Victoria - driving to the end

by Burkard Polster and Marty Ross

The Age, 22 June 2009

It is a time of bad news, sickness and economic turmoil. On top of all that, Victorians are facing a mathematical crisis: we are running out of number plates!

The standard Victorian number plate consists of a three-letter combination followed by a three-digit number. The plates are issued in alphabetical order. The first number of the current batch was AAA 000, issued in 1977, and the last one will be ZZZ 999. This means that the first letter roughly indicates how many plates have been used and how many are left. It’s only a rough guide, since some combinations – XXX, for example – will never be released, and others are reserved for government and other special vehicles.

Plates beginning with an X are now being released, so the end is nigh. But how nigh? In recent years the plates have been ticking over at about one letter per year. With three letters to go, this means that Number Plate Doomsday is about three years away.

There are 26 letters in the alphabet, and there are 10 digits. This means that there are a total of 26x26x26x10x10x10 possible licence plate numbers, about 17.6 million. Cycling at one letter per year means that more than half a million number plates are issued every year. Given that there are only about five million Victorians, this tells us that Victorians are crazy about cars. The first calculation also tells us that at any given time there are plenty of retired combinations. So, why not just recycle those combinations? The reason given by VicRoads is … they didn’t get back to us with their reason.

Whatever the thinking, a new numbering scheme seems to be on the cards. Probably the simplest adjustment is to switch around the number and letter blocks, resulting in number plates similar to the current ones. We could even issue them in reverse alphabetical order to keep the right most letter in rough sync with the passing years.

We have an alternative plan. Actually, mathematicians are constantly nagged by a shortage of symbols. So what do they do? They steal from other alphabets. Hence the Greek π and φ, and all the rest.

Our Maths Masters proposal is simply to permit any standard letter and any lowercase Greek letter, giving a total of 50 choices for each spot. Doing the multiplication, this comes to about fifteen billion possible number plates.

So, even if a million cars were registered per year, we’d have 15,000 years to plan our next act of alphabetical theft. As a bonus, we could finally get our AXIOM licence plate in the original Greek: αξίωμα. We’d be the envy of all maths motorheads – and all WALL-E fans.