Since 2019, I’ve lived in Minnesota’s “twin” cities.

(Effectively, I reside in one in every of them. Foolish to have a home in each.)

Twinhood is a particular relationship, for cities as a lot as for individuals. Positive, we could tease one another, develop rivalrous, or jockey for statewide supremacy by falsifying the outcomes of the 1890 census. However in the long run, our bond is powerful.

So what, precisely, earns Minneapolis and St. Paul the title of “Twin Cities”? Effectively, clearly twinhood is about greater than numbers, however in mathematical phrases:

1. They’re large (every greater than 300,000 individuals).
2. They’re shut collectively (the downtowns are solely 7 miles aside).
3. They’re related in inhabitants (Minneapolis is about 38% bigger).

The result’s a particular form of stability. Every metropolis is large enough to dominate a metropolitan space—but neither is large enough to dominate the opposite.

Nonetheless, I can’t resist a blasphemous thought. Are we actually the twins? Or merely a pair of twins? To qualify as twins, let’s say that two cities should meet these three standards (barely relaxed variations of the Minnesota relationship):

Now, right here comes the puzzle. It’s a two-part problem:

1. Discover a full listing of all pairs of U.S. cities that meet this definition (at most 10 miles aside, with a minimum of 200,000 individuals every, and populations inside an element of two).
2. From this listing of dual cities, make a cogent and persuasive case for which pair deserves to be referred to as THE twin cities.

I’ll hand-choose a winner (or randomly select, if there are a bunch of fine entries) and ship them a free copy of my ebook Math with Unhealthy Drawings, with a customized signature.

Oh, wait, extra becoming: I’ll hand-choose two winners. (They needn’t be twins.)

E-mail your entry to me (title of the weblog at gmail.com) by 12pm ET on December 18th, 2023. Use the topic line “Twin Cities.”

(NOTE: Solutions to #1 will differ barely relying on what information units you utilize. Solutions to #2 could differ dramatically relying in your private standards.)