Number Plates News

A Very Large Number of Number Plates

28 April 2011

We received the following intriguing email from Mr Ron Smith:

"My son has asked me to email you regarding a school project. From the letters A-Z, how many vehicles will be able to have different registrations in one year."

After dusting down an ancient pure mathematics school text book, we were able to provide the following response:

In order to accurately address your question, we must first look in a little more detail at the system employed.

The last three letters are a random selection of all the alphabetic characters, except for 'I' and 'Q'. The total variations can, therefore, be calculated simply as:

24³ = 13,824

The first and second letters are the regional identifiers which indicate the geographic place of registration and the local DVLA office responsible. In this instance, as well as 'I' and 'Q', the letter 'Z' is also omitted.  More importantly, only 435 of the resulting (23²=529) possibilities are currently assigned to particular issuing offices.

We must not forget to include the seven single letter identifiers 'A', 'B', 'C', 'D', 'E' and 'F', which are used on temporary export plates, and 'M', which is reserved for The Isle of Man.)

So, by multiplying a total of 442 by the earlier figure of 13,824, we get a result of 6,110,208.

Finally, we must remember that there are two issues each year: one in March, currently indicated by the number '11' in the third and fourth positions of the plate, and another in September, which for 2011 will be represented by the number '61'. 

Consequently, we need to double the amount accumulated so far in order to arrive at a grand total of 6,110,208 x 2 =  12,220,416. Probably more than enough!

It is worth noting that the licensing authorities may decide to with-hold any registrations which, in whole or part, they consider to represent offensive words. This factor is, of course, impossible to quantify.

We hope that this information has been helpful and wish Smith junior every success in his school project.