Readers reply: Is it possible that 3 is the most common number in UK street addresses?

I tried recently to buy sticky vinyl numbers for a new wheelie bin. At two stores, I could find every number from 0 to 9 except the number 3, which I wanted. Is it possible that 3 could be more common in UK street addresses than other numbers?
John Gorrill at No 31, Oxford

Send new questions to nq@theguardian.com.

Readers reply

Having pondered this situation overnight, my unverified reasoning is that it is influenced solely by the prevalence of short roads and streets in most of the UK. The number 1 is going to figure highly in roads with fewer than 20 houses (a total of 13). The number 2, similarly (an unlucky 13), with roads of fewer than 30 houses. Numbers 3 to 9 obviously feature less in this scenario. I suspect the lack of 3s and above becomes more apparent as the average number of houses per street or road rises. If we had long streets like the US, with house numbers frequently in the thousands, the demand for certain numbers would even itself out. FrankieandDexy

I live at No 33 and I have seven bins. Sorry. lexicon_mistress

The question isn’t whether 3 is the most popular number, but whether DIY stores have underestimated how popular 3 is compared with 1 and 2. Like other posters here, they may have considered only main door numbers, ignoring flats or divided houses. In my experience, houses divided into two append a letter (eg 65b), but any more than that use a slash then a second digit (eg 65/3), but rarely higher than 3. Some flats – common in Scotland – use a floor number and a digit or letter modifier (eg 3F2 or 3FC), but as most tenements have fewer than four floors, they rarely require digits higher than 3, even if there are 9 or more flats.

The upshot is that while 1 and 2 will be overwhelmingly popular, 3 may be a lot more popular than you might initially expect – closer to the popularity of 1 and 2 than to 4 to 9. But if purveyors of door furniture assumed the opposite, their stock will be constantly short of 3s. HaveYouFedTheFish

Maybe you share a house with some others and they all decided, without your knowledge, to pop out and sort it out? parasamgate

I appreciate that two might seem like a lot of stores, because of the toll it’s taken on your day, but if I were your PhD supervisor I’d ask for some more data. klingerdinger

Benford’s law is the empirical observation that the distribution of leading digits in many large datasets is heavily weighted towards the smaller digits: 1 – 30.1%, 2 – 17.5%, 3 – 12.5%, and so on, up to 9 – 4.6%. It applies to human-generated data (eg finance, vote counts, addresses, areas of geographical divisions) as well as many datasets in nature (populations, gene expression). It has been used for detecting fraud in finance and vote-counting. While this does not answer the question directly, it strongly suggests that it is unlikely that 3 is the most common digit. seameadow

Benford’s law concerns how leading digits are distributed in datasets and says 1 occurs in around 30% of labels. It shouldn’t strictly apply to house numbering, because streets are generally short and there aren’t usually enough houses to get to numbers that start with 9. However, in practice, the pattern does approximate to house numbering. This isn’t too hard to demonstrate from address files, or from examining some long streets, for example, Duke Street and Gallowgate (Glasgow) and King Street (Aberdeen).

Tangentially, when the kids were young, we did some crafting together to make the new house more homely. There’s a homemade sign on the wall saying WELCOME, except the hobby shop had no more Ls, so we bought a J and turned it around. Guests don’t spot the difference, but to this day I still read it as WEJCOME when I walk past. Dorkalicious

You wouldn’t expect a set of numbers to follow Benford’s law if they were allocated sequentially – as house numbers are. You generally also need a set of numbers which span several orders of magnitude. So, in the UK, at least, the prevalence of short(ish) streets also works against Benford’s law. mutie

Maybe the company selling the number stickers badly misjudged the demand for number 3s? Perhaps they stocked heaps and heaps of 1s and 2s, thinking they’re common like commenters do here, and failed to turn out enough 3s to keep up with demand? Randomusername222

A sample of a single column of a random page of an Edinburgh telephone directory from a few years ago – 128 addresses containing 236 digits – gives the following:
0 – 8%
1 – 21%
2 – 17%
3 – 12%
4 – 9%
5 – 8%
6 – 8%
7 – 9%
8 – 5%
9 – 3%
There are several obvious problems with such a calculation. For example, a tenement will probably have an entry for each flat, so the number on the front door will be counted multiple times. ebcdic

I was born in No 13, but my superstitious parents refused to acknowledge it (the number, not my birth) and only ever referred to the house by the name they gave it. Wormlover

More likely that it’s a fluke. Someone at number 33 bought four of them and now they are sold out. It’s such a low sample size that random noise in the data is larger than any actual effect of sales. NyuszNo1

Ordnance Survey provides a few free samples of address data. These cover Inverness, Newport and Exeter. After a bit of spreadsheet work, I find that a total of 218,126 digits appear in street addresses in these locations. These are split as follows:
0 – 6%
1 – 22%
2 – 15%
3 – 12%
4 – 10%
5 – 8%
6 – 8%
7 – 7%
8 – 6%
9 – 6%
If Exeter, Inverness and Newport are representative, then 3 is not the most common number in UK street addresses. FGBootis

De La Soul, it turns out, were correct: 3 is the magic number. Seems like it does a disappearing act. catchytitled

The average number of houses in a street in the UK is 30, therefore the most common numbers are 1 and 2, equally. Obviously, if the predominant new builds were high-rise flats, this might change but, as far as I am aware, they are not. slojdare

No. If you look at the numbers 1 to 40, the digits 1, 2 and 3 all occur 14 times. I assume that you’d get the same result with the digits 1 to 9 if you went up to 99. Beyond that, 1 is obviously most common between 100 and 199, 2 between 200 and 299, and 3 between 300 and 399. I suspect, though, that 1, 2 and 3 would be equally common between 1 and 399, and that 1 to 9 would be equally common in an infinite road*. 0 wouldn’t be, because addresses are not numbered by mathematicians, so there is no number 0 and we don’t use leading zeros. mutie
* The proof has been left as an exercise for the reader.

If the road were infinitely long, all the digits including 0 would be used infinity times, so equally common. There’d be no stock of any sticky numbers left anywhere. Randomusername222

This can be explicitly checked if you get the official UPRN data for all house and maisonette data (usually used in GIS software), assuming you discount flats that have communal bin rooms. Some houses have one digit and others can go up to four digits, I guess, and some can have letters, for example 9999A or 9999B. So, really, the frequency of number requests per house in an area can be calculated. As 13 is often omitted, the probability of 1 and 3 being requested will be fractionally lower. The lack of availability mentioned is probably due to bad supply and demand management in the store, or poor replenishment of shelves. James Martin, via email

Just buy three sticky vinyl letter Is and dress up in a toga every time you take the bin out. EddieChorepost

Surely simpler and cheaper to buy an 8 and use a pair of scissors? Wormlover

Or two 1s and assume the postie understands you’ve switched to using binary for house numbers. Dorkalicious