Listener Anil Arakkal lives in the Kalamazoo area. Last year he noticed a new license plate on the road.
“It caught my attention not only because it’s a dark color with a light letter,” he said.
Bearing the slogan “WATER-WINTER WONDERLAND” at the bottom.
“It’s also a vintage or historical plate and kind of makes you look twice.”
The plates are indeed a “throwback,” reviving a design from the 1960s. As Anil saw more and more of them, he realized that except on vanity plates, the second character was always a letter N as in New Buffalo. And he wondered why. We’ll find out, and we’ll even calculate how many of those N-plates are out there. First, we learn more about why the state revived the Water-Winter-Wonderland plates.
Here’s Department of State spokesman Jake Rollow.
“It's the plate that Michigan was issuing in 1965 when the Voting Rights Act was passed. And for Secretary Benson, that was important,” he said.
Rollow added that lots of motorists had asked the state to bring back Water-Winter-Wonderland.
“Motorists, vehicle collectors and just history buffs, people seem to love this plate.”
But Rollow said even then, his office was surprised by the public’s response. The new Water-Winter Wonderland has only been available for a little over a year. But already it’s on around 10 percent of Michigan’s passenger cars and trucks.
“Which is really a meteoric rise for a license plate."
Rollow said, by comparison, the Mackinac Bridge design graces about 17 percent of cars. That’s more than Water-Winter Wonderland. But Mackinac Bridge has been around for nearly a decade.
Rollow says you see Water-Winter Wonderland everywhere these days.
“Perhaps particularly in southern Michigan, and, you know, southeast Michigan,” closer to the University of Michigan, whose school colors resemble those of the plate.
So why is the second letter always fixed? Rollow said, first, consider the challenge the Department of State faces in issuing license plates.
“We have to keep track of all the various combinations of letters and numbers that you could have on a plate to make sure that we never issue two that are the same.”
Then consider the millions of cars and trucks licensed in Michigan right now, and all the license plates the state’s issued in the past. Rollow says the Michigan could use completely random series. But fixing one letter helps keep the system tidy.
“’To know, ‘okay, this is the series that's going out right now, we'll get to the next series, you know, whatever, in six months,’ or depending on how quickly the plate is being picked up.”
When our question-asker Anil Arakkal wrote in last fall, the fixed letter was always N. Rollow explained why.
“Looking at the series that we had already issued across other plates over many decades, we picked a series where we could continue to proceed for a while. And the place where we were in that series was starting with the second character as an N.”
But the N-series recently ran out. We thought it might fun to figure out just how many of the N-plates are out there.
So we turned to Andrzej Dudek, a math professor at Western Michigan University. He agreed to walk us through the problem, and made notes as we met virtually:
“So what you want to do we want to count the number of all plates and all these plates, they need to follow some rules, yeah? They need to follow some rules so maybe let’s start with the rules,” he said.
The license plate has three numbers. They’re pretty straightforward; they each have ten possible values, zero through nine. The plate also has three letters. But of course, one of them is fixed. So it’s only got one possible value. As for the other two letters...
“Okay, we’re talking about English alphabet. And theoretically there would be 26,” Dudek said.
Except the state excludes the letter O, because it looks too much like zero, and that could make a plate hard to identify. So our two unfixed letters have 25 possible values.
Multiply each number’s set of possible values by each letter’s set of possible values and you get 625,000. That’s how many N-series Water-Water-Wonderland plates the state could print before it ran out of combinations.
Now it’s on to the letter P, since, again, the state does not use O.
Our question-asker Anil Arakkal says it’s cool to have an answer, “versus, you know, just noticing a pattern without any logic behind it.”
