When Will Vehicle Registration Numbers Come To An End?


The Sunday Nation


24 April 2005


Here is a short test: Count down from 26 to one and check how long it takes. Now try saying the alphabet in reverse from Z to A see how long it takes. While it may take you 30 seconds to count from 26 to one, you will probably need two minutes to say the alphabet in backwards.

Counting is easy, but sometimes when the string of digits in the number becomes too long, we mix numbers with letters; then things become tricky. Consider, for example in the registration of motor vehicles in Kenya. Our scheme has three letters followed by three numbers and then one letter. The sequence has now reached KAT. To find out how many vehicles have been registered since KAA 001A, we must proceed as follows:

First, we note that there were 999 vehicles with the letters KAA – A (i.e., from 001 to 999), another 999 with KAA – B, and so on. Thus from KAA 001A to KAA 999Z, there were 999 x 24 = 23,976 vehicles registered. The multiplication is by 24 instead of 26 because the letters I and O are skipped to avoid confusion with the numbers one and zero, respectively.

From KAA 999Z, the next registration was KAB 001A. Similarly, there were 23,976 vehicles with the KAB prefix. But the series KAF, KAI and KAO were skipped. KAF was jumped because it sounds like Kenya Air Force. Now, from A to S there are 18 letters therefore; dropping F, I and O leaves only 15. Thus from KAA 001A to KAS 999Z, there were 23,976 x 15 = 359,640 vehicles registered.

Every letter sequence, say, KAT – A, lasts for about one year, therefore, approximately 24,000 vehicles are registered in Kenya per year. Thus, we can find out how long it will take before the series of registration comes to the end, that is, when the vehicle, KZZ 999Z will be registered.

The KAT series will last about one year, and then we will move to KAU and stay there for another year. Thus it will take seven years from now to get to the KAZ series. From KAZ 999Z we will move to KBA 001A. The KB series will last about 24 years then we move on to KCA and so on.

If we continue with this system, it will take 24 x 23 = 552 years to get from KBA 001A to KZZ 999Z. To this we add the seven years between KAT and KAZ and that makes a total of 559 years.

This is assuming that the registration rate remains 24,000 vehicles throughout the period. That is not a good assumption because the economy is growing, albeit slowly. If we allow a 3 percent growth in registration per year, it turns out that the series will end in about 97 years. It’s not too far away, is it?

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