? Or me unpossibly fail at mathing?
Title: Re: Largest differences between intersecting numbers
Post by: agentsteel53 on June 13, 2013, 02:05:14 PM
Quote from: NE2 on June 13, 2013, 11:28:07 AM
(And in any case sqrt(4*9411) is only 194. That gets totally crushed by so many other intersections.)

speaking of square roots... how about the MA-4/MA-225 multiplex?  any larger difference among perfect squares?  certainly not in Massachusetts, as there is no MA-256, MA-289, or higher than 295... and US-1 does not intersect any perfect square in Massachusetts larger than MA-16.

I'll bet some SR-1 or US-1 intersects something like VA-90000 (is there one of those?)
Title: Re: Largest differences between intersecting numbers
Post by: bassoon1986 on June 13, 2013, 02:57:48 PM
The best I found with square roots with LA-1 is an intersection with LA-400 in Supreme, Louisiana.
Title: Re: Largest differences between intersecting numbers
Post by: kkt on June 13, 2013, 03:48:46 PM
Quote from: NE2 on June 13, 2013, 11:28:07 AM
Quote from: CNGL-Leudimin on June 13, 2013, 05:29:17 AM
At least you remarked it's only USA, since if we go worldwide it gets beaten by the concurrency of G4 and G9411 in southern China. Going multiplicative, that intersection holds the world record, I believe.
God damn it. Multiplicative DOES NOT MEAN you multiply the numbers.

(And in any case sqrt(4*9411) is only 194. That gets totally crushed by so many other intersections.)

If multiplicative doesn't mean you multiply, what the hell does it mean?

Math is easy if you use the right words for what you're talking about.  :banghead:
Title: Re: Largest differences between intersecting numbers
Post by: agentsteel53 on June 13, 2013, 03:52:38 PM
Quote from: kkt on June 13, 2013, 03:48:46 PM

If multiplicative doesn't mean you multiply, what the hell does it mean?

"additive difference" is a mathematically sound way to express "the result when A is subtracted from B".  "multiplicative difference" is, while kinda stilted, a valid synonym for "quotient".
Title: Re: Largest differences between intersecting numbers
Post by: agentsteel53 on June 13, 2013, 03:55:01 PM
so, just to really fuck with things, let's explore other differences.  greatest Hamming distance between two route numbers expressed in binary?  offhand, MA-127 and MA-128 have a Hamming distance of 8. 

generally speaking, that property is true for x and 255-x, and if we want 9, we just have to find x and 511-x, and so on with 1023, 2047, 4195 (looking at you, HB Elkins).
Title: Re: Largest differences between intersecting numbers
Post by: Doctor Whom on June 13, 2013, 03:57:38 PM
With regard to signed routes, Virginia signs at least some of its 10xxx secondary routes, e.g., Route 10500 (Dogue Hill Lane) at Route 193 (Georgetown Pike).  The VDOT traffic volume estimates also list an intersection between Routes 1 and 10333, although I don't know whether 10333 is signed.
Title: Re: Largest differences between intersecting numbers
Post by: kkt on June 13, 2013, 04:13:51 PM
Quote from: agentsteel53 on June 13, 2013, 03:52:38 PM
Quote from: kkt on June 13, 2013, 03:48:46 PM

If multiplicative doesn't mean you multiply, what the hell does it mean?

"additive difference" is a mathematically sound way to express "the result when A is subtracted from B".  "multiplicative difference" is, while kinda stilted, a valid synonym for "quotient".

I was taught that the result of a subtraction problem is the "difference".  Never heard the term "additive difference" and I wouldn't know what it meant if I did.

California's highest quotient, I think, is the junction of CA-271 and CA-1.
Title: Re: Largest differences between intersecting numbers
Post by: Rover_0 on June 13, 2013, 04:14:23 PM
Generally signed Utah routes:

Largest Difference (Signed)
   State: UT-318 and UT-9
   US Routes: US-491 and US-191
   Interstates: I-215 and I-15

Largest Product: UT-196 and UT-901 (http://en.wikipedia.org/wiki/Utah_State_Route_901#901)*

Largest Multiplicative: UT-198 and US-6

*Not signed nor meant to be a major route. If also included, 901-196 would also be greatest difference.
Title: Re: Largest differences between intersecting numbers
Post by: agentsteel53 on June 13, 2013, 04:19:55 PM
Quote from: kkt on June 13, 2013, 04:13:51 PM
California's highest quotient, I think, is the junction of CA-271 and CA-1.

probably.  I don't know anything beyond the bears.  the largest product of two 1934 state routes is 180 at 198.

