If you’re like me you’ve probably argued about silly things, like the total number of houses in Zimbabwe or how many cars pass through a particular tollgate each day. These are the kinds of questions that arise after one too many drinks or during a very slow day. They are also the kind of questions you may be asked in an interview at Google or other tech companies.¹

Coming from a ~~village~~ small town, I have always thought Harare’s roads are too congested (don’t tell me about Beijing, New York or whatever, I live in Zimbabwe). The number of cars in Zimbabwe has risen dramatically in the past couple of years due to cheap second hand cars being imported from Japan.

So today, while caught up in traffic, my brother started talking about the high number of cars on our roads. He said there are probably so many cars in Harare that every person over the age of 18 can get one. We argued about this for a while and he said there are enough cars in the city for every household. Eventually I asked him how many cars he thinks there are in the whole country.

“Maybe 3 million,” he replied offhandedly.

But my brother is a lawyer and his understanding of numbers is ehmmm ….shaky. My own estimate was 1.5 million, a number he disputed with all the energy of a lawyer.

So I started thinking about how to get the total number of cars in Zimbabwe. There are a number of ways to go about it. The most accurate would be to go the Vehicle Registration offices and just ask, or somehow find the information from them or other official sources but then where would be the fun in that?

One could also use some statistical methods for a small sample, assume it’s random, and then extrapolate the results for the whole country.

However a better method is to use the number (vehicle registration) plates. In 2006 the government introduced a new type of number plates. These new plates are composed of three letters and four numbers such as in the image below.

Assuming that there are no plates with any letter combination followed by four zeros, eg ABX 0000 (and I haven’t seen any), any unique letter combination can have 9999 different set of plates i.e from 0001- 9999.

So far the latest cars getting registered are getting the letter combination ADX or maybe ADY. The task here is to establish how many unique combinations of letters- in incremental order and without repeating- there are from AAA up to ADX.

It’s not too difficult, just a little maths and knowledge of the alphabet.

There are 26 letters in the alphabet. Therefore from AAA – AAZ there are 26 different letter combinations and 26 × 9999 different number plates.

From AAZ the series goes to ABA up to ABZ where there are 26 other combinations, then another 26 from ACA to ACZ and so on. So from AAA to ADX there are 26 + 26 + 26 + 24 = 102 letter combinations, each capable of holding 9999 items. ²

Thus the total number of cars is 9999 × 102 = 1 019 898.

That’s it folks there are just over a million (registered & private) cars in Zimbabwe. There are of course other cars belonging to the government, military, police and other special classes. I’m also not sure where commecial vehicles- such as buses, kombis and trucks fit in.

If you add up all those- and the President’s considerable fleet- you may arrive at maybe 1.1 – 1.2 million cars which is actually near the official number according to the Zimbabwe National Roads Administration, ZINARA.³

Which means there’s roughly a car for every 11 Zimbabweans. Or a car for every 2 families.†

So I won the argument. That merits a blog post.

*In case you are wondering, one of the reasons why the old plates were phased out was that we would one day run out of numbers. Under this new system the total number of possible number plates is a staggering 175 742 424 i.e 26 cubed × 9999 or 26 × 26 × 26 × 9999. *

*Huge as that number may seem it’s still less than the estimated 254 million cars in the US. For comparison, Germany which is roughly the same size as Zimbabwe (but with way more people) has around 55 million cars.*

Notes:

- Funny interview questions to test analytical skills are common in tech jobs, as reported by Forbes, Business Insider, Geekwire & others
- As far as
~~I know~~a few minutes of observation revealed there are no cars with ADY plates, thus the 24 - ZINARA, on its website says “According to the central vehicle registry (CVR), Zimbabwe’s vehicle population stands at an estimated 1, 2 million”
- † There are almost 13 million people in Zimbabwe Wikipedia