Problem Incubator     2023 Sep 21

Glen Whitney

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.

### 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

Smallest nontrivial village
Warm up slowly…

What’s the smallest village with at least

Fewest Houses 5 2
A new neighbor

Feel the burn…

What’s the smallest village with at least

Fewest Houses 5 2 6 2
Now you’re getting it…

What’s the smallest village with at least

Fewest Houses 5 2 6 2 7 3

### Let’s found some villages!

More discoveries

What’s the smallest village with at least

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

Perfectly Parsimonious Postal Planning (ca. 2015)

## Thanks!

… and happy house numbering!