So, to achieve the proximity effect, you want to find two towns which are close together, but which have expanded to form a continuous conurbation.
You then need a road which either 'clips' one of these towns, and hence has numbers starting from 1 but then quickly moves to another town, where the numbers get reset, or, where the road starts just over the border into one town, and hence again, starts from 1 before quickly crossing into another town.
We live in the UK city of Brighton. Actually, Brighton had a neighbouring town, Hove, and the two councils merged in the 90s to form 'Brighton and Hove' but this is often abbreviated to Brighton, and this town became a city in 2000.
So, any road that crosses between Brighton and Hove will have this number reset problem. We happen to live 200 yards from the Brighton and Hove 'border' for want of a better name, and our road crosses, so we have another identically numbered house on the same road 400 yards away.
The road itself runs for a number of miles, so there is at least one other house with the same address that I know of (in Portslade, the next town along). We occasionally get confused delivery drivers and post from the postman where we try and work out from the address who the package is for. I've met the current owners of the other two similar addresses, so we can help point things in the right direction.
Because in .nl, I know this happens and I'm pretty sure this is the common thing for major roads connecting small hubs. Actually, a road connecting village A to hamlet B would typically be called "A'seweg" (A road) in B and "B'seweg" (B road) in A. If they go through and connect more municipalities, they might become a numbered road (eg, N281), but that you cannot use in an address.
We also have quite a number of roman roads, although not that many around where we live, which criss cross the country, and can travel for hundreds of miles, for example, the Fosse Way, here's google's name match, but if you zoom in on sections of this, you can see the fairly straight roman road with different 'B' road numbers (but still called Fosse Way):
https://www.google.com/maps/search/fosse+way/@52.3459536,-2....
We were in the west half of a duplex on East 1st Street, so the address was 123W E First St. I called 911 and in the process sent the first responders to 123 W First St. (Everything turned out okay, but response was delayed by at least 10 minutes. I recommended they change the addresses to 123A and 123B instead of East and West. That was denied.)
We knew who lived there as it wasn't too infrequent that their post arrived at ours or vice versa.
Same postie too! He'd typically correct it based on surname but occasionally something would get it through (and this was 30 years ago).
When I moved in (pre-consumer GPS days) I used to be regularly berated by service people for giving them the wrong address when I told them Main St. because a lot of the maps still showed North Main at least a decade or two later. And, somewhat amusingly, I observe that the telcos (Verizon and Comcast) STILL (maybe 5 decades out) still show my address at N MAIN. (When I bought the house, as I recall, there was even some paperwork that XXX Main St. was really the same address as XXX North Main St.
Although this change probably predated that, the introduction of E911 in the US led to a lot of cleanup of address irregularities such as summer cabins that didn't really have a proper address, rural delivery without a street address, roads with a break in the middle, etc.
Now OK in this particular case you're still screwed as they are literally next door, but normally you'd find it by putting in "M27 8TD" and you'd be set.
While UK postcodes can cover a large area, they usually don't.
My understanding of zip codes like 90210 is they aren't anywhere near as precise as M27 8TD, they're more like just the "M27" part.
These last 4 provide the resolution needed to avoid this confusion.
I too live in the Seattle area and have this same doppelgänger problem, so I use the full zip code when possible (not all web sites allow it, and the last mile delivery is by hand, so can still go wrong)
Closer inspection revealed the postcode was wrong -- the goons had hand delivered it to an address 5 miles away. Same number, same street, same council area, completely different postcode (M28 vs M5)
And it's maddening. I'd be curious to know if this situation is similarly common.
Here's a route that starts on Tramway Vista Loop NE, makes a right onto Tramway Vista Place NE, a left onto Tramway Lane NE, a left onto Tramway Place NE, bears left as it changes names to Tramway Circle NE, (makes a left onto Cedar Hill Road NE, sorry!), makes a left onto Tramway Boulevard NE, then a right onto Tramway Road NE, and finally a left onto Tramway Circle NE.
Many of these also have overlapping address number ranges, but I'll leave that as an exercise to the reader.
https://i.imgur.com/7sKNNIQ.png
For more, try Peachtree in Atlanta.
Can't they put up their own signs?
I learned that in Japan, it's quite common for neighbors to have the exact same address, if the entrances fall in the same number zone.
As always, addressing is a story that shows us that all our nice simple abstractions don't suffice. An address is not always street+house number.
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I had address "123 Some AVE." in the town. There was also a road named "Some PLACE" in the town but there was not a 123 for the house number anywhere on the "Some Pl." road. "123 Some Pl." does not exist in the town.
BUT, you can type in "123 Some Pl." in Google or Apple Maps along with the town name and the maps program will just throw you at the closest numbering house on "Some Pl." If you're not paying attention you just think it's the correct address.
Somehow my voter registration was set to the "123 Some Pl." (but my driver's license was correct) so I was in the wrong voting district (quick phone call cleared that up). Also sometimes packages would try to get delivered over there to "123 Some Pl.".
Google Maps[1] seems to confirm it, there are two 441's several houses away from each other separated by the two 443's (actually just separated by 1 house because they're semi-detached houses), and then two 439's, two 437's, and it goes on..
It's weirder than that. On the odd side, Bolton counts up to 443 and then, as you cross into Manchester, Manchester counts down from 443. But at least the progression of numbers makes sense.
On the even side, it looks like Bolton counts up to 538 (which is directly across from 443) and then, once you cross the border, Manchester counts down from 408 (also directly across from 443).
Why are the even numbers so disconnected from the odd numbers?
I suppose the failure mode would be that one side refuses to propose a new name, and it's unfair to reward that side by letting them keep the existing name. Also, the two sides might both vote for the same new name, but maybe that could be resolved with a coin toss.
Another alternative would be some sort of Dutch auction, where the two sides try to under-bid each other for some cash reward for having their side renamed. Actually running that auction in a democratically legitimate way might be a bit complicated, though, and obviously the money would have to come from somewhere.
It was a PITA to explain to delivery people, especially because it was before there were Eircodes, so there was no postal code in common use to direct people there without the confusing names.