6/466 is the greatest difference in US routes (1938-1964), and is the greatest quotient as well.  1/466 exists if we count both systems.

greatest product is in Bakersfield: US-399 at US-466.  they were signed through downtown Bakersfield - 399 had a short multiplex with 99/466, which is a Hell of a product right there. 
Title: Re: Largest differences between intersecting numbers
Post by: Eth on June 13, 2013, 09:04:18 PM
Georgia:

Difference:
All routes (signed or otherwise): GA-11 and I-985
State routes: GA-1 and GA-520
US routes: US-23 and US-441
Interstates: I-85 and I-985

Multiplicative:
All routes: GA-1 and GA-520; also US-1 and I-520
State routes: GA-1 and GA-520
US routes: US-1 and US-341
Interstates: I-20 and I-520

Largest product (signed routes only): I-985 and GA-369 (for bonus points, I-985 is also multiplexed with US-23)
Title: Re: Largest differences between intersecting numbers
Post by: Alps on June 13, 2013, 09:48:15 PM
Quote from: spooky on June 13, 2013, 07:43:40 AM
Quote from: Steve on June 12, 2013, 05:57:18 PM

* RI: 2, 295
     ~ Multiplicative: 1, 216

If I understand your premise correctly, wouldn't this be 1 and 403? RI 403 intersects US 1 in North Kingstown.
D'oh, I forgot the 400 routes while I was at work. Additive and multiplicative, yes.
Title: Re: Largest differences between intersecting numbers
Post by: Alps on June 13, 2013, 09:50:14 PM
Quote from: agentsteel53 on June 13, 2013, 03:55:01 PM
so, just to really fuck with things, let's explore other differences.  greatest Hamming distance between two route numbers expressed in binary?  offhand, MA-127 and MA-128 have a Hamming distance of 8. 

generally speaking, that property is true for x and 255-x, and if we want 9, we just have to find x and 511-x, and so on with 1023, 2047, 4195 (looking at you, HB Elkins).
So, NJ 4 intersects CR 507, and CR 510/513 intersect where NJ 24 used to pass, so there are distances of 9 and 10 for you.
Title: Re: Largest differences between intersecting numbers
Post by: agentsteel53 on June 13, 2013, 09:59:27 PM
Quote from: Steve on June 13, 2013, 09:50:14 PM

So, NJ 4 intersects CR 507, and CR 510/513 intersect where NJ 24 used to pass, so there are distances of 9 and 10 for you.

looking for two Kentucky routes which add up to 4095.  Elkins?  Bueller?
Title: Re: Largest differences between intersecting numbers
Post by: hbelkins on June 13, 2013, 10:52:33 PM
Quote from: agentsteel53 on June 13, 2013, 09:59:27 PM
Quote from: Steve on June 13, 2013, 09:50:14 PM

So, NJ 4 intersects CR 507, and CR 510/513 intersect where NJ 24 used to pass, so there are distances of 9 and 10 for you.

looking for two Kentucky routes which add up to 4095.  Elkins?  Bueller?

Don't make me go plowing through all 120 county maps to find this. LOL
Title: Re: Largest differences between intersecting numbers
Post by: Roadsguy on June 14, 2013, 09:31:34 AM
Quote from: PHLBOS on June 13, 2013, 12:28:43 PM
Quote from: Roadsguy on June 13, 2013, 10:02:45 AM
For PA, it might be the intersection of PA 3 and 926 in Willistown, east of West Chester.
For PennDOT's 'secret' route numbers (SR XXXX, first X>0) one would think that it likely be along the SR 0001 (US 1) corridor in southeastern PA.

Right. I only counted signed routes because I don't know the vast majority of the "secret" ones, and no map (except OSM, though not completely) seems to label them. :P
Title: Re: Largest differences between intersecting numbers
Post by: formulanone on June 14, 2013, 09:44:25 AM
Quote from: agentsteel53 on June 13, 2013, 09:59:27 PM
looking for two Kentucky routes which add up to 4095.  Elkins?  Bueller?

Louisiana might have a case, here. Some of their routes have easy subtraction problems included.