Inverted Addresses
Problem Incubator     2023 Sep 21

Glen Whitney

studioinfinity.org/address

 

Our villages have rules

  1. Every road is a line segment

Our villages have rules

  1. Every road is a line segment on a distinct line

Our villages have rules

  1. Every road is a line segment on a distinct line
  2. There are at least three houses on every road and at least one road

Rules naturally come in threes

  1. Every road is a line segment on a distinct line
  2. There are at least three houses on every road and at least one road
  3. Every road must be assigned the number equal to the number of houses on it.

We are the Math Problem Incubator, after all

Definition. The address of a house is the collection i.e. multiset of numbers of the streets it is on.

The OG Inverted Address Problem

Is there any village in our country where the postal service can deliver the mail?

It’s good to stretch

What’s the smallest village with at least

Fewest
Houses Streets
2 distinct addresses?
3 distinct addresses?
4 distinct addresses?
5 distinct addresses?
6 distinct addresses?
7 distinct addresses?
8 distinct addresses?
Smallest nontrivial village
Warm up slowly…

What’s the smallest village with at least

Fewest
Houses Streets
2 distinct addresses? 5 2
3 distinct addresses?
4 distinct addresses?
5 distinct addresses?
6 distinct addresses?
7 distinct addresses?
8 distinct addresses?
A new neighbor

Feel the burn…

What’s the smallest village with at least

Fewest
Houses Streets
2 distinct addresses? 5 2
3 distinct addresses? 6 2
4 distinct addresses?
5 distinct addresses?
6 distinct addresses?
7 distinct addresses?
8 distinct addresses?
Now you’re getting it…

What’s the smallest village with at least

Fewest
Houses Streets
2 distinct addresses? 5 2
3 distinct addresses? 6 2
4 distinct addresses? 7 3
5 distinct addresses?
6 distinct addresses?
7 distinct addresses?
8 distinct addresses?

Let’s found some villages!

More discoveries

What’s the smallest village with at least

Fewest
Houses Streets
2 distinct addresses? 5 2
3 distinct addresses? 6 2
4 distinct addresses? 7 3
5 distinct addresses? 8 3
6 distinct addresses? 9 3
7 distinct addresses?   4
8 distinct addresses?
The oldest known postal-safe village (ca. 2013)

Perfectly Parsimonious Postal Planning (ca. 2015)

Thanks!

… and happy house numbering!

studioinfinity.org/address