Largest differences between intersecting numbers

[jp the roadgeek]

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

[NE2]

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.)

[PHLBOS]

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.

[formulanone]

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.

Multiplicative

Isn't "quotient" easier to type and understand? Or me unpossibly fail at mathing?

[agentsteel53]

(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?)

[bassoon1986]

The best I found with square roots with LA-1 is an intersection with LA-400 in Supreme, Louisiana.

[kkt]

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. 

[agentsteel53]

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".

[agentsteel53]

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).

[Doctor Whom]

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.

[kkt]

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.

[Rover_0]

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*

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.

[agentsteel53]

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. 

[Eth]

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)

[Alps]

* 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.

[Alps]

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.

[agentsteel53]

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?

[hbelkins]

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

[Roadsguy]

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.

[formulanone]

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.